LIVEFELT · REPORT 1 OF 2 · MAPPING AND FAIRNESS PROOF

EVERY SPORT,
EVERY MODE,
PROVEN FAIR.

One real play in the world = one event in the game. This report builds the event map for 13 sports plus a markets bucket against all five LiveFelt mechanics and proves each map lands on the casino target: true two-dice odds for LiveRoll, a fair crash curve for LiveCrash, 95% RTP for LiveSlots, and a fair 52-card deck for LiveHit and LiveDeal. Every frequency is a real, cited, published rate. No number in this report is invented, and no outcome in any map is random: where a common event must span two outcomes, the split rides a named, real attribute of the play (yardage, pitch location, rally length, field side), never a random draw. API feasibility, latency, rights and cost are deliberately out of scope: that is Report 2.

16 streams5 mechanics 80 verdict cells LiveRoll edge 1.41% pass LiveCrash edge 2.0% flat LiveSlots RTP 95.0% exact Deck games 1/13 per rank exact Season data 2023-2025, cited
THE VERDICT MATRIX · WHICH SPORT FITS WHICH MECHANIC
SPORT / STREAMLIVEROLLLIVECRASHLIVESLOTSLIVEHITLIVEDEAL
NFLNATURALNATURALNATURALNATURALNATURAL
NCAAFNATURALNATURALNATURALNATURALNATURAL
NBANATURALNATURALNATURALNATURALNATURAL
NCAAMNATURALNATURALNATURALNATURALNATURAL
WNBANATURALNATURALNATURALNATURALNATURAL
SOCCERNATURALNATURALFORCEDNATURALNATURAL
MLBNATURALNATURALNATURALNATURALNATURAL
NCAA BSBNATURALNATURALNATURALNATURALNATURAL
NHLNATURALNATURALNATURALNATURALNATURAL
GOLFFORCEDNATURALNATURALFORCEDFORCED
UFC / MMAFORCEDNATURALNATURALFORCEDNO
TENNISNATURALNATURALNATURALNATURALNATURAL
CRICKETNATURALNATURALNATURALNATURALNATURAL
CRYPTO (BTC)NATURALNATURALFORCEDNATURALNATURAL
INDICES (ES)NATURALNATURALNONATURALNATURAL
ESPORTS (CS2)FORCEDFORCEDNATURALNATURALNATURAL
NATURAL 69 FORCED 9 DOESN'T-WORK 2 of 80 cells · hover any cell for the one-line reason · full analysis per sport below
THE MATH · FOUR CONSTRUCTIONS, ONE DRIFT TEST

LiveRoll · exact stacked map

The sport's exclusive event classes (plus declared attribute splits) are packed into the 15 hard/soft dice rows so each row's probability equals its true craps odds exactly. Big events that straddle a row boundary are cut on a named continuous mark (probability integral transform), flagged with a dagger in every table. Because the map is exact, every felt bet settles at book odds:

BETPAYSHOUSE EDGE (LOCKED)
Pass line1:11.41%
Don't pass (bar 12)1:11.36%
Pass odds (behind the line)true odds 2:1 / 3:2 / 6:50.00%
Field (2 and 12 pay double)1:1 / 2:15.56%
Place 6 / 87:61.52%
Place 5 / 97:54.00%
Place 4 / 109:56.67%
Hard 6 / 89:19.09%
Hard 4 / 107:111.11%

The honest number per sport is the drift band: if any single event's true frequency moves ±10% before recalibration, where can the pass-line edge go? Reported on every map below.

LiveCrash · martingale + instant bust

Pick the sport's bust event with measured hazard h per tick. Growth per surviving tick:

g = 1 / (1 - h)

which makes survival x multiplier a martingale: P(reach m) x m = 1, exactly fair at every cash-out. The whole house edge is applied as a 2.0% instant bust (bustabit construction), so

P(crash >= m) = 0.98 / m for all m

The audit point is hazard stationarity: where h varies by state (down, round, phase), production uses the state-conditional table g_t = 1/(1-h_t), cited per sport.

LiveSlots · shipped grammar, solved

Three reels bind to three different live games; one real play locks one reel. Payout follows the shipped scoreLine grammar (single pays base, pair base squared, triple cubed, summed over distinct symbols) times a line multiplier m:

RTP = m x SUM_i SUM_k C(3,k) p_i^k (1-p_i)^(3-k) b_i^k = 95%

Closed form, exact, per sport. Every spin returns something; the game is a grind with a jackpot line (3 of the top symbol).

LiveHit / LiveDeal · fair deck

Events stack into 13 ranks of exactly 1/13 each, prestige ascending (the sport's best moment is the ace). Ten-value density is exactly 16/52. Already-dealt cards are skipped (rejection), which makes the live stream deal statistically identical to a shuffled shoe. Sensitivity of the blackjack edge to calibration drift is bounded first-order with Griffin's effect-of-removal coefficients; LiveDeal draws its suit from a second real mark (side of field, court, corner).

Audit of the existing demo math (as instructed: not trusted blindly)

calibration.json stores the fair dice pmf as every sport's "craps" block: it is the target, not an achieved distribution, and its meta edge is 0.05 where this report standardizes 1.41% (pass) / 2.0% (crash). rollmaps.json assigns one event to several rows (MLB groundout on 3, 5 and 7) with no stated sub-allocation rule; this report formalizes those as attribute splits so the felt copy stays deterministic.

LiveSlots shipped BASE table (2/2/2/3/4/5/8/12/20) under the live single/pair/cube grammar returns 7.78 stakes per spin with true 2024 Statcast pitch rates: at a 1-stake spin cost that is 778% RTP. It needs the line multiplier m = 0.122 to hit the advertised 95%. The separately quoted "worked 95%" pure three-of-a-kind paytable (HR x3220 ... BALL x5) actually returns 55.4% RTP on three independent reels at true rates. The per-sport paytables below replace both with exact solves.

NFL

unit: scrimmage play (resolved) · 124.3 events/game · ~40s between snaps; 124 resolved plays/game
LiveRoll NATURAL LiveCrash NATURAL LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

18 measured exclusive outcomes, none oversized; penalty = authentic no-roll

NO-ROLL RULE · Penalty no-play (12.3%), kneel, spike = NO-ROLL push (flag wipes the snap, bets stand)
ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Interception 1.16% · Fumble lost 0.71% · Incomplete pass 0.50% · Sack 0.41%
31-2 2-15.56%Rush 4-9 yd 2.26% · Completion 0-4 yd 3.29%
HARD 42-22.78%Rushing TD 1.53% · Completion 5-9 yd 0.44% · Completion 0-4 yd 0.78% · QB scramble 0.03%
SOFT 41-3 3-15.56%Rush stuffed (<=0 yd) 5.56%
51-4 4-1 2-3 3-211.11%Rush 1-3 yd 11.11%
HARD 63-32.78%QB scramble 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Rush 4-9 yd 11.11%
71-6 6-1 2-5 5-2 3-4 4-316.67%Incomplete pass 16.67%
HARD 84-42.78%Sack 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Completion 5-9 yd 11.11%
93-6 6-3 4-5 5-411.11%Completion 10-19 yd 9.76% · Completion 0-4 yd 1.35%
HARD 105-52.78%Rush 1-3 yd 2.42% · Sack 0.35%
SOFT 104-6 6-45.56%Rush 10+ yd 3.86% · Rush stuffed (<=0 yd) 1.62% · QB scramble 0.08%
115-6 6-55.56%Completion 20+ yd 3.99% · Completion 0-4 yd 1.57%
126-62.78%Passing TD 2.43% · Sack 0.18% · QB scramble 0.17%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.36%, 2.76%] · 22 boundary cuts (†) · 23% of stream mass placed whole

LIVECRASH survival map NATURAL

drive-survival is the native tension of football; h=.176 measured

bust event Drive ends (any cause) hazard 0.1758 per scrimmage play growth per survival x1.2133 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 4
nflverse 2024: 5,944 drive-ends / 33,812 real snaps; mean drive 5.69 snaps
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.79354.87%0.9800
x2.17445.22%0.9800
x3.19630.72%0.9800
x5.70917.20%0.9800
x10.18129.63%0.9800
x26.76173.66%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 10.10% (-10%: -6.63%) - this is the recalibration tolerance
Hazard varies by down/distance/field position; production uses state-conditional g_t = 1/(1-h_t) from the same pbp table

LIVESLOTS paytable, shipped pay grammar NATURAL

9 legible play-class symbols; 3 reels = 3 Sunday games

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
GRINDrush 1-3 / comp 0-4 / scramble27.71%x20.140.290.5712.8%
INCincomplete16.40%x20.140.290.577.5%
RUSH+rush 4-914.77%x30.210.641.9311.7%
SHORTcomp 5-911.04%x30.210.641.938.4%
CHUNK10-19 yd gain10.81%x40.291.144.5712.1%
STUFFstuff/sack10.40%x50.361.788.9215.9%
BIG2020+ yd gain3.81%x80.574.5736.548.6%
TDpass+rush TD3.27%x120.8610.28123.3312.1%
TOINT/fumble1.79%x201.4328.55570.9810.9%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.0714 normalizes the raw expectation (13.31 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 24.2% · RTP under ±10% symbol drift: ±1.9pp

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit rank ladder follows play quality; low split load
LiveDeal 1 play = 1 board card at ~40s cadence fits flop/turn/river pacing
RANKTARGETEVENT COMPOSITION
27.69%Incomplete pass 7.69%
37.69%Incomplete pass 7.69%
47.69%Incomplete pass 1.79% · Rush 1-3 yd 5.84% · Fumble lost 0.06%
57.69%Rush 1-3 yd 7.69%
67.69%Rush 4-9 yd 7.69%
77.69%Rush 4-9 yd 5.68% · Passing TD 2.01%
87.69%Completion 5-9 yd 7.69%
97.69%Completion 5-9 yd 3.86% · Completion 10-19 yd 2.07% · Rushing TD 1.53% · Fumble lost 0.23%
T7.69%Completion 10-19 yd 7.69%
J7.69%Rush stuffed (<=0 yd) 7.17% · Passing TD 0.42% · Fumble lost 0.10%
Q7.69%Completion 0-4 yd 6.98% · Interception 0.71%
K7.69%Completion 20+ yd 3.99% · QB scramble 3.06% · Interception 0.45% · Fumble lost 0.19%
A7.69%Rush 10+ yd 3.86% · Sack 3.72% · Fumble lost 0.11%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 20 boundary cuts (†) · 30% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.45pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: possession side (home/away) x field half = 4 real suits; board fills one card per resolved play · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal
SOURCES nflverse-data play-by-play 2024 (nflfastR) TeamRankings NFL plays per game Pro-Football-Reference 2024 season · taxonomy rows: 27 measured / 0 cited-estimate (full per-figure citations in maps.json)

