Wizard Of Odds Baccarat Game
- Appendices
- Baccarat Analysis
- Miscellaneous
Introduction
In either blackjack or baccarat a good first step in developing a card counting strategy is to determine the effect of removing any given card from the game. The following table shows the number of banker, player, and tie wins resulting from the removing of one card in an 8-deck shoe. The card removed is indicated in the image--leftolumn.
Number
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Card Removed | Banker Win | Player Win | Tie Win |
---|---|---|---|
1 | 2259266202814720 | 2198201626637560 | 468838163231312 |
2 | 2259390347439480 | 2198279181695870 | 468636463548240 |
3 | 2259415336955130 | 2198240411263230 | 468650244465232 |
4 | 2259565639560830 | 2198132965463160 | 468607387659600 |
5 | 2259056540713470 | 2198626760121850 | 468622691848272 |
6 | 2259230629854970 | 2198942636434940 | 468132726393680 |
7 | 2259288625471740 | 2198847351781120 | 468170015430736 |
8 | 2258880877214840 | 2198299582316670 | 469125533152080 |
9 | 2259013211112320 | 2198292198535290 | 469000583035984 |
10 | 2259094649086970 | 2198163195365880 | 469048148230736 |
The next table puts these number is some perspective by indicating the probability of a banker, player, and tie win according to the card removed.
Probability
Card Removed | Banker Win | Player Win | Tie Win |
---|---|---|---|
1 | 0.458613 | 0.446217 | 0.09517 |
2 | 0.458638 | 0.446233 | 0.095129 |
3 | 0.458643 | 0.446225 | 0.095132 |
4 | 0.458673 | 0.446203 | 0.095123 |
5 | 0.45857 | 0.446303 | 0.095127 |
6 | 0.458605 | 0.446367 | 0.095027 |
7 | 0.458617 | 0.446348 | 0.095035 |
8 | 0.458534 | 0.446237 | 0.095229 |
9 | 0.458561 | 0.446235 | 0.095203 |
10 | 0.458578 | 0.446209 | 0.095213 |
The next table shows the house edge of each bet by card removed.
House Edge
Card Removed | Banker | Player | Tie |
---|---|---|---|
1 | 0.010535 | 0.012396 | 0.143467 |
2 | 0.010527 | 0.012405 | 0.143836 |
3 | 0.010514 | 0.012418 | 0.14381 |
4 | 0.010463 | 0.01247 | 0.143889 |
5 | 0.010662 | 0.012267 | 0.143861 |
6 | 0.010692 | 0.012238 | 0.144756 |
7 | 0.010662 | 0.012269 | 0.144688 |
8 | 0.010629 | 0.012298 | 0.142942 |
9 | 0.010602 | 0.012326 | 0.14317 |
10 | 0.01056 | 0.012369 | 0.143083 |
The next table shows the effect on the house edge of each bet according to the card removed. A negative number indicates removal is bad for the player, positive indicates removal is good.
House Edge
Card Removed | Banker | Player | Tie |
---|---|---|---|
0 | 0.000019 | -0.000018 | 0.000513 |
1 | 0.000044 | -0.000045 | 0.000129 |
2 | 0.000052 | -0.000054 | -0.000239 |
3 | 0.000065 | -0.000067 | -0.000214 |
4 | 0.000116 | -0.000120 | -0.000292 |
5 | -0.000083 | 0.000084 | -0.000264 |
6 | -0.000113 | 0.000113 | -0.001160 |
7 | -0.000083 | 0.000082 | -0.001091 |
8 | -0.00005 | 0.000053 | 0.000654 |
9 | -0.000023 | 0.000025 | 0.000426 |
The next table multiplies the above numbers by ten million.
Count Adjustment
Card Removed | 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 |
Average | 0 | 0 | 0 |
To adapt this information to a card counting strategy, the player should start with three running counts of zero. As each card is seen as it leaves the shoe the player should add the point values of that card to each running count. For example if the first card to be played is an 8 then the three running counts would be: banker=-502, player=533, tie=6543. Of course the player does not have to keep a running track of all three counts. In fact the point values for the banker and player are nearly opposite of each other. A high running count for the banker would mean a corresponding low count for the player, and vise versa.
In order for any given bet to become advantageous the player should divide the running count by the ratio of cards left in the deck to get the true count. A bet hits zero house edge at the following true counts:
- Banker: 105791
- Player: 123508
- Tie: 1435963
Assuming you were able to actually play this strategy perfectly you would notice that the true counts seldom passed the point of zero house edge. The next table shows the ratio of hands played, based on a sample of 100 million, in which the true count passes the break even points above. The image--leftolumn indicates the ratio of cards dealt before the cards are shuffled.
Positive Expectation
Penetration | Banker | Player | Tie |
---|---|---|---|
90 percent | 0.000131 | 0.000024 | 0.000002 |
95 percent | 0.001062 | 0.000381 | 0.000092 |
98 percent | 0.005876 | 0.003700 | 0.002106 |
The final table indicates the expected revenue per 100 bets and a $1000 wager every time a positive expected value occured. Please remember that this table assumes the player is able to keep a perfect count and the casino is not going to mind the player only making a bet once every 475 hands of less.
