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 10) + (from removal of card 20)
Tie +

(+ from Removal of card 20)

+ + +

In other words:

  1. 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.
  2. For the Banker, removal of the 1s through to 4s and 6s and 7s would be advantageous. Do note the peculiarities at card 10 for 6 and card 20 for 7.
  3. 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

Concepts 16 Player

Banker

Concepts 16 Banker

Tie

Concepts 16 Tie

Good luck!