NCAAF

unit: scrimmage play (resolved) · 137.6 events/game · fastest-scoring football variant; 137.6 snaps/game
LiveRoll NATURAL LiveCrash NATURAL LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

same granularity as NFL with 2x the TD rate; verdict carries

NO-ROLL RULE · Accepted penalty (8.0% of events) = NO-ROLL push
ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Interception 1.19% · Fumble lost 0.79% · Completion 10-19 yd 0.71% · Sack 0.08%
31-2 2-15.56%Incompletion 4.91% · Completion <=0 yd 0.64%
HARD 42-22.78%Rush TD 2.46% · Rush 1-3 yd 0.29% · Sack 0.03%
SOFT 41-3 3-15.56%Rush 4-9 yd 4.72% · Completion <=0 yd 0.83%
51-4 4-1 2-3 3-211.11%Incompletion 11.11%
HARD 63-32.78%Completion 10-19 yd 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Rush 4-9 yd 11.11%
71-6 6-1 2-5 5-2 3-4 4-316.67%Rush 1-3 yd 16.67%
HARD 84-42.78%Sack 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Completion 1-9 yd 11.11%
93-6 6-3 4-5 5-411.11%Rush stuffed 8.70% · Rush 10-19 yd 2.41%
HARD 105-52.78%Rush 10-19 yd 2.78%
SOFT 104-6 6-45.56%Rush 20+ yd 2.28% · Completion 10-19 yd 3.28%
115-6 6-55.56%Completion 20+ yd 3.37% · Completion 1-9 yd 2.06% · Completion <=0 yd 0.08% · Sack 0.04%
126-62.78%Pass TD 2.35% · Rush 10-19 yd 0.24% · Completion <=0 yd 0.19%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.30%, 2.71%] · 22 boundary cuts (†) · 21% of stream mass placed whole

LIVECRASH survival map NATURAL

drive hazard .178 measured; more explosive plays = livelier multipliers

bust event Drive ends (any cause) hazard 0.1780 per scrimmage play growth per survival x1.2165 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 4
cfbstats 2024: 24.4 drives / 137.6 snaps; mean drive 5.63 plays
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.80354.43%0.9800
x2.19444.74%0.9800
x3.24630.23%0.9800
x5.84916.79%0.9800
x10.51129.33%0.9800
x28.00173.50%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 10.22% (-10%: -6.77%) - this is the recalibration tolerance
Wider team variance than NFL (57.8-79.9 plays/gm); condition g_t on matchup

LIVESLOTS paytable, shipped pay grammar NATURAL

8 legible symbols; Saturday slates give 3+ concurrent games all day

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
GRINDrush 1-3 / comp 1-9 / comp<=031.88%x20.170.340.6917.9%
INCincompletion16.03%x20.170.340.698.8%
MOVErush 4-915.84%x30.260.772.3215.3%
CHUNK10-19 yd12.20%x30.260.772.3211.3%
STUFFstuff/sack11.63%x40.341.385.5116.0%
XPLO20+ yd5.65%x50.432.1510.769.1%
TDpass+rush TD4.81%x80.695.5144.0713.8%
TOINT/fumble1.98%x121.0312.39148.737.8%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.0861 normalizes the raw expectation (11.04 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 28.7% · RTP under ±10% symbol drift: ±1.8pp

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit as NFL
LiveDeal as NFL
RANKTARGETEVENT COMPOSITION
27.69%Rush 1-3 yd 7.69%
37.69%Rush 1-3 yd 7.69%
47.69%Rush 1-3 yd 1.57% · Incompletion 0.64% · Rush 4-9 yd 0.45% · Completion 20+ yd 3.37% · Completion <=0 yd 1.66%
57.69%Incompletion 7.69%
67.69%Incompletion 7.69%
77.69%Rush 4-9 yd 7.69%
87.69%Rush 4-9 yd 7.69%
97.69%Completion 1-9 yd 7.69%
T7.69%Completion 1-9 yd 5.48% · Rush stuffed 1.01% · Interception 1.19% · Fumble lost 0.01%
J7.69%Rush stuffed 7.69%
Q7.69%Completion 10-19 yd 6.77% · Pass TD 0.05% · Rush 20+ yd 0.02% · Completion <=0 yd 0.09% · Fumble lost 0.78%
K7.69%Rush 10-19 yd 5.43% · Rush 20+ yd 2.26%
A7.69%Sack 2.93% · Rush TD 2.46% · Pass TD 2.30%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 21 boundary cuts (†) · 22% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.49pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: possession side x field half · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal
SOURCES cfbstats.com 2024 National Team Leaders (SportSource Analytics) TeamRankings CFB team stats 2024 Bless Your Chart post 070 FOX Sports (AP) 2-pt conversions · taxonomy rows: 13 measured / 10 cited-estimate (full per-figure citations in maps.json)

NBA

unit: chance (possession segment) · 225.4 events/game · ~1.7 chances/min per game; ~14s between events
LiveRoll NATURAL LiveCrash NATURAL LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

11-way chance partition with real zone/miss-type splits; 14s cadence

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Bonus FTs 1.50% · Made 2 | rim 0.37% · Turnover | steal 0.91%
31-2 2-15.56%Miss | def reb (off 2PA) 5.19% · Turnover | steal 0.37%
HARD 42-22.78%Made 3 2.78%
SOFT 41-3 3-15.56%Turnover | dead ball 5.40% · Miss | def reb (off 3PA) 0.03% · Turnover | steal 0.12%
51-4 4-1 2-3 3-211.11%Miss | def reb (off 2PA) 11.11%
HARD 63-32.78%Made 3 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Miss | off reb (new chance) 9.10% · Shooting foul, FTs 1.14% · Made 3 0.69% · Turnover | steal 0.18%
71-6 6-1 2-5 5-2 3-4 4-316.67%Miss | def reb (off 3PA) 16.67%
HARD 84-42.78%Turnover | steal 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Made 2 | jumper 11.11%
93-6 6-3 4-5 5-411.11%Made 2 | rim 11.11%
HARD 105-52.78%Turnover | steal 2.78%
SOFT 104-6 6-45.56%Shooting foul, FTs 5.56%
115-6 6-55.56%Made 3 5.56%
126-62.78%And-one 2.00% · Made 2 | jumper 0.61% · Turnover | steal 0.17%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.31%, 2.71%] · 21 boundary cuts (†) · 18% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (4) · every "|" label is a real feed mark, not RNG
  • Made 2 | rim: zone split: rim makes 14.0 of 28.2 2PM (B-R shooting)
  • Made 2 | jumper: zone split
  • Miss | def reb (off 3PA): miss-type split: 24.1 of 47.6 misses are 3s
  • Miss | def reb (off 2PA): miss-type split

LIVECRASH survival map NATURAL

scoreless-possession hazard .49: punchy 2-possession median runs

bust event Possession ends scoreless hazard 0.4900 per possession growth per survival x1.9608 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 2
pbpstats 2024-25: scoring possessions 50.9% (PPP 1.1484 / 99.1 poss)
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.96149.98%0.9800
x3.84225.49%0.9800
x7.54313.00%0.9800
x14.7846.63%0.9800
x28.9853.38%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 19.93% (-10%: -17.74%) - this is the recalibration tolerance
Near coin-flip and empirically ~iid (hot-hand effects 1-2pp); the fastest-cadence crash in the set

LIVESLOTS paytable, shipped pay grammar NATURAL

8 legible symbols; any night has 3+ concurrent games

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
BRICKmiss + def reb33.00%x20.180.350.7119.1%
BUCKETmade 223.20%x20.180.350.7113.2%
TRIPLEmade 311.80%x30.270.802.3911.2%
OREBoff reb9.10%x30.270.802.398.4%
FTSFT trip8.20%x40.351.425.6610.8%
STEALlive-ball TO7.30%x50.442.2111.0612.7%
TOVdead-ball TO5.40%x80.715.6645.3016.5%
AND1and-one2.00%x121.0612.74152.898.1%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.0885 normalizes the raw expectation (10.74 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 26.5% · RTP under ±10% symbol drift: ±1.7pp

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit modest split load; Made-3 = face-card tier is instantly legible
LiveDeal board fills a card every ~14s; hand completes inside 90s
RANKTARGETEVENT COMPOSITION
27.69%Miss | def reb (off 3PA) 7.69%
37.69%Miss | def reb (off 3PA) 7.69%
47.69%Miss | def reb (off 3PA) 1.32% · Miss | def reb (off 2PA) 0.92% · Made 3 4.11% · And-one 1.35%
57.69%Miss | def reb (off 2PA) 7.69%
67.69%Miss | def reb (off 2PA) 7.69%
77.69%Made 3 7.69%
87.69%Made 2 | jumper 7.69%
97.69%Made 2 | jumper 4.03% · Miss | off reb (new chance) 1.41% · Turnover | dead ball 1.50% · And-one 0.65% · Bonus FTs 0.12%
T7.69%Made 2 | rim 7.69%
J7.69%Made 2 | rim 3.79% · Turnover | dead ball 3.90%
Q7.69%Miss | off reb (new chance) 7.69%
K7.69%Turnover | steal 7.30% · Bonus FTs 0.39%
A7.69%Shooting foul, FTs 6.70% · Bonus FTs 0.99%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 21 boundary cuts (†) · 14% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.49pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: offense side x halfcourt side of floor · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

NCAAM

unit: possession (terminal) · 137.7 events/game · ~1.1 terminal events/min per game
LiveRoll NATURAL LiveCrash NATURAL LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

5-way terminal partition splits cleanly; OREB as no-roll is authentic

NO-ROLL RULE · Offensive rebound (15.3% of possessions) extends the possession = NO-ROLL (dice stay hot)
ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Miss | def reb (off 2PA) 0.19% · Made 2 | rim 2.21% · Turnover | dead ball 0.38%
31-2 2-15.56%Turnover | dead ball 5.56%
HARD 42-22.78%Made 2 | jumper 2.21% · Turnover | dead ball 0.57%
SOFT 41-3 3-15.56%Miss | def reb (off 3PA) 3.69% · Turnover | steal 1.60% · Made 3 0.21% · Turnover | dead ball 0.06%
51-4 4-1 2-3 3-211.11%FT trip 11.11%
HARD 63-32.78%Made 3 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Miss | def reb (off 3PA) 11.11%
71-6 6-1 2-5 5-2 3-4 4-316.67%Miss | def reb (off 2PA) 16.67%
HARD 84-42.78%Turnover | steal 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Made 2 | rim 11.11%
93-6 6-3 4-5 5-411.11%Made 2 | jumper 11.11%
HARD 105-52.78%Made 3 2.78%
SOFT 104-6 6-45.56%Turnover | steal 5.56%
115-6 6-55.56%Made 3 5.56%
126-62.78%FT trip 2.14% · Turnover | dead ball 0.64%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.33%, 2.73%] · 22 boundary cuts (†) · 0% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (4) · every "|" label is a real feed mark, not RNG
  • Made 2 | rim: zone split ~50/50 of made 2s (est; D1 zone tables not public)
  • Made 2 | jumper: zone split (est)
  • Miss | def reb (off 3PA): miss-type split: 30.2:34.4 three:two misses (S-R aggregates)
  • Miss | def reb (off 2PA): miss-type split

