SideBet_Comp — Differential Labs

Reconciling results with previous work by others

Much excellent work has done by on identifying advantage play risks on Baccarat by prominent casino mathematicians. We took a slightly different approach influenced by Asian gaming and addressing the risk of Bot play and computer-aided rings. The following is reconciliation between our results and those reported elsewhere.

Updated: 29/Aug/2026

Common measurement basis

All Differential results on this page use flat one-unit wagering: wager one unit whenever the calculated expected value is positive. Results from the separate optimal-wagering analysis are not used here.

The Differential simulations averaged approximately 79.38 completed hands per shoe. Therefore:

Units won per 100 hands = flat profit per shoe × (100 ÷ 79.38)

The same result can be checked from unrounded hand-level data:

Units won per 100 hands = betting frequency × average edge when betting × 100

The four principal reconciliation factors are:

Penetration: Differential used a 26-card cut; several published studies used a 14-card cut. The last cards in the shoe contribute disproportionately to advantage-play profit.
Strategy basis: Differential uses the exact remaining-card composition. Published practical systems compress that composition into integer tags and a true-count trigger. Exact composition should weakly dominate a tag system when every other assumption is identical.
Payoff: Even a one-unit payoff change can move many marginal shoe states from negative to positive EV. Tiered pay tables can have still larger effects.
Rules: Burn procedure, whether the cut-card round is completed, whether another round is dealt after the cut card appears, and the exact winning-event definition can change the opportunity.

Flat-betting comparison

Wager	Differential flat units/100	Published units/100	Primary reconciliation
Big Tiger, 50-to-1	0.231	0.256	Same payoff and event; deeper published penetration adds value, partly offset by tag compression
Dragon 7, 40-to-1	0.672	0.734	Same payoff and event; deeper penetration adds value, partly offset by tag compression
Panda 8, 25-to-1	0.251	0.293	Same payoff and event; deeper penetration adds value, partly offset by tag compression
Banker and Player Pair, 11-to-1	0.214	0.405	Same payoff; difference is concentrated in late-shoe penetration and possibly final-round procedure
Lucky 7, 6/15 versus 7/15	0.039	0.146	Higher published two-card payoff plus deeper penetration; tag compression offsets part of the gain
Small Tiger, 22-to-1 versus 23-to-1	0.272	0.518	One-unit payoff increase and deeper penetration; tag compression offsets part of the gain
Lucky Six, 12/20 versus 12/23	0.146	0.194–0.289	Higher three-card payoff and deeper penetration; Level 1/Level 2 counts capture different shares of the exact opportunity
Tie, 8-to-1	0.0014	0.0101	Both opportunities are extremely small; penetration and final-round conventions dominate the absolute difference
Tie, 9-to-1	0.052	approximately 0.096	Same payoff and exact-composition basis; penetration and final-round procedure are the remaining causes
Player base bet	approximately 0.00023	approximately 0.0010	Too small for a reliable allocation from rounded summaries
Banker base bet	approximately 0.00004	approximately 0.0008	Too small for a reliable allocation from rounded summaries
High Tie 7, 40-to-1 versus 45-to-1	0.852	2.65	Payoff is the largest cause, followed by penetration; the published count gives back part of the exact-composition opportunity

The Differential figures above come from the unrounded 80-file flat-betting results. Rounded profit-per-shoe figures may reproduce slightly different last decimals.

Back-of-the-envelope allocation method

The allocations below are estimates, not controlled cut-14 simulations. Payoff effects were estimated by rescoring the same remaining-shoe states under the published pay table. Penetration was estimated from the observed late-shoe profit gradient in a 100,000-shoe file and extrapolated from a 26-card cut to a 14-card cut. The remaining difference is assigned to tag-system compression or, where both studies use exact composition, to cut-card/final-round rules and extrapolation error.

Because late-shoe opportunity is nonlinear, these values should be treated as explanatory decompositions rather than new benchmark results.

Big Tiger

Both studies use the same event and 50-to-1 payoff. Differential's flat result is approximately 0.231 units per 100 hands; AAP reports 0.256.

Component	Approximate units/100
Differential exact composition, cut 26	0.231
Estimated value of moving to cut 14	+0.074
Estimated exact-composition result at cut 14	0.305
Tag-system compression and residual procedure differences	−0.049
AAP reported result	0.256

Payoff contribution: zero. Event-rule contribution: zero under the stated definitions. The reconciliation is deeper penetration adding opportunity and the practical tag system giving back part of that exact-composition value.

The information loss is observable in the scored data. Two states with 31 cards remaining can both have a Big Tiger running count of +13 and true count of +21.81, yet one has exact EV of −6.40% and another +50.06%. The tag system makes the same decision in both states because it cannot distinguish their detailed compositions.

Dragon 7

Both studies use a winning three-card Banker 7 paying 40-to-1.

Component	Approximate units/100
Differential exact composition, cut 26	0.672
Estimated value of moving to cut 14	+0.118
Estimated exact-composition result at cut 14	0.790
Tag compression and residual procedure differences	−0.056
Published result	0.734

Payoff and event rules contribute approximately zero. Penetration explains the positive movement; the practical count's compression explains the estimated reduction from computer-perfect selection.

Panda 8

Both figures should be compared only if Panda 8 means a winning three-card Player total of 8 paying 25-to-1. That is the Differential rule and the standard Panda 8 definition.

