Don’t bet: How advantage players optimize profit with variable wager $
Smart advantage players (APs) are like smart traders: they vary their wager amount based on the strength of their convictions.
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EV or Expected value is the likely $ value of a bet based on the probability of an outcome. As the payoffs for a winning outcome is fixed by the game rules, the only dynamic in a game is the probability of a winning outcome. For any game dealt out of shoe the probability of a winning outcome will fluctuate based on the remaining composition of the shoe. Advantage players look for shoes with a high concentration cards which favor a winning outcome.
“One of the most important things when it comes to advantage play, card counting, poker, and options trading is bet sizing”
We developed optimal wagering pattern for each of the 34 bets using a GenAI tool - developed by our sister company, www.HexGaming.AI. The tool finds the ‘optimal’ wager amount based on the strength of the count which maximizes profit while minimizing risk of ruin.
The tool uses an specially tune large language model or LLM to guide an optimization technique called reinforcement learning to find an "optimal" wagering pattern, where:
The total wagered amount must be the same in the flat-betting and optimal-betting scenarios
The AI must bet at least one unit when EV is positive
Profit per shoe and risk-of-ruin must be balanced
For the typical bet, an AP using optimal wagering can amplify her profit per shoe by +50% while risking the same amount as in flat betting. And on some bets — especially those with multi-level payoffs or with in-frequent positive EV situations — optimal wagering can lift profit per shoe by nearly triple digits. The table below outlines the profit per shoe an AP can earn with simple flat betting and the enhanced profit from optimal wagering.
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The Profit per shoe table below shows - by game - how many units are wagered assuming AP bets when there is a positive EV and then the resultant profit per shoe in units. For instance, on High-Tie-0 an AP would bet 9.73 units on avg from which she will win 1.72 units if she is flat betting (a return rate of 18%) or 2.16 is she using optimal wagering.
| Profit per shoe (# of units) | |||||
|---|---|---|---|---|---|
| Game | Wager in units | Flat | Optimal | Variance | Flat → Optimal range |
| High Tie - 0 | 9.73 | 1.72 | 2.16 | 0.44 | |
| High Tie - 3 | 10.79 | 1.52 | 2.09 | 0.57 | |
| High Tie - 9 | 11.07 | 1.42 | 1.78 | 0.36 | |
| High Tie - 8 | 10.48 | 1.35 | 1.66 | 0.31 | |
| High Tie - 2 | 6.44 | 1.04 | 1.35 | 0.30 | |
| Player Fabulous 4 | 6.61 | 0.77 | 1.04 | 0.27 | |
| High Tie - 1 | 4.34 | 0.69 | 1.04 | 0.35 | |
| High Tie - 7 | 5.25 | 0.67 | 0.94 | 0.27 | |
| High Tie - 4 | 3.93 | 0.61 | 0.91 | 0.30 | |
| High Tie - 5 | 3.65 | 0.54 | 0.86 | 0.32 | |
| Dragon 7 | 8.51 | 0.53 | 0.86 | 0.33 | |
| 4 Card Tie | 8.36 | 0.52 | 0.59 | 0.07 | |
| High Tie - 6 | 3.05 | 0.40 | 0.65 | 0.25 | |
| Banker Fabulous 4 | 2.83 | 0.29 | 0.41 | 0.12 | |
| Super Lucky 7 | 3.31 | 0.27 | 0.43 | 0.16 | |
| Small Tiger | 2.39 | 0.21 | 0.30 | 0.09 | |
| Small Dragon | 2.72 | 0.21 | 0.35 | 0.14 | |
| Banker 2 card 7 | 2.72 | 0.21 | 0.35 | 0.14 | |
| Panda 8 | 3.52 | 0.20 | 0.36 | 0.17 | |
| Big Tiger | 2.48 | 0.18 | 0.27 | 0.09 | |
| Monkey No Monkey | 1.52 | 0.18 | 0.25 | 0.08 | |
| Pair Plus | 1.15 | 0.16 | 0.33 | 0.17 | |
| Tiger Tie | 0.98 | 0.14 | 0.21 | 0.08 | |
| Lucky Six / Tiger | 1.39 | 0.11 | 0.19 | 0.07 | |
| Big Dragon | 1.70 | 0.10 | 0.22 | 0.12 | |
| Player 3 card 7 | 1.70 | 0.10 | 0.22 | 0.12 | |
| 6 Card Tie | 1.15 | 0.09 | 0.15 | 0.06 | |
| Banker Pair | 1.19 | 0.08 | 0.16 | 0.08 | |
| Player Pair | 1.19 | 0.08 | 0.16 | 0.07 | |
| Tiger Pair | 0.71 | 0.07 | 0.14 | 0.07 | |
| Tie_9 | 1.62 | 0.04 | 0.08 | 0.04 | |
| 5 Card Tie | 0.73 | 0.04 | 0.08 | 0.04 | |
| Lucky 7 | 0.52 | 0.03 | 0.06 | 0.03 | |
| Banker 3 card 7 | 0.07 | 0.00 | 0.01 | na | |
| Tie_8 | 0.03 | 0.00 | 0.00 | na | |
| Banker no-commission | 0.07 | 0.00 | 0.00 | na | |
| Player (base bet) | 0.06 | 0.00 | 0.00 | na | |
| Banker (base bet) | 0.06 | 0.00 | 0.00 | na | |
Variable betting is more powerful on bets with a low level frequency of positive EV situations. But to an advantage player, the juice from optimal wagers is worth the squeeze. For instance, an AP who varies her wager size relative to strength of the count and is targeting Big Tiger or Super Lucky Seven - both of which have large payoffs - can increase her profit by 60%+ (see the chart below).
Chart one: Relationship between game hit rate and effectiveness of variable betting
An advantage player targeting bets with infrequent positive EV therefore needs a counting system which, above all else, can correctly find situations where the player has a positive EV. We explore this idea of countability and accuracy in our next Baccarat Advantage Play blog.