LIVECRASH survival map NATURAL

scoreless hazard .498 is a near-perfect coin flip

bust event Possession ends scoreless hazard 0.4980 per possession growth per survival x1.9920 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 2
S-R 2024-25 D1 aggregates: TO .1714 + miss-DRB .3166 + scoreless FT trip .0104
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.99149.20%0.9800
x3.97224.70%0.9800
x7.90312.40%0.9800
x15.7546.22%0.9800
x31.3753.12%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 20.48% (-10%: -18.41%) - this is the recalibration tolerance
Higher TO rate than NBA (17.1% vs 12.6%) keeps busts dramatic

LIVESLOTS paytable, shipped pay grammar NATURAL

6 symbols; March slates run 16 concurrent games

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
BRICKmiss + def reb31.66%x20.210.430.8522.0%
BUCKETmade 226.64%x20.210.430.8518.4%
FTSFT trip13.25%x30.320.962.8815.4%
TRIPLEmade 311.32%x30.320.962.8812.9%
STEALsteal9.93%x40.431.716.8216.3%
TOVdead-ball TO7.21%x50.532.6613.3215.0%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.1066 normalizes the raw expectation (8.91 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 23.9% · RTP under ±10% symbol drift: ±1.2pp

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit as NBA with slightly coarser event classes
LiveDeal cadence supports the board fill
RANKTARGETEVENT COMPOSITION
27.69%Miss | def reb (off 2PA) 7.69%
37.69%Miss | def reb (off 2PA) 7.69%
47.69%Miss | def reb (off 2PA) 1.47% · Made 2 | rim 5.63% · Turnover | dead ball 0.59%
57.69%Miss | def reb (off 3PA) 7.69%
67.69%Miss | def reb (off 3PA) 7.11% · Turnover | dead ball 0.59%
77.69%Made 2 | rim 7.69%
87.69%Made 2 | jumper 7.69%
97.69%Made 2 | jumper 5.63% · Turnover | dead ball 2.07%
T7.69%FT trip 7.69%
J7.69%FT trip 5.56% · Turnover | dead ball 2.14%
Q7.69%Made 3 7.69%
K7.69%Made 3 3.63% · Turnover | steal 2.24% · Turnover | dead ball 1.83%
A7.69%Turnover | steal 7.69%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 20 boundary cuts (†) · 0% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.45pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: offense side x floor side · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

WNBA

unit: chance (possession segment) · 180.0 events/game · ~1.5 chances/min per game; ~13s between events
LiveRoll NATURAL LiveCrash NATURAL LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

same 11-way chance partition as NBA with real WNBA splits; ~13s cadence

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Bonus FTs 1.67% · Made 3 1.11%
31-2 2-15.56%Shooting foul, FTs 5.56%
HARD 42-22.78%Miss | def reb (off 2PA) 1.11% · Made 3 1.66%
SOFT 41-3 3-15.56%Turnover | dead ball 5.56%
51-4 4-1 2-3 3-211.11%Miss | def reb (off 3PA) 11.11%
HARD 63-32.78%Miss | def reb (off 3PA) 2.56% · Turnover | dead ball 0.22%
SOFT 61-5 5-1 2-4 4-211.11%Miss | off reb (new chance) 10.67% · Turnover | dead ball 0.44%
71-6 6-1 2-5 5-2 3-4 4-316.67%Miss | def reb (off 2PA) 16.67%
HARD 84-42.78%Turnover | steal 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Made 2 | jumper 11.05% · Turnover | dead ball 0.06%
93-6 6-3 4-5 5-411.11%Made 2 | rim 10.62% · Turnover | dead ball 0.49%
HARD 105-52.78%Shooting foul, FTs 1.88% · Made 3 0.78% · Turnover | dead ball 0.11%
SOFT 104-6 6-45.56%Turnover | steal 5.55% · Turnover | dead ball 0.00%
115-6 6-55.56%Made 3 5.56%
126-62.78%And-one 2.22% · Turnover | dead ball 0.56%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.29%, 2.70%] · 20 boundary cuts (†) · 36% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (11) · every "|" label is a real feed mark, not RNG
  • Made 2 | rim: zone split ~49% of 2PM at rim (est; WNBA zone tables thin)
  • Made 2 | jumper: zone split (est)
  • Made 3: 3PM 8.2/team-game / 90.0 chances (HHS 2025)
  • And-one: ~2.0/team-game from FTA composition (est)
  • Shooting foul, FTs: ~6.7 non-and1 shooting-foul trips / 90.0 (est)
  • Bonus FTs: ~1.5 penalty trips / 90.0 (est)
  • Miss | def reb (off 3PA): miss-type split: 16.5 of 37.9 misses are 3s (HHS 2025)
  • Miss | def reb (off 2PA): miss-type split
  • Miss | off reb (new chance): OREB% 25.4 -> ~9.6 off rebs / 90.0 (HHS 2025)
  • Turnover | steal: STL 7.5/team-game (live-ball TO) / 90.0 (HHS 2025)

LIVECRASH survival map NATURAL

scoreless-possession hazard .534: slightly punchier busts than NBA, still short runs

bust event Possession ends scoreless hazard 0.5340 per possession growth per survival x2.1459 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 1
Her Hoop Stats 2025 (est): PPP 1.01 (81.5 pts / 80.4 poss); scoring possessions ~46.6% (FGM 29.7 + FT-only ~7.8 / 80.4) => scoreless hazard .534
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x2.15145.67%0.9800
x4.61221.28%0.9800
x9.8839.92%0.9800
x21.2144.62%0.9800
x45.5152.15%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 13.23% (-10%: -9.23%) - this is the recalibration tolerance
Higher scoreless hazard than NBA (WNBA PPP 1.01 vs 1.15; FG% .439 vs .467); empirically near-iid, short ~2-possession median runs

LIVESLOTS paytable, shipped pay grammar NATURAL

8 legible symbols; in-season slate carries concurrent games

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
BRICKmiss + def reb31.45%x20.160.320.6416.4%
BUCKETmade 221.67%x20.160.320.6411.1%
OREBoff reb10.67%x30.240.722.169.0%
TRIPLEmade 39.11%x30.240.722.167.6%
FTSFT trip9.11%x40.321.285.1211.1%
STEALlive-ball TO8.33%x50.402.0010.0013.5%
TOVdead-ball TO7.44%x80.645.1240.9722.9%
AND1and-one2.22%x120.9611.52138.268.3%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.0800 normalizes the raw expectation (11.87 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 25.1% · RTP under ±10% symbol drift: ±2.3pp

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit modest split load; Made-3 = face-card tier is instantly legible
LiveDeal board fills a card every ~13s; hand completes inside ~90s
RANKTARGETEVENT COMPOSITION
27.69%Miss | def reb (off 2PA) 7.69%
37.69%Miss | def reb (off 2PA) 7.69%
47.69%Miss | def reb (off 2PA) 2.40% · Made 2 | jumper 3.36% · And-one 1.94%
57.69%Miss | def reb (off 3PA) 7.69%
67.69%Miss | def reb (off 3PA) 5.98% · Made 3 1.42% · And-one 0.28% · Bonus FTs 0.02%
77.69%Made 2 | jumper 7.69%
87.69%Miss | off reb (new chance) 7.69%
97.69%Miss | off reb (new chance) 2.98% · Made 2 | rim 2.93% · Turnover | steal 0.64% · Bonus FTs 1.15%
T7.69%Made 2 | rim 7.69%
J7.69%Made 3 7.69%
Q7.69%Turnover | steal 7.69%
K7.69%Shooting foul, FTs 7.44% · Bonus FTs 0.25%
A7.69%Turnover | dead ball 7.44% · Bonus FTs 0.25%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 21 boundary cuts (†) · 15% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.43pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: offense side x halfcourt side of floor · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal
SOURCES Her Hoop Stats 2025 WNBA League Summary Basketball-Reference WNBA 2025 (cross-ref) · taxonomy rows: 3 measured / 10 cited-estimate (full per-figure citations in maps.json)

SOCCER

unit: on-ball event (Opta) · 1650 events/game · ~17 events/min - the densest stream in sport
LiveRoll NATURAL LiveCrash NATURAL LiveSlots FORCED LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

Opta's 1,650-event stream is the richest outcome space of any sport

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Yellow card 0.31% · Own goal 0.01% · Red card 0.01% · Tackle 2.45%
31-2 2-15.56%Ball recovery 5.56%
HARD 42-22.78%Corner 0.74% · Pass complete | def third 0.72% · Pass incomplete 1.05% · Take-on success 0.18% · Offside 0.10%
SOFT 41-3 3-15.56%Throw-in 3.32% · Foul 1.60% · Interception 0.64%
51-4 4-1 2-3 3-211.11%Pass complete | final third 11.11%
HARD 63-32.78%Shot blocked 0.52% · Pass complete | mid, right 1.93% · Interception 0.32% · Offside 0.01%
SOFT 61-5 5-1 2-4 4-211.11%Pass complete | mid, left 11.11%
71-6 6-1 2-5 5-2 3-4 4-316.67%Pass complete | def third 16.67%
HARD 84-42.78%Shot on target (saved) 0.65% · Pass complete | mid, left 1.93% · Tackle 0.00% · Take-on fail 0.03% · Offside 0.16%
SOFT 82-6 6-2 3-5 5-311.11%Pass complete | mid, right 11.11%
93-6 6-3 4-5 5-411.11%Pass incomplete 11.11%
HARD 105-52.78%Save 0.41% · Ball recovery 1.20% · Take-on success 1.17%
SOFT 104-6 6-45.56%Goal kick 1.23% · Pass complete | final third 3.38% · Clearance 0.56% · Interception 0.39%
115-6 6-55.56%Shot off target 0.80% · Aerial duel 3.32% · Take-on fail 1.44%
126-62.78%Goal 0.25% · Penalty awarded 0.02% · Clearance 2.51%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.30%, 2.70%] · 26 boundary cuts (†) · 13% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (4) · every "|" label is a real feed mark, not RNG
  • Pass complete | def third: zone split ~30% of completes (Opta zones; est)
  • Pass complete | mid, left: zone+side split
  • Pass complete | mid, right: zone+side split
  • Pass complete | final third: zone split ~25% (est)

