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Card Counting in Baccarat
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Introduction
For many years, I've been stating that fundamentally, baccarat it functions as a series of independent trials. In simpler terms, analyzing previous outcomes in the shoe won't provide any advantage. Although reviewing the trends in Banker versus Player wins may not help, applying some card counting strategies can provide slight advantages.
To prevent misunderstandings in my writing about baccarat, I will refer to the player in lowercase and capitalize 'Player' when discussing the bet.
Effect of Removal
Any analysis of card counting’s effectiveness in blackjack or baccarat—games that involve multiple hands before a shuffle—needs to focus on the influence of eliminating specific cards. For instance, in blackjack, removing a five generally benefits the player, whereas taking out an ace is detrimental. This is due to fives being unfavorable and aces advantageous. The subsequent table illustrates how the removal of all ten card values affects the three primary bets, showing the increase in expected value for players given the removal of a card from an eight-deck shoe, multiplied by ten million.
Effect of Removal
| Card | Banker | Player | Tie |
|---|---|---|---|
| 0 | 188 | -178 | 5129 |
| 1 | 440 | -448 | 1293 |
| 2 | 522 | -543 | -2392 |
| 3 | 649 | -672 | -2141 |
| 4 | 1157 | -1195 | -2924 |
| 5 | -827 | 841 | -2644 |
| 6 | -1132 | 1128 | -11595 |
| 7 | -827 | 817 | -10914 |
| 8 | -502 | 533 | 6543 |
| 9 | -231 | 249 | 4260 |
For further details on how this table was calculated, please refer to my baccarat appendix 2 .
From the viewpoint of placing a bet on the Player, having a deck filled with high cards is favorable. This means that the deck losing high cards works against the Player bet. Conversely, a deck low on cards benefits the Banker bet. Therefore, if a lower card is drawn from the shoe, it enhances the probabilities for the Player, while the departure of a higher card favors the Banker.
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Running Count
To simplify this method, I've created a straightforward plus-minus strategy for levels 1 and 2. To implement it, adhere to these guidelines.
- At the commencement of a new shoe, initialize the Running Count at 0.
- As cards are dealt, tally the following values corresponding to each revealed card.
- 1 to 4 points = +1
- 5 to 8 points = -1
- 0 and 9 points = 0
- You will place your bets on the Player or Banker based on the Running Count as you continue to play. This will be further clarified based on whether you’re utilizing Level 1 or Level 2 strategies (see below).
The next table provides the expected value (EV) of bets on the Player and Banker based on the running count, ranging from -25 to +25.
Expected Values by Running count
| Running Count |
Probability | Player EV |
Banker EV |
|---|---|---|---|
| -25 | 0.01% | -0.83% | -1.46% |
| -24 | 0.02% | -0.81% | -1.47% |
| -23 | 0.03% | -0.76% | -1.52% |
| -22 | 0.05% | -0.83% | -1.45% |
| -21 | 0.07% | -0.85% | -1.44% |
| -20 | 0.10% | -0.89% | -1.40% |
| -19 | 0.15% | -0.87% | -1.42% |
| -18 | 0.20% | -0.88% | -1.41% |
| -17 | 0.28% | -0.91% | -1.37% |
| -16 | 0.38% | -0.92% | -1.36% |
| -15 | 0.51% | -0.94% | -1.35% |
| -14 | 0.67% | -0.95% | -1.34% |
| -13 | 0.87% | -0.98% | -1.31% |
| -12 | 1.11% | -0.98% | -1.31% |
| -11 | 1.40% | -1.01% | -1.28% |
| -10 | 1.75% | -1.01% | -1.28% |
