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Baccarat Odds Given Known Card
Introduction
There are ways of knowing the exact position of a particular card in baccarat. By counting down the cards, the player will know when exactly to expect the known card. Lest any advantage players get angry at me who already know how to do this, I won't reveal the secret. However, I will present the following tables showing the probability of winning and expected value (EV) of all three bets given the position of the known card. Cells in red indicate a positive expected value.
Position = 1 or 3
| Card | Player Probability |
Banker Probability |
Tie Probability |
Player EV |
Banker EV |
Tie EV |
|---|---|---|---|---|---|---|
| 0 | 0.415228 | 0.495203 | 0.089568 | -0.079975 | 0.055215 | -0.193885 |
| 1 | 0.415476 | 0.493789 | 0.090736 | -0.078313 | 0.053623 | -0.183380 |
| 2 | 0.417197 | 0.490844 | 0.091959 | -0.073647 | 0.049105 | -0.172366 |
| 3 | 0.419852 | 0.487016 | 0.093132 | -0.067164 | 0.042814 | -0.161815 |
| 4 | 0.423290 | 0.479533 | 0.097177 | -0.056242 | 0.032266 | -0.125406 |
| 5 | 0.433347 | 0.468070 | 0.098583 | -0.034723 | 0.011320 | -0.112754 |
| 6 | 0.450141 | 0.442579 | 0.107279 | 0.007562 | -0.029691 | -0.034485 |
| 7 | 0.483157 | 0.409506 | 0.107337 | 0.073651 | -0.094126 | -0.033970 |
| 8 | 0.538370 | 0.365435 | 0.096195 | 0.172935 | -0.191207 | -0.134247 |
| 9 | 0.559462 | 0.344181 | 0.096357 | 0.215281 | -0.232490 | -0.132789 |
Position = 2 or 4
| Card | Player Probability |
Banker Probability |
Tie Probability |
Player EV |
Banker EV |
Tie EV |
|---|---|---|---|---|---|---|
| 0 | 0.482923 | 0.424876 | 0.092200 | 0.058047 | -0.079291 | -0.170196 |
| 1 | 0.479480 | 0.428435 | 0.092085 | 0.051045 | -0.072467 | -0.171236 |
| 2 | 0.475867 | 0.432106 | 0.092027 | 0.043761 | -0.065366 | -0.171760 |
| 3 | 0.472411 | 0.435284 | 0.092306 | 0.037127 | -0.058891 | -0.169246 |
| 4 | 0.465526 | 0.440687 | 0.093788 | 0.024839 | -0.046873 | -0.155910 |
| 5 | 0.452179 | 0.454358 | 0.093463 | -0.002179 | -0.020539 | -0.158834 |
| 6 | 0.433199 | 0.460388 | 0.106413 | -0.027189 | 0.004170 | -0.042287 |
| 7 | 0.400152 | 0.493067 | 0.106781 | -0.092916 | 0.068262 | -0.038972 |
| 8 | 0.356026 | 0.548373 | 0.095600 | -0.192347 | 0.164928 | -0.139597 |
| 9 | 0.334672 | 0.569564 | 0.095764 | -0.234892 | 0.206414 | -0.138127 |
Position = 5
| Card | Player Probability |
Banker Probability |
Tie Probability |
Player EV |
Banker EV |
Tie EV |
|---|---|---|---|---|---|---|
| 0 | 0.380218 | 0.534474 | 0.085308 | -0.154257 | 0.127533 | -0.232225 |
| 1 | 0.420820 | 0.479574 | 0.099606 | -0.058754 | 0.034776 | -0.103546 |
| 2 | 0.456504 | 0.430362 | 0.113134 | 0.026142 | -0.047660 | 0.018204 |
| 3 | 0.497991 | 0.391163 | 0.110846 | 0.106828 | -0.126386 | -0.002386 |
| 4 | 0.538285 | 0.355126 | 0.106590 | 0.183159 | -0.200915 | -0.040694 |
| 5 | 0.514847 | 0.377449 | 0.107704 | 0.137398 | -0.156270 | -0.030660 |
| 6 | 0.490071 | 0.399824 | 0.110105 | 0.090246 | -0.110237 | -0.009055 |
| 7 | 0.468767 | 0.426246 | 0.104987 | 0.042521 | -0.063833 | -0.055115 |
| 8 | 0.460376 | 0.471510 | 0.068114 | -0.011133 | -0.012442 | -0.386972 |
| 9 | 0.432676 | 0.492616 | 0.074708 | -0.059941 | 0.035310 | -0.327628 |
Position = 6
| Card | Player Probability |
Banker Probability |
Tie Probability |
Player EV |
Banker EV |
Tie EV |
|---|---|---|---|---|---|---|
| 0 | 0.516285 | 0.384990 | 0.098725 | 0.131295 | -0.150545 | -0.111471 |
| 1 | 0.478876 | 0.421323 | 0.099801 | 0.057553 | -0.078619 | -0.101793 |
| 2 | 0.440520 | 0.458751 | 0.100729 | -0.018230 | -0.004707 | -0.093442 |
| 3 | 0.403863 | 0.497170 | 0.098966 | -0.093307 | 0.068448 | -0.109303 |
| 4 | 0.379405 | 0.524860 | 0.095735 | -0.145454 | 0.119211 | -0.138384 |
| 5 | 0.368326 | 0.540489 | 0.091185 | -0.172163 | 0.145139 | -0.179338 |
| 6 | 0.371184 | 0.542547 | 0.086270 | -0.171363 | 0.144236 | -0.223572 |
| 7 | 0.400481 | 0.512086 | 0.087433 | -0.111605 | 0.086001 | -0.213103 |
| 8 | 0.432286 | 0.478288 | 0.089426 | -0.046002 | 0.022088 | -0.195163 |
| 9 | 0.461125 | 0.446294 | 0.092581 | 0.014831 | -0.037145 | -0.166770 |