Hi friends,
This topic follows the study on the most beneficial cards to the Player, Banker and Tie wagers in Baccarat.
The 3 tables below show the effect on the probabilities of the Player, Banker and Tie as 1, 2 and 3 cards are removed in isolation from each card value. Do take note of the changes in probability as each card is removed and their relationship to the respective wager.
Player
| Card Value: | Permutations | Player Win % Compared to Other Wagers | Player Win % by Card Value | Effect of 1 Card Removed | Effect of 2 Cards Removed | Effect of 3 Cards Removed |
| 4 | 1,036,330,148,130,820 | 44.9220% | 7.7436% | – 0.0000435175 | – 0.0000870460 | – 0.0001305855 |
| 0 | 1,035,362,791,243,780 | 44.8801% | 7.7363% | – 0.0000373810 | – 0.0000749287 | – 0.0001126377 |
| J | 1,035,362,791,243,780 | 44.8801% | 7.7363% | – 0.0000373810 | – 0.0000749287 | – 0.0001126377 |
| Q | 1,035,362,791,243,780 | 44.8801% | 7.7363% | – 0.0000373810 | – 0.0000749287 | – 0.0001126377 |
| K | 1,035,362,791,243,780 | 44.8801% | 7.7363% | – 0.0000373810 | – 0.0000749287 | – 0.0001126377 |
| 1 | 1,034,132,990,550,020 | 44.8268% | 7.7272% | – 0.0000295798 | – 0.0000594307 | – 0.0000895596 |
| 3 | 1,032,891,882,528,770 | 44.7730% | 7.7179% | – 0.0000217068 | – 0.0000440304 | – 0.0000669774 |
| 2 | 1,031,651,228,684,290 | 44.7192% | 7.7086% | – 0.0000138368 | – 0.0000279871 | – 0.0000424652 |
| 9 | 1,031,234,689,822,720 | 44.7012% | 7.7055% | – 0.0000111945 | – 0.0000236585 | – 0.0000374332 |
| 8 | 1,030,998,408,818,690 | 44.6909% | 7.7037% | – 0.0000096956 | – 0.0000214609 | – 0.0000353579 |
| 5 | 1,020,528,719,052,800 | 44.2371% | 7.6255% | 0.0000567188 | 0.0001128483 | 0.0001683503 |
| 7 | 1,013,469,785,956,350 | 43.9311% | 7.5728% | 0.0001014971 | 0.0002024677 | 0.0003028843 |
| 6 | 1,010,420,677,033,980 | 43.7989% | 7.5500% | 0.0001208391 | 0.0002418228 | 0.0003629233 |
Banker
| Card Value: | Permutations | Banker Win % Compared to Other Wagers | Banker Win % by Card Value | Effect of 1 Card Removed | Effect of 2 Cards Removed | Effect of 3 Cards Removed |
| 8 | 1,067,894,055,137,280 | 46.2902% | 7.7645% | – 0.0000629994 | – 0.0001283117 | – 0.0001959930 |
| 9 | 1,063,659,370,418,180 | 46.1067% | 7.7337% | – 0.0000361367 | – 0.0000740128 | – 0.0001136737 |
| 5 | 1,062,272,823,181,310 | 46.0466% | 7.7236% | – 0.0000273411 | – 0.0000544194 | – 0.0000812294 |
| 0 | 1,061,053,355,229,180 | 45.9937% | 7.7148% | – 0.0000196054 | – 0.0000395286 | – 0.0000597675 |
| J | 1,061,053,355,229,180 | 45.9937% | 7.7148% | – 0.0000196054 | – 0.0000395286 | – 0.0000597675 |
| Q | 1,061,053,355,229,180 | 45.9937% | 7.7148% | – 0.0000196054 | – 0.0000395286 | – 0.0000597675 |
| K | 1,061,053,355,229,180 | 45.9937% | 7.7148% | – 0.0000196054 | – 0.0000395286 | – 0.0000597675 |
| 6 | 1,056,701,970,653,180 | 45.8051% | 7.6831% | 0.0000079976 | 0.0000143452 | 0.0000189833 |
| 1 | 1,055,563,635,941,380 | 45.7557% | 7.6749% | 0.0000152186 | 0.0000304640 | 0.0000457306 |