| -9 | 2.15% | -1.03% | -1.26% |
| -8 | 2.61% | -1.05% | -1.23% |
| -7 | 3.13% | -1.07% | -1.22% |
| -6 | 3.68% | -1.09% | -1.20% |
| -5 | 4.27% | -1.12% | -1.17% |
| -4 | 4.88% | -1.14% | -1.15% |
| -3 | 5.47% | -1.17% | -1.13% |
| -2 | 6.03% | -1.19% | -1.10% |
| -1 | 6.42% | -1.21% | -1.08% |
| 0 | 7.81% | -1.24% | -1.05% |
| 1 | 6.40% | -1.26% | -1.03% |
| 2 | 5.97% | -1.29% | -1.01% |
| 3 | 5.43% | -1.32% | -0.98% |
| 4 | 4.84% | -1.33% | -0.97% |
| 5 | 4.24% | -1.36% | -0.94% |
| 6 | 3.65% | -1.38% | -0.92% |
| 7 | 3.10% | -1.39% | -0.90% |
| 8 | 2.59% | -1.41% | -0.88% |
| 9 | 2.14% | -1.42% | -0.88% |
| 10 | 1.73% | -1.44% | -0.86% |
| 11 | 1.39% | -1.45% | -0.84% |
| 12 | 1.10% | -1.47% | -0.83% |
| 13 | 0.86% | -1.49% | -0.81% |
| 14 | 0.66% | -1.50% | -0.80% |
| 15 | 0.50% | -1.51% | -0.79% |
| 16 | 0.37% | -1.53% | -0.76% |
| 17 | 0.28% | -1.53% | -0.77% |
| 18 | 0.20% | -1.55% | -0.75% |
| 19 | 0.14% | -1.59% | -0.71% |
| 20 | 0.10% | -1.57% | -0.72% |
| 21 | 0.07% | -1.55% | -0.75% |
| 22 | 0.05% | -1.59% | -0.71% |
| 23 | 0.03% | -1.65% | -0.65% |
| 24 | 0.02% | -1.55% | -0.75% |
| 25 | 0.01% | -1.76% | -0.55% |
The previous table indicates that the optimal bet is on the Player for running counts of -4 or lower, while it favors the Banker otherwise.
Level 1 Strategy
Using the Level 1 strategy, simply wager on the Player when the Running Count is -4 or lower. If it exceeds that, place your bet on the Banker.
According to this strategy, the player will bet on the Player 28.4% of the time. The subsequent analysis presents the results of these Player bets. The lower right corner reveals a house edge of 1.06%, which is to be compared with a house edge of 1.24% for the Player bet when counting is ignored.
Level 1 Player Bets
| Event | Pays | Probability | Return |
|---|---|---|---|
| Win | 1 | 0.447281 | 0.447281 |
| Push | 0 | 0.094824 | 0.000000 |
| Loss | -1 | 0.457895 | -0.457895 |
| Total | 1.000000 | -0.010614 |
The following table displays the outcomes of 71.6% of the time when the player bets on the Banker. The lower right cell presents a house edge of 0.99%, which contrasts with a house edge of 1.06% for the Banker bet when card counting is not utilized.
Level 1 Banker Bets
| Event | Pays | Probability | Return |
|---|---|---|---|
| Win | 0.95 | 0.458875 | 0.435932 |
| Push | 0 | 0.095281 | 0.000000 |
| Loss | -1 | 0.445844 | -0.445844 |
| Total | 1.000000 | -0.009912 |
The next table encapsulates the results from both previous tables by showing the potential outcomes across Player and Banker bets. The cell in the lower right corner shows a combined house edge of 1.01%, compared with a house edge of 1.06% for only betting on the Banker or 1.11% for wagering on both sides at the same ratios of 28.4% for Player and 71.6% for Banker.
Level 1 Combined Return Table
| Bet | Winning Side | Pays | Probability | Return |
|---|---|---|---|---|
| Player | Player | 1 | 0.126836 | 0.126836 |
| Player | Tie | 0 | 0.026889 | 0.000000 |
| Player | Banker | -1 | 0.129846 | -0.129846 |
| Banker | Player | 0.95 | 0.328751 | 0.312314 |
| Banker | Tie | 0 | 0.068262 | 0.000000 |
| Banker | Banker | -1 | 0.319415 | -0.319415 |
| Total | 1.000000 | -0.010111 |
The table detailing the expected value for both bets indicates they are most similar at a count of -4. The further the count moves away from -4, the distinction between the two bets increases. It is advisable for the player to refrain from playing when the count hovers near -4 to minimize the house edge.