LIVECRASH survival map NATURAL

pass-sequence survival IS tiki-taka tension; hazard .29 measured

bust event Possession sequence ends hazard 0.2900 per pass growth per survival x1.4085 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 3
Opta: league mean ~3.4 passes per open-play sequence; team spread .20 (City) to .35
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.98249.40%0.9800
x2.79335.08%0.9800
x3.94424.90%0.9800
x5.54517.68%0.9800
x10.9978.91%0.9800
x30.72103.19%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 13.52% (-10%: -10.51%) - this is the recalibration tolerance
Hazard rises with field position (long/final-third passes fail 2-4x more); state-conditional g_t from pass-zone hazard table

LIVESLOTS paytable, shipped pay grammar FORCED

stream is 57% passes: symbols need curated event-classes and the reel reads pass-heavy between shots

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
PASS+completed pass59.15%x20.240.480.9549.6%
DUELrecovery/tackle/aerial/interception12.78%x20.240.480.959.6%
PASS-incomplete12.41%x30.361.073.2115.9%
RESETthrow/goal kick/clearance/offside8.02%x30.361.073.219.8%
BOXfinal-third entry class: corner+takeon+foul+card5.39%x40.481.907.619.0%
SHOT+shot on target/blocked1.19%x50.592.9714.862.3%
SHOT-shot off target0.81%x80.957.6160.852.6%
GOALgoal0.25%x121.4317.11205.361.2%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.1188 normalizes the raw expectation (7.99 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 18.4% · RTP under ±10% symbol drift: ±0.8pp
stream renormalized to these 8 classes for the reel

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit 26-event taxonomy stacks into ranks with low split load
LiveDeal 17 events/min fills a board in seconds; World Cup shootouts = native side-bet
RANKTARGETEVENT COMPOSITION
27.69%Pass complete | def third 7.69%
37.69%Pass complete | def third 7.69%
47.69%Pass complete | def third 2.00% · Pass complete | mid, left 5.35% · Goal kick 0.17% · Offside 0.17%
57.69%Pass complete | final third 7.69%
67.69%Pass complete | final third 6.80% · Shot off target 0.80% · Yellow card 0.02% · Goal 0.08%
77.69%Pass complete | mid, left 7.69%
87.69%Pass complete | mid, right 7.69%
97.69%Pass complete | mid, right 5.35% · Foul 1.60% · Corner 0.74% · Own goal 0.01% · Red card 0.00%
T7.69%Pass incomplete 7.69%
J7.69%Pass incomplete 4.46% · Clearance 3.07% · Goal 0.16%
Q7.69%Ball recovery 6.75% · Shot on target (saved) 0.65% · Yellow card 0.29%
K7.69%Aerial duel 3.32% · Throw-in 3.32% · Goal kick 1.06%
A7.69%Tackle 2.46% · Take-on fail 1.47% · Take-on success 1.35% · Interception 1.35% · Shot blocked 0.52% · Save 0.41% · Offside 0.10% · Goal 0.01% · Penalty awarded 0.02% · Red card 0.01%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 22 boundary cuts (†) · 28% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.45pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: team in possession x pitch half · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

MLB

unit: pitch · 292 events/game · ~1.8 pitches/min; pitch clock makes cadence metronomic
LiveRoll NATURAL LiveCrash NATURAL LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

pitch outcomes + location/spray marks give exact-granularity rows; the shipped demo already plays this way

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Triple 0.10% · Hit by pitch 0.28% · In-play out | air 2.38% · Single 0.02%
31-2 2-15.56%Foul | third-base side 5.56%
HARD 42-22.78%Foul | straight back 2.78%
SOFT 41-3 3-15.56%Foul | first-base side 5.56%
51-4 4-1 2-3 3-211.11%Ball | low 8.89% · Swinging strike | fastball 2.23%
HARD 63-32.78%Swinging strike | fastball 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Ball | inside 8.89% · Swinging strike | fastball 1.07% · Foul | straight back 1.07% · Single 0.09%
71-6 6-1 2-5 5-2 3-4 4-316.67%In-play out | ground 6.52% · Ball | high 8.89% · Foul | third-base side 0.53% · Foul | first-base side 0.53% · Single 0.20%
HARD 84-42.78%Single 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Ball | outside 8.89% · Foul | straight back 2.23%
93-6 6-3 4-5 5-411.11%Called strike | heart 8.15% · In-play out | air 2.96%
HARD 105-52.78%Called strike | edge 2.78%
SOFT 104-6 6-45.56%Double 1.10% · Called strike | edge 4.45%
115-6 6-55.56%Swinging strike | offspeed 5.56%
126-62.78%Home run 0.77% · Swinging strike | offspeed 0.51% · Called strike | edge 0.93% · Single 0.57%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [0.55%, 2.15%] · 22 boundary cuts (†) · 52% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (13) · every "|" label is a real feed mark, not RNG
  • Ball | high: location split: Statcast plate_z above zone midline (~even; est)
  • Ball | low: location split
  • Ball | inside: location split
  • Ball | outside: location split
  • Called strike | edge: location split (~even; est)
  • Called strike | heart: location split
  • Swinging strike | fastball: pitch-type split (~even; Statcast)
  • Swinging strike | offspeed: pitch-type split
  • Foul | third-base side: spray split (~even by symmetry)
  • Foul | first-base side: spray split

LIVECRASH survival map NATURAL

PA-resolution hazard .257 measured; count-state conditioning available

bust event Plate appearance resolves hazard 0.2571 per pitch growth per survival x1.3461 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 3
B-Ref 2024: 3.89 pitches per PA -> per-pitch resolution hazard 1/3.89
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.81254.09%0.9800
x2.44340.18%0.9800
x3.28429.85%0.9800
x5.95616.47%0.9800
x10.7889.09%0.9800
x26.29113.73%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 11.83% (-10%: -8.53%) - this is the recalibration tolerance
Alternative slow curve: out-recorded per PA (h=.680) for inning-length runs; count-conditional hazard table available from Statcast

LIVESLOTS paytable, shipped pay grammar NATURAL

the shipped 9-symbol set is the template; pays recalibrated to true Statcast rates

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
BALLball35.54%x20.230.460.9327.2%
Kcalled+swinging strike28.46%x20.230.460.9321.4%
FOULfoul18.24%x30.351.053.1424.4%
OUTin-play out11.86%x30.351.053.1414.8%
1Bsingle3.65%x40.461.867.435.8%
2Bdouble1.10%x50.582.9014.522.1%
HRhome run0.77%x80.937.4359.462.4%
HBPhit by pitch0.28%x121.3916.72200.661.3%
3Btriple0.10%x202.3246.45928.990.7%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.1161 normalizes the raw expectation (8.18 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 24.0% · RTP under ±10% symbol drift: ±1.0pp
matches the LIVE LiveSlots symbol set; recalibrated pays below replace the shipped BASE guesses

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit ball/strike mass quantizes into low ranks, hits take the faces
LiveDeal metronomic pitch clock = ideal board-fill rhythm
RANKTARGETEVENT COMPOSITION
27.69%Ball | outside 7.69%
37.69%Ball | outside 1.19% · Ball | low 1.19% · Ball | high 1.19% · Ball | inside 1.19% · Called strike | edge 0.47% · Called strike | heart 0.46% · In-play out | air 1.99%
47.69%Ball | low 7.69%
57.69%Ball | high 7.69%
67.69%Ball | inside 7.69%
77.69%Called strike | edge 7.69%
87.69%Called strike | heart 7.69%
97.69%In-play out | ground 6.52% · In-play out | air 0.10% · Single 0.42% · Home run 0.64%
T7.69%Foul | third-base side 6.08% · Single 1.61%
J7.69%Foul | first-base side 6.08% · Double 1.10% · Home run 0.13% · Hit by pitch 0.28% · Triple 0.10%
Q7.69%Foul | straight back 6.07% · In-play out | air 1.62%
K7.69%Swinging strike | fastball 6.07% · Single 1.62%
A7.69%Swinging strike | offspeed 6.06% · In-play out | air 1.63%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 21 boundary cuts (†) · 38% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.31pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: pitcher hand (L/R) x batter side = real 4-way suit · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

NCAA BSB

unit: plate appearance · 80.7 events/game · ~0.46 PA/min; pitch-level feed (TrackMan, licensed) would 4x cadence
LiveRoll NATURAL LiveCrash NATURAL LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

same grammar as MLB one level up; HBP/error chaos is a real college flavor

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Triple 0.50% · Reached on error 1.70% · Hit by pitch 0.58%
31-2 2-15.56%Strikeout | looking 5.56%
HARD 42-22.78%Hit by pitch 2.78%
SOFT 41-3 3-15.56%In-play out | line 5.56%
51-4 4-1 2-3 3-211.11%Walk 11.11%
HARD 63-32.78%In-play out | ground 1.33% · In-play out | pop 1.44%
SOFT 61-5 5-1 2-4 4-211.11%In-play out | fly 11.11%
71-6 6-1 2-5 5-2 3-4 4-316.67%In-play out | ground 16.67%
HARD 84-42.78%In-play out | fly 2.39% · Strikeout | looking 0.24% · In-play out | line 0.14%
SOFT 82-6 6-2 3-5 5-311.11%Single 11.11%
93-6 6-3 4-5 5-411.11%Strikeout | swinging 11.11%
HARD 105-52.78%Strikeout | swinging 2.29% · Walk 0.49%
SOFT 104-6 6-45.56%Double 4.60% · In-play out | pop 0.69% · Hit by pitch 0.14% · Walk 0.10% · Home run 0.02%
115-6 6-55.56%Single 4.19% · In-play out | pop 1.37%
126-62.78%Home run 2.78%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.25%, 2.66%] · 23 boundary cuts (†) · 7% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (6) · every "|" label is a real feed mark, not RNG
  • Strikeout | swinging: K-type split ~70/30 (MLB convention; college split not public)
  • Strikeout | looking: K-type split
  • In-play out | ground: GO/AO-style split .44/.33/.14/.09 of outs (MLB shares)
  • In-play out | fly: split
  • In-play out | line: split
  • In-play out | pop: split