| 7 | 1,054,846,110,916,610 | 45.7246% | 7.6696% | 0.0000197702 | 0.0000379094 | 0.0000543471 |
| 2 | 1,051,591,007,948,800 | 45.5835% | 7.6460% | 0.0000404189 | 0.0000808770 | 0.0001213820 |
| 3 | 1,050,791,343,448,060 | 45.5489% | 7.6402% | 0.0000454916 | 0.0000893156 | 0.0001314284 |
| 4 | 1,045,981,660,065,790 | 45.3404% | 7.6052% | 0.0000760018 | 0.0001513286 | 0.0002259417 |
Tie
| Card Value: | Permutations | Tie % Compared to Other Wagers | Tie % by Card Value | Effect of 1 Card Removed | Effect of 2 Cards Removed | Effect of 3 Cards Removed |
| 6 | 239,830,402,545,152 | 10.3960% | 8.4040% | – 0.0001288367 | – 0.0002561680 | – 0.0003819067 |
| 7 | 238,637,153,359,360 | 10.3443% | 8.3622% | – 0.0001212674 | – 0.0002403772 | – 0.0003572314 |
| 4 | 224,641,242,035,712 | 9.7376% | 7.8718% | – 0.0000324844 | – 0.0000642826 | – 0.0000953562 |
| 5 | 224,151,507,998,208 | 9.7163% | 7.8546% | – 0.0000293777 | – 0.0000584289 | – 0.0000871209 |
| 2 | 223,710,813,599,232 | 9.6972% | 7.8391% | – 0.0000265822 | – 0.0000528899 | – 0.0000789169 |
| 3 | 223,269,824,255,488 | 9.6781% | 7.8237% | – 0.0000237848 | – 0.0000452853 | – 0.0000644510 |
| 1 | 217,256,423,740,928 | 9.4175% | 7.6130% | 0.0000143612 | 0.0000289667 | 0.0000438290 |
| 9 | 212,058,989,991,424 | 9.1922% | 7.4309% | 0.0000473311 | 0.0000976713 | 0.0001511069 |
| 0 | 210,536,903,759,360 | 9.1262% | 7.3775% | 0.0000569865 | 0.0001144573 | 0.0001724053 |
| J | 210,536,903,759,360 | 9.1262% | 7.3775% | 0.0000569865 | 0.0001144573 | 0.0001724053 |
| Q | 210,536,903,759,360 | 9.1262% | 7.3775% | 0.0000569865 | 0.0001144573 | 0.0001724053 |
| K | 210,536,903,759,360 | 9.1262% | 7.3775% | 0.0000569865 | 0.0001144573 | 0.0001724053 |
| 8 | 208,060,586,276,352 | 9.0188% | 7.2907% | 0.0000726950 | 0.0001497726 | 0.0002313508 |
In summary, you will notice that shoes with a higher number of certain card values remaining will lead to a better probability on specific wagers. The following table shows the simplified effect of removal of each card value on the respective probabilities of the Player, Banker and Tie wagers:-
| Effect of Removal on Probability by Card Value | ||||||||||
| Wager | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 |
| Player | – | – | – | – | + | + | + | – | – | – |
| Banker | + | + | + | + | – | + (– from removal of card 6) | + (–from removal of card 12) | – | – | – |
| Tie | + | – | –
(+ from Removal of card 20) |
– | – | – | – | + | + | + |
In other words:
- For the Player, it would be advantageous to have as many 5s, 6s and 7s removed from the shoe as possible and to keep the rest in.
- For the Banker, removal of the 1s through to 4s and 6s and 7s would be advantageous. Do note the peculiarities at card 6 for 6 and card 12 for 7.
- For Tie, removal of the 1s and 8s through to Ks would be advantageous. Do note the peculiarity at card 20 for 3.
The 3 charts below show the effect on probability as 1 to 32 cards of each value are removed.
Player
Banker
Tie
Good luck!
excelpunks. Training - Consultancy - Solutions. 