The following table illustrates how the proportion of hands played and the corresponding house edge are affected by the ranges of true counts that are skipped by choosing not to bet. For instance, if a player opts out when the true count is between -8 and 0, they will engage in 55.69% of hands, and the average house edge for the hands played will be 0.95%.
Skipping Bad Counts
| Counts Skipped |
Ratio Hands Played |
House Edge |
|---|---|---|
| None | 100.00% | 1.01% |
| -4 | 95.12% | 1.00% |
| -5 to -3 | 85.37% | 0.99% |
| -6 to -2 | 75.66% | 0.98% |
| -7 to -1 | 66.11% | 0.96% |
| -8 to 0 | 55.69% | 0.95% |
| -9 to +1 | 47.13% | 0.93% |
Players might also consider increasing their bets as the running count diverges from -4.
Level 2
To further reduce the house edge by an additional 0.01%, players wishing to bet every hand might employ this Level 2 strategy.
The primary distinction between Level 1 and Level 2 lies in the adjusting threshold for when the running count is deemed low enough to justify placing a bet on the Player as the game progresses through the shoe. This adjustment is due to the dilution effect of any given count early in the shoe, due to the larger number of cards that remain.
The specific 'index point' for when players should consider betting on the Player will depend on which column of the Bead Plate they are currently observing. The Bead Plate serves as a historical record of Player and Banker victories. For instance, the image below was taken from my score board To clarify, this table presents the index point for each column in the Bead Plate. Players should place their bets on the Player when the running count is equal to or lower than the index value. baccarat trainer , the player is in the sixth column.
The subsequent table illustrates the results from a Level 2 simulation focused solely on Player bets, which are made 18.3% of the time. The lower right corner displays a house edge of 0.99%.
Level 2 Index Values
| Column | Index Value |
|---|---|
| 1 | -15 |
| 2 | -14 |
| 3 | -13 |
| 4 | -12 |
| 5 | -11 |
| 6 | -10 |
| 7 | -9 |
| 8 | -8 |
| 9 | -7 |
| 10 | -6 |
| 11 | -5 |
| 12 | -4 |
| 13 | -3 |
| 14 | -2 |
| 15 | -1 |
The next table presents the outcomes from a Level 2 simulation aimed solely at Banker bets, occurring 81.7% of the time. The bottom right corner reveals a house edge of 1.01%.
Level 1 Player Bets
| Event | Pays | Probability | Return |
|---|---|---|---|
| Win | 1 | 0.447709 | 0.447709 |
| Loss | -1 | 0.457639 | -0.457639 |
| Tie | 0 | 0.094651 | 0.000000 |
| Total | 1.000000 | -0.009930 |
The following table summarizes the combined results of both Player and Banker bets while utilizing the Level 2 strategy. The lower right cell shows a house edge of 1.00%.
Level 2 Banker Bets
| Card | Player | Banker | Tie |
|---|---|---|---|
| Win | 0.95 | 0.458810 | 0.435870 |
| House | Edge | 0.445926 | None |
| -4 | 0 | 0.095264 | 0.000000 |
| -5 to -3 | 1.000000 | -6 to -2 |
Ultimately, a mere 0.01% reduction may not be significant enough to warrant additional effort for most players, especially when compared to the Level 1 strategy. Nonetheless, since I performed all this analysis, I’ve decided to document it.
-7 to -1
| -8 to 0 | -9 to +1 | Level 2 | score board |
|---|---|---|---|
| baccarat trainer | 1 | 0.081815 | 0.081815 |
| , the player is in the sixth column. | 0.95 | 0.374967 | 0.356219 |
| Bead Plate | 0 | 0.095152 | 0.000000 |
| Level 2 Index Values | Column | 0.448066 | Index Value |
| -15 | 1.000000 | -14 |
Level 3 represents a modification of Level 1, wherein the running count purely determines betting decisions on which side to wager on, disregarding the position within the shoe or the column in the bead plate. Level 3 enhances these strategies by assigning more proportional value to each card's effect on betting odds. The forthcoming table details how to adjust the running count based on the point values of the cards drawn.