LIVECRASH survival map NATURAL

out hazard .599 measured from 124k PAs; CWS drama fits

bust event Batter out hazard 0.5990 per plate appearance growth per survival x2.4938 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 1
pooled 2025 D1 totals: P(reach) = .401 -> out hazard .599
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x2.49139.30%0.9800
x6.22215.76%0.9800
x15.5136.32%0.9800
x38.6742.53%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 16.64% (-10%: -12.64%) - this is the recalibration tolerance
College reach-rate (.40) beats MLB (.32): longer average runs, same mechanic

LIVESLOTS paytable, shipped pay grammar NATURAL

9 symbols mirror the MLB set with BB/ROE added

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
OUTin-play out40.76%x20.200.400.7926.9%
Kstrikeout19.18%x20.200.400.7912.2%
1Bsingle15.28%x30.300.892.6816.9%
BBwalk11.69%x30.300.892.6812.4%
2Bdouble4.60%x40.401.596.356.3%
HBPhit by pitch3.50%x50.502.4812.396.1%
HRhome run2.80%x80.796.3550.778.3%
ROEerror chaos1.70%x121.1914.28171.347.5%
3Btriple0.50%x201.9839.66793.233.4%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.0992 normalizes the raw expectation (9.58 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 25.9% · RTP under ±10% symbol drift: ±1.6pp

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit as MLB at PA granularity
LiveDeal PA cadence is slower but a 5-card board still fills inside 2 innings-halves
RANKTARGETEVENT COMPOSITION
27.69%In-play out | ground 7.69%
37.69%In-play out | ground 7.69%
47.69%In-play out | ground 2.60% · Walk 4.00% · In-play out | pop 0.50% · Reached on error 0.60%
57.69%Single 7.69%
67.69%Single 7.59% · Triple 0.10%
77.69%In-play out | fly 7.69%
87.69%In-play out | fly 5.79% · Home run 0.80% · Reached on error 1.10%
97.69%Strikeout | swinging 7.69%
T7.69%Strikeout | swinging 5.69% · Hit by pitch 2.00%
J7.69%Walk 7.69%
Q7.69%Strikeout | looking 5.79% · Hit by pitch 1.50% · Triple 0.40%
K7.69%In-play out | line 5.69% · Home run 2.00%
A7.69%Double 4.60% · In-play out | pop 3.10%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 21 boundary cuts (†) · 16% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.47pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: batter side x pitcher hand · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

NHL

unit: RTSS event · 303.8 events/game · ~2 events/min of recorded play; bursts during pressure
LiveRoll NATURAL LiveCrash NATURAL LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

10 measured RTSS classes + symmetric side splits; goal on 12 at .0205 vs .0278 target is the largest semantic gap

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Penalty 2.44% · Takeaway 0.34%
31-2 2-15.56%Hit | away 5.56%
HARD 42-22.78%Blocked shot | away 2.78%
SOFT 41-3 3-15.56%Stoppage | frozen/out 5.56%
51-4 4-1 2-3 3-211.11%Faceoff won | home 9.26% · Stoppage | frozen/out 1.65% · Takeaway 0.20%
HARD 63-32.78%Giveaway 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Faceoff won | away 9.25% · Stoppage | icing/offside 1.64% · Takeaway 0.22%
71-6 6-1 2-5 5-2 3-4 4-316.67%Shot saved | away shooter 8.88% · Hit | home 7.71% · Takeaway 0.08%
HARD 84-42.78%Takeaway 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Shot saved | home shooter 8.89% · Hit | away 2.15% · Takeaway 0.07%
93-6 6-3 4-5 5-411.11%Missed shot 8.79% · Giveaway 2.15% · Takeaway 0.17%
HARD 105-52.78%Blocked shot | away 2.74% · Takeaway 0.04%
SOFT 104-6 6-45.56%Blocked shot | home 5.52% · Takeaway 0.04%
115-6 6-55.56%Stoppage | icing/offside 5.56%
126-62.78%Goal 2.05% · Takeaway 0.73%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [0.56%, 2.15%] · 20 boundary cuts (†) · 63% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (10) · every "|" label is a real feed mark, not RNG
  • Faceoff won | home: side split (exactly symmetric by construction)
  • Faceoff won | away: side split
  • Shot saved | home shooter: side split (~even)
  • Shot saved | away shooter: side split
  • Hit | home: side split
  • Hit | away: side split
  • Stoppage | icing/offside: detail-type split ~even (RTSS detail; est)
  • Stoppage | frozen/out: detail-type split
  • Blocked shot | home: side split
  • Blocked shot | away: side split

LIVECRASH survival map NATURAL

whistle-hazard .227 measured from 29,704 event transitions

bust event Play segment ends (whistle) hazard 0.2270 per live event growth per survival x1.2937 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 3
NHL API 120-game sample: mean 4.40 live events per faceoff-to-whistle segment
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.67258.56%0.9800
x2.17345.27%0.9800
x3.62527.05%0.9800
x6.06716.16%0.9800
x10.1599.66%0.9800
x28.42133.45%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 10.38% (-10%: -6.89%) - this is the recalibration tolerance
Measured directly from event transitions; near-geometric segment lengths

LIVESLOTS paytable, shipped pay grammar NATURAL

10 legible symbols with real 9:1 save/goal tension

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
FACEfaceoff18.51%x20.100.210.416.1%
SOGshot saved17.77%x20.100.210.415.8%
HIThit15.42%x30.150.461.398.8%
STOPstoppage14.41%x30.150.461.398.2%
BLOCKblocked11.04%x40.210.823.288.9%
MISSmissed shot8.79%x50.261.286.419.2%
GIVEgiveaway4.93%x80.413.2826.288.5%
TAKEtakeaway4.65%x120.627.3988.6814.0%
PENpenalty2.44%x201.0320.53410.5611.9%
GOALgoal2.05%x321.6452.551681.6318.6%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.0513 normalizes the raw expectation (18.51 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 20.5% · RTP under ±10% symbol drift: ±2.5pp

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit side splits keep ranks semantic
LiveDeal 2 events/min fills boards; icing lulls are the only dead air
RANKTARGETEVENT COMPOSITION
27.69%Faceoff won | home 7.69%
37.69%Faceoff won | home 1.57% · Faceoff won | away 1.56% · Shot saved | home shooter 1.20% · Shot saved | away shooter 1.19% · Missed shot 1.10% · Hit | home 0.02% · Hit | away 0.02% · Goal 1.05%
47.69%Faceoff won | away 7.69%
57.69%Shot saved | home shooter 7.69%
67.69%Shot saved | away shooter 7.69%
77.69%Missed shot 7.69%
87.69%Hit | home 7.69%
97.69%Hit | away 7.69%
T7.69%Stoppage | frozen/out 7.21% · Goal 0.48%
J7.69%Stoppage | icing/offside 7.20% · Goal 0.49%
Q7.69%Blocked shot | home 5.52% · Takeaway 1.89% · Penalty 0.27% · Goal 0.02%
K7.69%Blocked shot | away 5.52% · Penalty 2.17%
A7.69%Giveaway 4.93% · Takeaway 2.76%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 22 boundary cuts (†) · 30% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.31pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: event team x attacking zone · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal
SOURCES NHL API gamecenter play-by-play (RTSS-derived) Hockey-Reference NHL League Averages Hockey-Reference 2023-24 Hat Tricks Daily Faceoff goalie goals · taxonomy rows: 10 measured / 0 cited-estimate (full per-figure citations in maps.json)

GOLF

unit: hole result (field-multiplexed) · 2808 events/game · full-field day: ~2,800 hole results over ~11h = ~4.2/min at peak waves
LiveRoll FORCED LiveCrash NATURAL LiveSlots NATURAL LiveHit FORCED LiveDeal FORCED

LIVEROLL event to dice map FORCED

works only field-multiplexed; par mass (.626) forces heavy par-type/nine splits and arrivals come in waves

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Double bogey 1.57% · Triple+ 0.21% · Par | par-4, scramble 0.41% · Par | par-5 0.55% · Birdie | par-3 0.04%
31-2 2-15.56%Bogey | par-3 3.59% · Birdie | par-5 1.97%
HARD 42-22.78%Birdie | par-3 2.78%
SOFT 41-3 3-15.56%Par | par-4 (other) 4.25% · Bogey | par-4 1.14% · Birdie | par-5 0.05% · Birdie | par-3 0.12%
51-4 4-1 2-3 3-211.11%Par | par-4 (other) 11.11%
HARD 63-32.78%Bogey | par-4 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Par | par-4, GIR 11.11%
71-6 6-1 2-5 5-2 3-4 4-316.67%Par | par-3 15.85% · Par | par-4, GIR 0.41% · Bogey | par-5 0.32% · Birdie | par-3 0.08%
HARD 84-42.78%Par | par-5 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Par | par-4, scramble 11.11%
93-6 6-3 4-5 5-411.11%Birdie | par-4 10.08% · Bogey | par-5 1.03%
HARD 105-52.78%Par | par-5 2.78%
SOFT 104-6 6-45.56%Birdie | par-5 5.56%
115-6 6-55.56%Bogey | par-4 5.56%
126-62.78%Eagle 0.51% · Albatross/Ace 0.01% · Par | par-5 2.26%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.21%, 2.65%] · 22 boundary cuts (†) · 32% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (12) · every "|" label is a real feed mark, not RNG
  • Par | par-4, GIR: par-type + front/back split of the .3840 par-4-par mass
  • Par | par-4, scramble: split
  • Par | par-4 (other): split
  • Par | par-3: par-type split (measured: 59,128/372,834 total)
  • Par | par-5: par-type split (measured)
  • Birdie | par-4: par-type split (measured: 37,591)
  • Birdie | par-5: par-type split (measured: 28,237)
  • Birdie | par-3: par-type split (measured: 11,255)
  • Bogey | par-4: par-type split (measured)
  • Bogey | par-3: par-type split

LIVECRASH survival map NATURAL

the bogey-free streak IS golf's native drama; hazard .162 from exact 372,834-hole counts

bust event Bogey or worse (streak breaker) hazard 0.1618 per hole played growth per survival x1.1931 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 4
ShotLink 2022-23: 60,331 of 372,834 holes; survival .838/hole; P(bogey-free round)=4.2%
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.70357.71%0.9800
x2.03448.37%0.9800
x3.44728.48%0.9800
x5.841016.77%0.9800
x11.84148.28%0.9800
x28.61193.42%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 9.35% (-10%: -5.79%) - this is the recalibration tolerance
Per-par hazard varies (par-3 .173 / par-4 .180 / par-5 .088); follow one player = authentic, or field-average