Component	Approximate units/100
Differential exact composition, cut 26	0.251
Estimated value of moving to cut 14	+0.062
Estimated exact-composition result at cut 14	0.313
Tag compression and residual procedure differences	−0.020
Published result	0.293

Payoff contribution: zero. If the published wording “three-card total of 8” includes a non-winning Player 8, the event rules are different and this reconciliation does not apply; the published off-the-top house edge should be used to confirm the intended rule.

Banker and Player Pair

Both sides pay 11-to-1 and are combined because the published figure also assumes that both are played.

Component	Approximate units/100
Differential exact composition, both sides, cut 26	0.214
Linear late-shoe estimate for moving to cut 14	+0.114
Preliminary exact-composition estimate at cut 14	0.328
Unallocated late-tail/final-round difference	+0.077
Published trigger-and-weights result	0.405

Payoff and stated event rules contribute zero. A practical trigger system should not outperform exact composition under identical dealing conditions, so the positive residual should not be credited to the counting method. It indicates that the linear penetration estimate is too low for this highly concentrated late-shoe opportunity, or that the final-round/cut-card conventions differ. A direct cut-14 run is required for a firm allocation.

Lucky 7

Differential uses 6-to-1 for a two-card winning Player 7 and 15-to-1 for a three-card winning Player 7. The published game uses 7-to-1 and 15-to-1.

Component	Approximate units/100
Differential 6/15 game, exact composition, cut 26	0.039
Estimated payoff effect of changing 6/15 to 7/15	+0.086
Estimated penetration effect at the 7/15 pay table	+0.048
Estimated exact-composition 7/15 result at cut 14	0.172
Tag compression and residual procedure differences	−0.026
Published result	0.146

The payoff change is the largest component because it converts many marginal two-card-7 states into positive-EV bets. The event rule is otherwise the same.

Small Tiger

Differential uses 22-to-1; the published analysis uses 23-to-1 for the same winning two-card Banker 6 event.

Component	Approximate units/100
Differential 22-to-1, exact composition, cut 26	0.272
Estimated payoff effect of moving to 23-to-1	+0.188
Estimated penetration effect at 23-to-1	+0.110
Estimated exact-composition 23-to-1 result at cut 14	0.570
Tag compression and residual procedure differences	−0.052
Published result	0.518

The one-unit payoff improvement has a much larger effect than its 4.5% nominal increase suggests because it also increases betting frequency. The event rule is the same.

Lucky Six

Differential uses 12-to-1 on a two-card winning Banker 6 and 20-to-1 on a three-card winning Banker 6. The Wizard of Odds comparison uses 12-to-1 and 23-to-1.

Component	Approximate units/100
Differential 12/20 exact composition, cut 26	0.146
Estimated payoff effect of changing 12/20 to 12/23	+0.172
Estimated penetration effect at 12/23	+0.087
Estimated exact-composition 12/23 result at cut 14	0.404
Level 2 count/procedure residual	−0.115
Published Level 2 result	0.289
Additional Level 1 compression	−0.095
Published Level 1 result	0.194

The previous statement that Differential “falls between” the two published systems resulted from using the optimized-wagering column. On a flat basis, Differential's lower-paytable result is below both. After adjusting payoff and penetration, exact composition is above both, as expected.

Tie paying 9-to-1

Both comparisons use the same payoff and are based on exact remaining composition.

Component	Approximate units/100
Differential cut-26 result	0.052
Linear penetration estimate	+0.018
Preliminary cut-14 estimate	0.070
Remaining penetration/final-round-rule residual	+0.026
Published result	approximately 0.096

Payoff contribution: zero. Strategy-basis contribution: approximately zero. The remaining gap belongs to penetration, burn/cut procedure, treatment of the final round, and the weakness of a linear extrapolation for rare late-shoe opportunities.

High Tie 7

Differential's High Tie 7 pays 40-to-1; the published UR Way Egalite wager pays 45-to-1. Both win on a 7–7 tie.

Component	Approximate units/100
Differential 40-to-1 exact composition, cut 26	0.852
Estimated payoff effect of moving to 45-to-1	+1.624
Estimated penetration effect at 45-to-1	+0.289
Estimated exact-composition 45-to-1 result at cut 14	2.765
Count compression and residual procedure differences	−0.115
Published result	2.65

The payoff is the dominant explanation. It raises the return on already-positive states and makes many additional states playable. Penetration is the second-largest contributor. The event rule appears equivalent.

Small absolute differences

Tie paying 8-to-1 and the Player and Banker base bets have extremely small expected profits. Relative percentage gaps look large because the denominator is near zero. Rounded bets-per-shoe and profit-per-shoe values are unsuitable for allocating these differences. They should be compared from unrounded hand-level totals under identical burn, cut-card and final-round rules.

Conclusion

Big Tiger, Dragon 7 and Panda 8 are close after allowing for cut 26 versus cut 14 and the information loss in practical tag systems.
Lucky 7, Small Tiger, Lucky Six and High Tie 7 differ principally because of their pay tables; penetration is the next-largest factor.
Pairs and Tie 9 require direct cut-14, same-rule simulations because their residual gaps cannot be honestly assigned to strategy basis.
Very small base-bet and 8-to-1 Tie opportunities should not be reconciled from rounded summaries.

Exact-composition analysis and practical tag counts answer related but different questions. Exact composition estimates what a fully informed computer can identify under the specified dealing procedure. A tag system estimates how much of that opportunity can be captured with a compressed, playable count. Neither result should be compared until wager sizing, penetration, payoff and event rules are aligned.