-13
As with the Level 1 strategy, begin the shoe by establishing a running count of 0, and increment this count based on the point value of each rank revealed.
-12
| -11 | -10 |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2 | 3 |
| 3 | 3 |
| 4 | 6 |
| 5 | -9 |
| 6 | -8 |
| 7 | -7 |
| 8 | -6 |
| 9 | -5 |
In contrast to the Level 1 strategy, players should place bets on the Player with a running count of -15 or lower.
Using this Level 3 strategy, players will place bets on the Player 28.55% of the time. The following table recounts the results of these Player bets, showing a house edge of 1.05% in the lower right corner. This is in comparison to the house edge of 1.24% applicable to the Player bet when card counting is not utilized.
The next table consolidates the findings of the previous tables, presenting the possible outcomes for both Player and Banker bets. The lower right cell displays a combined house edge of 1.004%. This can be contrasted with the 1.06% house edge when exclusively betting on the Banker or the 1.11% house edge when placing bets in the same ratio of 28.4% for the Player and 71.6% for the Banker. To recap, the overall house edge for betting every hand using the Level 1 strategy stands at 1.011%, which is 0.007% higher.
-4
| -3 | -2 | -1 | Level 1 Player Bets |
|---|---|---|---|
| Event | 1 | 0.447480 | 0.447480 |
| Pays | 0 | 0.094542 | 0.000000 |
| Probability | Return | 0.457978 | Win |
| Loss | 1.000000 | -1 |
The following table displays the outcomes of 71.6% of the time when the player bets on the Banker. The lower right cell presents a house edge of 0.99%, which contrasts with a house edge of 1.06% for the Banker bet when card counting is not utilized.
-0.457639
| Tie | Total | -0.009930 | Level 2 Banker Bets |
|---|---|---|---|
| Card | 0.95 | 0.458844 | 0.435902 |
| Player | 0 | 0.095395 | 0.000000 |
| Banker | Tie | 0.445760 | Win |
| House | 1.000000 | Edge |
Aligning with the Level 1 strategy, players can further reduce their overall house edge by avoiding hands that are close to the range where both betting options would yield almost identical unfavorable odds. In this case, the specific point is a running count of -14.
None
| -4 | -5 to -3 | -6 to -2 | -7 to -1 | -8 to 0 |
|---|---|---|---|---|
| -9 to +1 | Level 2 | 1 | 0.127764 | 0.127764 |
| score board | baccarat trainer | 0 | 0.026994 | 0.000000 |
| , the player is in the sixth column. | Bead Plate | Level 2 Index Values | 0.130761 | Column |
| Index Value | -15 | 0.95 | 0.327836 | 0.311444 |
| -14 | -13 | 0 | 0.068158 | 0.000000 |
| -12 | -11 | -10 | 0.318487 | -9 |
| -8 | 1.000000 | -7 |
Considering everything, the house edge reduction in moving from Level 1 to Level 3 is only 0.01%. Thus, for most players, the added work may not be worthwhile.
The following table illustrates how the proportion of hands played and the corresponding house edge are affected by the ranges of true counts that are skipped by choosing not to bet. For instance, if a player opts out when the true count is between -8 and 0, they will engage in 55.69% of hands, and the average house edge for the hands played will be 0.95%.
-6
| -5 -4 |
-3 -2 |
-1 Level 1 Player Bets |
|---|---|---|
| Event | 100.00% | Pays |
| Probability | 86.55% | Return |
| Win | 74.42% | Loss |
| -1 | 61.46% | -0.457639 |
| Tie | 50.52% | Total |
As highlighted at the beginning, card counting indeed provides a means to lessen the house edge in baccarat. In my view, Level 1 is suitable for the majority of players. Levels 2 and 3 yield only a minimal reduction of approximately 0.01%, which may not justify the endeavor.
-0.009930
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