LIVESLOTS paytable, shipped pay grammar NATURAL

6 score symbols every golfer already knows; ACE line = true 1-in-2,302 jackpot

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
PARpar62.63%x20.260.521.0558.7%
BIRDIEbirdie20.67%x20.260.521.0517.4%
BOGEYbogey14.40%x30.391.183.5420.8%
DOUBLE+double or worse1.78%x30.391.183.542.3%
EAGLEeagle0.51%x40.522.108.390.9%
ACEalbatross/ace0.01%x50.663.2816.400.0%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.1312 normalizes the raw expectation (7.24 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 34.0% · RTP under ±10% symbol drift: ±0.7pp

LIVEHIT / LIVEDEAL event to rank map FORCED FORCED

LiveHit par-heavy mass quantizes into ranks only via par-type/nine cuts
LiveDeal wave arrivals stall the 5-card board between groups; playable but not native
RANKTARGETEVENT COMPOSITION
27.69%Par | par-3 7.69%
37.69%Par | par-3 7.69%
47.69%Par | par-3 0.47% · Par | par-4, GIR 3.83% · Birdie | par-4 2.39% · Par | par-5 0.67% · Bogey | par-5 0.27% · Triple+ 0.07%
57.69%Par | par-4 (other) 7.69%
67.69%Par | par-4 (other) 7.67% · Triple+ 0.02% · Albatross/Ace 0.00%
77.69%Par | par-4, GIR 7.69%
87.69%Par | par-4, scramble 7.69%
97.69%Par | par-4, scramble 3.83% · Bogey | par-4 1.78% · Double bogey 1.57% · Eagle 0.51% · Albatross/Ace 0.00%
T7.69%Birdie | par-4 7.69%
J7.69%Bogey | par-4 7.69%
Q7.69%Par | par-5 7.69%
K7.69%Birdie | par-5 7.57% · Triple+ 0.12%
A7.69%Bogey | par-3 3.59% · Birdie | par-3 3.02% · Bogey | par-5 1.08%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 22 boundary cuts (†) · 16% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.47pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: hole par-type x nine (front/back) · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

UFC / MMA

unit: significant strike attempt · 165 events/game · ~17 attempts/min; fight can end any second
LiveRoll FORCED LiveCrash NATURAL LiveSlots NATURAL LiveHit FORCED LiveDeal DOESN'T-WORK

LIVEROLL event to dice map FORCED

strike stream is binary land/miss at heart; rows need corner/position cuts and read samey

NO-ROLL RULE · Takedowns/knockdowns/sub attempts ride as overlay events (slots symbols, crash spikes), not dice rolls
ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Head strike misses | clinch/ground 1.93% · Body strike lands 0.85%
31-2 2-15.56%Head strike lands | blue 5.09% · Leg strike misses 0.38% · Leg strike lands 0.09%
HARD 42-22.78%Body strike misses 2.78%
SOFT 41-3 3-15.56%Head strike misses | red, distance 4.34% · Leg strike misses 1.22%
51-4 4-1 2-3 3-211.11%Head strike lands | blue 11.11%
HARD 63-32.78%Body strike misses 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Head strike misses | red, distance 11.11%
71-6 6-1 2-5 5-2 3-4 4-316.67%Head strike lands | red 16.20% · Body strike lands 0.34% · Leg strike lands 0.12%
HARD 84-42.78%Body strike misses 2.69% · Leg strike lands 0.08%
SOFT 82-6 6-2 3-5 5-311.11%Head strike misses | blue, distance 11.11%
93-6 6-3 4-5 5-411.11%Head strike misses | blue, distance 4.34% · Head strike misses | clinch/ground 6.77%
HARD 105-52.78%Leg strike misses 2.78%
SOFT 104-6 6-45.56%Body strike lands 5.56%
115-6 6-55.56%Leg strike lands 5.56%
126-62.78%Leg strike misses 2.78%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.25%, 2.68%] · 22 boundary cuts (†) · 16% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (9) · every "|" label is a real feed mark, not RNG
  • Head strike lands | red: target split (72/15/13 of landed, UFCStats) x corner
  • Head strike lands | blue: corner split
  • Body strike lands: target split
  • Leg strike lands: target split
  • Head strike misses | red, distance: corner + position split (distance ~78%)
  • Head strike misses | blue, distance: corner + position split
  • Head strike misses | clinch/ground: position split
  • Body strike misses: target split
  • Leg strike misses: target split

LIVECRASH survival map NATURAL

the finish IS a crash: every surviving minute grows the pot, one punch ends it

bust event Fight ends (KO/TKO/sub) hazard 0.0560 per fight minute growth per survival x1.0593 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 13
mma.social 8,470-fight aggregate: 53% finish rate / 9.53 avg minutes
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.59861.80%0.9800
x2.121346.33%0.9800
x3.172030.95%0.9800
x5.022819.52%0.9800
x10.03409.77%0.9800
x25.21563.89%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 9.29% (-10%: -5.83%) - this is the recalibration tolerance
Front-loaded (R1 .064, later .045) and division-dependent (HW 66% finish vs WSW 33%); production g_t conditions on round + weight class

LIVESLOTS paytable, shipped pay grammar NATURAL

KD/TD/SUB as rare symbols over the strike stream is legible fight grammar

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
MISSstrike misses53.60%x20.270.551.0950.6%
HEADhead strike lands32.40%x20.270.551.0928.9%
BODYbody lands6.75%x30.411.233.699.4%
LEGleg lands5.85%x30.411.233.698.0%
TDtakedown landed (1.26/fight)0.76%x40.552.188.741.3%
SUBsub attempt (0.67/fight)0.40%x50.683.4117.070.9%
KDknockdown per attempt-tick (0.39/fight over 165)0.24%x81.098.7469.900.8%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.1365 normalizes the raw expectation (6.96 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 27.2% · RTP under ±10% symbol drift: ±0.6pp
overlay events (KD/TD/SUB) folded into the attempt-tick stream at their per-attempt rates

LIVEHIT / LIVEDEAL event to rank map FORCED DOESN'T-WORK

LiveHit 9 sub-events for 13 ranks; heavy split load
LiveDeal a 5-card board can die mid-hand to a 1-punch finish; hand-completion risk breaks the game contract
RANKTARGETEVENT COMPOSITION
27.69%Head strike lands | red 7.69%
37.69%Head strike lands | red 7.69%
47.69%Head strike lands | red 0.82% · Head strike lands | blue 0.82% · Head strike misses | red, distance 0.07% · Head strike misses | blue, distance 0.07% · Head strike misses | clinch/ground 1.01% · Body strike misses 0.56% · Leg strike lands 4.37%
57.69%Head strike lands | blue 7.69%
67.69%Head strike lands | blue 7.69%
77.69%Head strike misses | red, distance 7.69%
87.69%Head strike misses | red, distance 7.69%
97.69%Head strike misses | blue, distance 7.69%
T7.69%Head strike misses | blue, distance 7.69%
J7.69%Head strike misses | clinch/ground 7.69%
Q7.69%Body strike misses 7.69%
K7.69%Leg strike misses 7.15% · Leg strike lands 0.54%
A7.69%Body strike lands 6.75% · Leg strike lands 0.94%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 19 boundary cuts (†) · 14% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.49pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: corner x target · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

TENNIS

unit: point · 148 events/game · ~1.5 points/min; ~25s between points with shot-level ticks inside
LiveRoll NATURAL LiveCrash NATURAL LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

point outcomes with serve-number and rally-length marks; ace on 12 (.0837 vs .0278) is the one showpiece overweight

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Double fault 2.78%
31-2 2-15.56%Server wins rally | 1st serve, long 5.56%
HARD 42-22.78%Returner wins rally | 2nd serve 0.94% · Server wins rally | 2nd serve 1.84%
SOFT 41-3 3-15.56%Return error | unforced 4.07% · Server wins rally | 1st serve, short 1.18% · Ace 0.04% · Double fault 0.27%
51-4 4-1 2-3 3-211.11%Server wins rally | 1st serve, short 11.11%
HARD 63-32.78%Returner wins rally | 1st serve, long 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Returner wins rally | 2nd serve 11.11%
71-6 6-1 2-5 5-2 3-4 4-316.67%Return error | forced 16.20% · Server wins rally | 2nd serve 0.39% · Double fault 0.08%
HARD 84-42.78%Ace 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Server wins rally | 2nd serve 11.11%
93-6 6-3 4-5 5-411.11%Returner wins rally | 1st serve, short 11.10% · Double fault 0.01%
HARD 105-52.78%Ace 2.78%
SOFT 104-6 6-45.56%Server wins rally | 1st serve, long 4.49% · Returner wins rally | 1st serve, long 0.75% · Double fault 0.31%
115-6 6-55.56%Returner wins rally | 1st serve, long 5.56%
126-62.78%Ace 2.78%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.25%, 2.68%] · 21 boundary cuts (†) · 31% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (8) · every "|" label is a real feed mark, not RNG
  • Return error | forced: real MCP category
  • Return error | unforced: real MCP category
  • Server wins rally | 1st serve, short: serve# + rally-length split (real marks)
  • Server wins rally | 1st serve, long: split
  • Server wins rally | 2nd serve: serve# split
  • Returner wins rally | 1st serve, short: split
  • Returner wins rally | 1st serve, long: split
  • Returner wins rally | 2nd serve: serve# split

LIVECRASH survival map NATURAL

rally survival is the native tension; exact hazard table measured to the shot

bust event Rally ends hazard 0.2100 per shot (from shot 5) growth per survival x1.2658 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 3
MCP 320,516 parsed points: hazard sawtooth shots 1-4 (.297/.158/.278/.195), plateau .21 from shot 5
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.60261.16%0.9800
x2.03348.32%0.9800
x3.25530.16%0.9800
x5.21718.82%0.9800
x10.56109.28%0.9800
x27.12143.61%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 9.61% (-10%: -6.02%) - this is the recalibration tolerance
Explicitly non-geometric early: production uses the exact 4-step hazard table then constant .21 tail (WTA .255)

LIVESLOTS paytable, shipped pay grammar NATURAL

6 point-ending symbols every fan reads instantly

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
UEunforced error end27.82%x20.210.420.8519.0%
WINNERrally winner23.04%x20.210.420.8515.6%
SRV+unreturned serve20.27%x30.320.952.8525.2%
FORCEDforced error end17.06%x30.320.952.8520.5%
ACEace8.37%x40.421.696.7613.2%
DFdouble fault3.45%x50.532.6413.216.4%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.1057 normalizes the raw expectation (8.99 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 28.6% · RTP under ±10% symbol drift: ±1.2pp
point-ending classes (winner/FE/UE measured from MCP terminators)