Expected Profit
Penetration | Banker | Player | Tie |
---|---|---|---|
90 percent | $0.01 | $0.00 | $0.00 |
95 percent | $0.20 | $0.06 | $0.15 |
98 percent | $2.94 | $1.77 | $11.93 |
I hope this section shows that for all practical purposes baccarat is not a countable game. For more information on a similar experiment I would recomment The Theory of Blackjack by Peter A. Griffin. Although the book is mainly devoted to blackjack he has part of a chapter titled 'Can Baccarat Be Beaten?' on pages 216 to 223. Griffin concludes by saying that even in Atlantic City, with a more liberal shuffle point than Las Vegas, the player betting $1000 in positive expectation hands can expect to profit 70 cents an hour.
For your further consideration I would recommend this baccarat odds calculator. You can put in any deck composition and it will give the house edge on all three bets.
Go back to baccarat
Go to baccarat appendix 1
Go to baccarat appendix 3
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Go to baccarat appendix 6
Go to baccarat appendix 7
Written by: Michael Shackleford
On This Page
Introduction
7 Up Baccarat is a baccarat variant offered at the Marina Bay Sands casino in Singapore. The rules and play of the game are mostly the same as conventional baccarat, except the Player hand always starts with a seven as the first card. This affects the probabilities, so the pays are different as well.
Rules
The rules are the same as conventional baccarat, except as noted. To avoid confusion, I capitalize Player and Banker when referring to the bets. When referring to the person playing the game, I use player in lower case.
- Six decks are used, with a continuous shuffler.
- The first card to the Player is always a seven. This is indicated with a seven printed on the felt.
- The Player receives one card to make his hand along with the seven, and the Banker receives two cards.
- Drawing rules are exactly the same as in conventional baccarat.
- Wins on the Player bet pay even money, except a Player win of 7 pays 1 to 2. Ties are still a push, and Banker bets result in a loss.
- Wins on the Banker bet pay even money, except a Banker win of 7 pays 9 to 5. Ties are still a push, and Player wins result in a loss.
- Tie bets pay 7 to 1, except a 7-point tie pays 9 to 1.
- There is also a side bet titled 'Super Sevens,' which pays according to the number of sevens between the Player and Banker hands, including the Player's first seven. The wins are indicated separately below.
Odds
All analysis in this report is based on six decks of cards.
The following table shows all the possible outcomes of the Player bet. The lower right cell reflects a house edge of 2.60%.
Player Bet
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Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|
Player win (other than 7) | 1 | 818,970,471,360 | 0.286077 | 0.286077 |
Player win on 7 | 0.5 | 561,338,904,384 | 0.196083 | 0.098041 |
Tie | 0 | 308,245,281,984 | 0.107674 | 0.000000 |
Loss | -1 | 1,174,211,488,512 | 0.410167 | -0.410167 |
Total | 2,862,766,146,240 | 1.000000 | -0.026049 |
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The following table shows all the possible outcomes of the Banker bet. The lower right cell reflects a house edge of 2.56%.
Banker Bet
Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|
Banker win on 7 | 1.8 | 166,043,860,992 | 0.058001 | 0.104402 |
Banker win (other than 7) | 1 | 1,008,167,627,520 | 0.352166 | 0.352166 |
Tie | 0 | 308,245,281,984 | 0.107674 | 0.000000 |
Loss | -1 | 1,380,309,375,744 | 0.482159 | -0.482159 |
Total | 2,862,766,146,240 | 1.000000 | -0.025592 |
The following table shows all the possible outcomes of the Tie bet. The lower right cell reflects a house edge of 4.05%.
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Tie Bet
Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|
Tie on 7 | 9 | 140,427,142,272 | 0.049053 | 0.441477 |
Tie on any other total | 7 | 167,818,139,712 | 0.058621 | 0.410347 |
Banker or Player win | -1 | 2,554,520,864,256 | 0.892326 | -0.892326 |
Total | 2,862,766,146,240 | 1.000000 | -0.040503 |
The following table shows all the possible outcomes of the Super Sevens bet. Remember, this includes the given Player seven, so there will always be at least one. The lower right cell reflects a house edge of 8.86%.
Super Sevens Bet
Sevens | Pays | Permutations | Probability | Return |
---|---|---|---|---|
6 | 700 | 5,100,480 | 0.000002 | 0.001247 |
5 | 70 | 208,099,584 | 0.000073 | 0.005088 |
4 | 17 | 5,689,804,032 | 0.001988 | 0.033788 |
3 | 5 | 81,285,488,640 | 0.028394 | 0.141970 |
2 | 2 | 666,866,329,344 | 0.232945 | 0.465889 |
1 | -1 | 2,108,711,324,160 | 0.736599 | -0.736599 |
Total | 2,862,766,146,240 | 1.000000 | -0.088616 |
Strategy
My general advice to baccarat players is if you like the Player and Banker bets, the odds are better in conventional baccarat. However, if you like the long odds on the side bets, 7 Up Baccarat is a better value. If you don't have the choice, and must play 7 Up, then the Banker is the best bet, at a house edge of 2.56%.
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Comparison to Baccarat
Bet | 7 Up Baccarat | Conventional Baccarat |
---|---|---|
Player | 2.60% | 1.24% |
Banker | 2.56% | 1.06% |
Tie | 4.05% | 14.38% |
Super Sevens | 8.86% | |
Player/Banker Pair | 11.25% |
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Written by:Michael Shackleford