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit low split load; ace = ace of the deck
LiveDeal 25s point cadence fills the board like a dealt street
RANKTARGETEVENT COMPOSITION
27.69%Return error | forced 7.69%
37.69%Return error | forced 7.69%
47.69%Return error | forced 0.82% · Server wins rally | 2nd serve 5.65% · Double fault 1.23%
57.69%Server wins rally | 2nd serve 7.69%
67.69%Server wins rally | 1st serve, short 7.69%
77.69%Server wins rally | 1st serve, short 4.60% · Server wins rally | 1st serve, long 2.36% · Ace 0.68% · Double fault 0.06%
87.69%Returner wins rally | 2nd serve 7.69%
97.69%Returner wins rally | 2nd serve 4.36% · Returner wins rally | 1st serve, long 1.39% · Double fault 1.95%
T7.69%Returner wins rally | 1st serve, short 7.69%
J7.69%Returner wins rally | 1st serve, short 3.41% · Return error | unforced 4.07% · Double fault 0.21%
Q7.69%Server wins rally | 1st serve, long 7.69%
K7.69%Returner wins rally | 1st serve, long 7.69%
A7.69%Ace 7.69%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 21 boundary cuts (†) · 4% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.44pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: server end x deuce/ad court (real) · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

CRICKET

unit: delivery (T20) · 245 events/game · ~1.2 balls/min steady; formats scale hazard (ODI/Test)
LiveRoll NATURAL LiveCrash NATURAL LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

ball-by-ball outcomes are already discrete casino symbols; phase splits are broadcast-native

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Wicket 2.78%
31-2 2-15.56%Single | middle 3.97% · Six 1.59%
HARD 42-22.78%Three runs 0.40% · Four 2.38%
SOFT 41-3 3-15.56%Wide 3.50% · Four 2.06%
51-4 4-1 2-3 3-211.11%Single | middle 11.11%
HARD 63-32.78%Bye/leg-bye 1.20% · Wicket 0.64% · Two runs 0.94%
SOFT 61-5 5-1 2-4 4-211.11%Dot | powerplay 10.05% · Single | death 0.07% · Six 0.64% · No-ball 0.35%
71-6 6-1 2-5 5-2 3-4 4-316.67%Dot | middle 15.08% · Wicket 1.59%
HARD 84-42.78%Single | death 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Single | powerplay 10.05% · Four 1.01% · Two runs 0.00% · No-ball 0.05%
93-6 6-3 4-5 5-411.11%Dot | death 8.37% · Single | death 2.74%
HARD 105-52.78%Single | death 2.78%
SOFT 104-6 6-45.56%Two runs 5.56%
115-6 6-55.56%Four 5.56%
126-62.78%Six 2.78%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.12%, 2.60%] · 21 boundary cuts (†) · 49% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (6) · every "|" label is a real feed mark, not RNG
  • Dot | powerplay: phase split (overs 1-6 ~30% of balls)
  • Dot | middle: phase split (7-15 ~45%)
  • Dot | death: phase split (16-20 ~25%)
  • Single | powerplay: phase split
  • Single | middle: phase split
  • Single | death: phase split

LIVECRASH survival map NATURAL

1-in-19 wicket hazard unchanged for 18 IPL seasons; the textbook crash sport

bust event Wicket falls hazard 0.0520 per delivery growth per survival x1.0549 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 13
Wisden: ~19 balls per dismissal, stable IPL 2008 through 2025
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.53863.93%0.9800
x2.001348.95%0.9800
x3.072131.93%0.9800
x5.243118.72%0.9800
x10.48449.35%0.9800
x25.98613.77%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 8.76% (-10%: -5.22%) - this is the recalibration tolerance
The most stable hazard in the survey; phase conditioning (PP .045 / mid .046 / death .080) available

LIVESLOTS paytable, shipped pay grammar NATURAL

7 symbols with SIX as jackpot; no-ball = free-hit bonus is a built-in feature

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
ONEsingle33.50%x20.210.420.8422.9%
DOTdot33.50%x20.210.420.8422.9%
FOURfour11.00%x30.310.942.8212.2%
RUNS2s and 3s6.90%x30.310.942.827.3%
EXTRAwide/no-ball/byes5.10%x40.421.676.687.5%
SIXsix5.00%x50.522.6113.059.6%
Wwicket5.00%x80.846.6853.4517.6%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.1044 normalizes the raw expectation (9.10 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 25.5% · RTP under ±10% symbol drift: ±1.6pp

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit runs ladder maps to rank ladder almost 1:1
LiveDeal steady over rhythm deals streets like hands
RANKTARGETEVENT COMPOSITION
27.69%Dot | middle 7.69%
37.69%Dot | middle 7.39% · Bye/leg-bye 0.14% · No-ball 0.07% · Three runs 0.10%
47.69%Single | middle 7.69%
57.69%Single | middle 7.39% · Three runs 0.30%
67.69%Four 7.69%
77.69%Four 3.31% · Dot | powerplay 2.36% · Dot | death 0.68% · Single | death 0.68% · Bye/leg-bye 0.67%
87.69%Dot | powerplay 7.69%
97.69%Single | powerplay 7.69%
T7.69%Single | powerplay 2.36% · Wicket 5.00% · No-ball 0.33%
J7.69%Dot | death 7.69%
Q7.69%Single | death 7.69%
K7.69%Two runs 6.50% · Wide 0.81% · Bye/leg-bye 0.38%
A7.69%Six 5.00% · Wide 2.69%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 23 boundary cuts (†) · 16% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.49pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: batting end x bowler type (pace/spin) · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

CRYPTO (BTC)

unit: 1-second bar · 3600 events/game · 60 ticks/min, 24/7/365 - the base layer
LiveRoll NATURAL LiveCrash NATURAL LiveSlots FORCED LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

price is continuous: quantile cuts ARE the semantics; exact fairness by construction, renormalized per vol regime

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Down | >= 0.05% 0.30% · Down | < 0.01% 0.78% · Flat | after up bar 0.33% · Flat | after down bar 0.33% · Down | 0.01-0.05% 1.03%
31-2 2-15.56%Flat | after up bar 5.56%
HARD 42-22.78%Up | 0.01-0.05% 2.78%
SOFT 41-3 3-15.56%Flat | after down bar 5.56%
51-4 4-1 2-3 3-211.11%Up | < 0.01% 6.33% · Up | 0.01-0.05% 4.78%
HARD 63-32.78%Down | 0.01-0.05% 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Down | < 0.01% 11.11%
71-6 6-1 2-5 5-2 3-4 4-316.67%Up | < 0.01% 16.67%
HARD 84-42.78%Down | 0.01-0.05% 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Down | < 0.01% 11.11%
93-6 6-3 4-5 5-411.11%Flat | after up bar 11.11%
HARD 105-52.78%Down | 0.01-0.05% 2.78%
SOFT 104-6 6-45.56%Flat | after down bar 5.56%
115-6 6-55.56%Flat | after down bar 5.56%
126-62.78%Up | >= 0.05% 0.30% · Up | 0.01-0.05% 2.14% · Down | 0.01-0.05% 0.33%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.10%, 2.54%] · 20 boundary cuts (†) · 1% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (8) · every "|" label is a real feed mark, not RNG
  • Up | >= 0.05%: magnitude buckets from RV-derived thresholds (quantile-exact by construction)
  • Up | 0.01-0.05%: magnitude bucket
  • Up | < 0.01%: magnitude bucket
  • Flat | after up bar: preceding-bar split (real mark)
  • Flat | after down bar: preceding-bar split
  • Down | < 0.01%: magnitude bucket
  • Down | 0.01-0.05%: magnitude bucket
  • Down | >= 0.05%: magnitude bucket

LIVECRASH survival map NATURAL

crash was literally invented for this stream (bustabit); run-survival hazard tunable

bust event Down bar ends the run hazard 0.3500 per 1s bar growth per survival x1.5385 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 2
HF microstructure: P(down) ~.33-.37; up-or-flat survives
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.54163.70%0.9800
x2.37241.41%0.9800
x3.64326.91%0.9800
x5.60417.49%0.9800
x13.2667.39%0.9800
x31.3883.12%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 12.27% (-10%: -8.84%) - this is the recalibration tolerance
Vol clustering breaks iid: renormalize thresholds by (30d RV / 45%) so the hazard stays pinned; bid-ask bounce makes long runs die slightly faster (house-safe direction)

LIVESLOTS paytable, shipped pay grammar FORCED

magnitude-bin symbols have no story between MOON and REKT; playable, not legible

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
FLATflat34.00%x20.220.440.8824.4%
UPup small23.00%x20.220.440.8816.2%
DOWNdown small23.00%x30.330.992.9630.6%
PUMPup 0.01-0.05%9.70%x30.330.992.9611.1%
DUMPdown 0.01-0.05%9.70%x40.441.757.0116.3%
MOONup >=0.05%0.30%x50.552.7413.680.5%
REKTdown >=0.05%0.30%x80.887.0156.050.8%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.1095 normalizes the raw expectation (8.68 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 21.4% · RTP under ±10% symbol drift: ±1.3pp

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit quantile-exact ranks; 24/7 uptime makes it the filler deck
LiveDeal same exactness; board fills in 5 seconds or slower gears
RANKTARGETEVENT COMPOSITION
27.69%Down | < 0.01% 7.69%
37.69%Down | < 0.01% 7.69%
47.69%Down | < 0.01% 7.62% · Up | >= 0.05% 0.08%
57.69%Up | < 0.01% 7.69%
67.69%Up | < 0.01% 7.69%
77.69%Up | < 0.01% 7.62% · Up | >= 0.05% 0.08%
87.69%Flat | after up bar 7.69%
97.69%Flat | after up bar 7.69%
T7.69%Flat | after up bar 1.62% · Flat | after down bar 1.62% · Down | 0.01-0.05% 2.01% · Up | 0.01-0.05% 2.01% · Down | >= 0.05% 0.30% · Up | >= 0.05% 0.15%
J7.69%Flat | after down bar 7.69%
Q7.69%Flat | after down bar 7.69%
K7.69%Down | 0.01-0.05% 7.69%
A7.69%Up | 0.01-0.05% 7.69%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 19 boundary cuts (†) · 0% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.59pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: direction x preceding-bar direction · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

INDICES (ES)

unit: 1-minute bar · 60 events/game · RTH + Globex ~23h weekdays; CLOSED weekends
LiveRoll NATURAL LiveCrash NATURAL LiveSlots DOESN'T-WORK LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map NATURAL

fair-coin bars + quantile magnitude cuts; session-bound (no weekends)

NO-ROLL RULE · Halts/circuit breakers = table closed (real market state)
ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Down | >= 2 ticks 2.78%
31-2 2-15.56%Up | 1 tick 5.22% · Unchanged 0.33%
HARD 42-22.78%Up | >= 2 ticks 1.11% · Down | >= 2 ticks 1.11% · Unchanged 0.56%
SOFT 41-3 3-15.56%Up | >= 2 ticks 5.56%
51-4 4-1 2-3 3-211.11%Up | 1 tick 11.11%
HARD 63-32.78%Down | >= 2 ticks 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Down | 1 tick 11.11%
71-6 6-1 2-5 5-2 3-4 4-316.67%Up | 1 tick 16.67%
HARD 84-42.78%Down | >= 2 ticks 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Down | 1 tick 11.11%
93-6 6-3 4-5 5-411.11%Down | 1 tick 10.78% · Unchanged 0.33%
HARD 105-52.78%Unchanged 2.78%
SOFT 104-6 6-45.56%Up | >= 2 ticks 5.56%
115-6 6-55.56%Down | >= 2 ticks 5.56%
126-62.78%Up | >= 2 ticks 2.78%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [-0.50%, 2.90%] · 19 boundary cuts (†) · 0% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (5) · every "|" label is a real feed mark, not RNG
  • Up | >= 2 ticks: tick-magnitude buckets (quantile-exact)
  • Up | 1 tick: bucket
  • Unchanged: bucket
  • Down | 1 tick: bucket
  • Down | >= 2 ticks: bucket

LIVECRASH survival map NATURAL

same construction as crypto at 1-min gear; circuit breakers = house-neutral voids

bust event Down bar ends the run hazard 0.5000 per 1-min bar growth per survival x2.0000 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 1
1-min direction ~50/50 (16% annualized RV -> sigma_1min .051%)
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x2.00149.00%0.9800
x4.00224.50%0.9800
x8.00312.25%0.9800
x16.0046.12%0.9800
x32.0053.06%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 11.80% (-10%: -7.80%) - this is the recalibration tolerance
Near-memoryless in RTH; vol regime renormalization as crypto

LIVESLOTS paytable, shipped pay grammar DOESN'T-WORK

five near-indistinguishable magnitude bins; no symbol identity, no jackpot story

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
UPuptick33.02%x20.240.490.9826.4%
DOWNdowntick33.02%x20.240.490.9826.4%
SURGE2+ ticks up14.96%x30.371.103.2920.3%
SLIDE2+ ticks down14.96%x30.371.103.2920.3%
FLATunchanged4.00%x40.491.957.816.7%
LIMITbig move0.05%x50.613.0515.250.1%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.1220 normalizes the raw expectation (7.79 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 18.0% · RTP under ±10% symbol drift: ±0.9pp

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit quantile-exact ranks during session hours
LiveDeal as livehit; halts void the hand by rule
RANKTARGETEVENT COMPOSITION
27.69%Up | 1 tick 7.69%
37.69%Up | 1 tick 7.69%
47.69%Up | 1 tick 7.69%
57.69%Up | 1 tick 7.69%
67.69%Up | 1 tick 2.23% · Down | 1 tick 2.23% · Unchanged 3.23%
77.69%Down | 1 tick 7.69%
87.69%Down | 1 tick 7.69%
97.69%Down | 1 tick 7.69%
T7.69%Down | 1 tick 7.69%
J7.69%Up | >= 2 ticks 7.69%
Q7.69%Up | >= 2 ticks 7.31% · Unchanged 0.38%
K7.69%Down | >= 2 ticks 7.69%
A7.69%Down | >= 2 ticks 7.31% · Unchanged 0.38%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 17 boundary cuts (†) · 0% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.91pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: direction x preceding bar · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal

ESPORTS (CS2)

unit: kill/objective tick · 150 events/game · ~7.3 kills/round in bursts; freezetime gaps between rounds
LiveRoll FORCED LiveCrash FORCED LiveSlots NATURAL LiveHit NATURAL LiveDeal NATURAL

LIVEROLL event to dice map FORCED

kills arrive in 2-8s bursts then 20s freezetime; roll rhythm fights the round structure

ROLLDICETRUE ODDSEVENT COMPOSITION (share of stream)
21-12.78%Kill | HS, T, 2nd half 2.29% · Round win | T 0.48%
31-2 2-15.56%Kill | HS, CT, 1st half 5.56%
HARD 42-22.78%Bomb plant 2.78%
SOFT 41-3 3-15.56%Kill | HS, CT, 1st half 3.92% · Kill | HS, CT, 2nd half 1.15% · Bomb plant 0.48%
51-4 4-1 2-3 3-211.11%Kill | body, T, 1st half 10.69% · Bomb plant 0.42%
HARD 63-32.78%Kill | HS, CT, 2nd half 2.78%
SOFT 61-5 5-1 2-4 4-211.11%Kill | body, T, 2nd half 10.69% · Bomb plant 0.42%
71-6 6-1 2-5 5-2 3-4 4-316.67%Kill | HS, T, 1st half 9.48% · Kill | HS, T, 2nd half 7.19%
HARD 84-42.78%Defuse / explode 2.78%
SOFT 82-6 6-2 3-5 5-311.11%Kill | body, CT, 1st half 10.69% · Bomb plant 0.42%
93-6 6-3 4-5 5-411.11%Kill | body, CT, 2nd half 10.69% · Bomb plant 0.42%
HARD 105-52.78%Defuse / explode 0.53% · Round win | T 2.25%
SOFT 104-6 6-45.56%Kill | HS, CT, 2nd half 5.56%
115-6 6-55.56%Round win | CT 5.52% · Round win | T 0.01% · Bomb plant 0.02%
126-62.78%Round win | T 2.78%
calibration exact (rows equal true craps odds by construction) · pass-line edge locked at 1.41% · under ±10% single-event calibration drift the pass edge stays in [0.49%, 2.24%] · 20 boundary cuts (†) · 58% of stream mass placed whole
DECLARED ATTRIBUTE SPLITS (12) · every "|" label is a real feed mark, not RNG
  • Kill | HS, T, 1st half: HS x side x half split (real)
  • Kill | HS, T, 2nd half: split
  • Kill | HS, CT, 1st half: split
  • Kill | HS, CT, 2nd half: split
  • Kill | body, T, 1st half: split
  • Kill | body, T, 2nd half: split
  • Kill | body, CT, 1st half: split
  • Kill | body, CT, 2nd half: split
  • Bomb plant: .45 plants / 9.05 ticks per round
  • Defuse / explode: .3 resolutions / 9.05

LIVECRASH survival map FORCED

round-end hazard is severely back-loaded; playable only with the kill-index hazard table and it still telegraphs

bust event Round ends at this kill hazard 0.1400 per kill growth per survival x1.1628 (= 1/(1-h)) instant bust 2.00% (the entire house edge) median events to 2x 5
HLTV: mean 7.3 kills/round -> average hazard 1/7.3
LADDER CASH OUT (g^k)EVENTS SURVIVED (k)P(REACH)P x PAYOUT (TARGET 0.98)
x1.57362.33%0.9800
x2.13546.10%0.9800
x3.34829.32%0.9800
x5.251118.65%0.9800
x11.17168.77%0.9800
x27.61223.55%0.9800
The multiplier advances one ladder step per surviving event, so the reachable cash-outs ARE the ladder; at every one of them expected return is exactly 0.98. A finer ladder (smaller visual increments between events) interpolates the same curve without changing the math.
martingale construction: P(reach m) x m = 0.98 at every step boundary, so edge is exactly 2.0% at any cash-out · if the true hazard drifts +10% while growth stays calibrated, realized edge at 2x becomes 9.72% (-10%: -6.24%) - this is the recalibration tolerance
Strongly BACK-LOADED (near 0 for kills 1-3, steep from kill 5): production must use the kill-index hazard table, not a constant

LIVESLOTS paytable, shipped pay grammar NATURAL

HS/ACE/KNIFE/CLUTCH are native fan vocabulary with true rarities

SYMBOLEVENTP (PER REEL)BASESINGLEPAIRTRIPLERTP SHARE
KILLbody kill32.82%x20.230.460.9124.5%
HSheadshot kill29.10%x20.230.460.9121.6%
PLANTbomb plant per round27.86%x30.341.033.0940.9%
OPENERopening kill tick8.48%x30.341.033.0910.0%
CLUTCH1vX won1.24%x40.461.837.311.8%
ACE5k round0.31%x50.572.8614.280.6%
KNIFEknife kill0.19%x80.917.3158.500.5%
payout = m x sum(base^count) over distinct symbols, 3 reels = 3 different live games · line multiplier m = 0.1143 normalizes the raw expectation (8.31 stakes) to RTP exactly 95.0% · P(spin nets a profit) = 24.2% · RTP under ±10% symbol drift: ±2.1pp
mixed per-kill and per-round symbol rates; reels bind to 3 concurrent matches

LIVEHIT / LIVEDEAL event to rank map NATURAL NATURAL

LiveHit kill attributes (HS, weapon, side) give real rank semantics
LiveDeal 5-card board per round maps to the round's kill sequence
RANKTARGETEVENT COMPOSITION
27.69%Round win | CT 7.69%
37.69%Round win | CT 6.31% · Bomb plant 0.88% · Defuse/explode resolution 0.50%
47.69%Round win | T 7.69%
57.69%Round win | T 6.31% · Defuse/explode resolution 1.38%
67.69%Utility damage tick 7.69%
77.69%Utility damage tick 5.95% · Bomb plant 1.74%
87.69%Kill | body, T side 7.69%
97.69%Kill | body, T side 3.63% · Kill | body, CT side 3.63% · Defuse/explode resolution 0.43%
T7.69%Kill | body, CT side 7.69%
J7.69%Kill | headshot, T side 7.69%
Q7.69%Kill | headshot, T side 2.36% · Kill | headshot, CT side 2.36% · Bomb plant 2.98%
K7.69%Kill | headshot, CT side 7.69%
A7.69%Flash assist / trade window 7.28% · Defuse/explode resolution 0.42%
every rank = exactly 1/13 by construction; ten-value density = 16/52 exactly · 21 boundary cuts (†) · 7% of mass placed whole · under ±10% single-event drift the basic-strategy blackjack edge moves at most 0.45pp (first-order Griffin effect-of-removal) · LiveDeal suit mark: side x weapon class · already-dealt cards are skipped (rejection), which reproduces the exact without-replacement deal