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
Friends, The following 3 tables show the most beneficial cards for each wager. This was calculated by observing the number of times the presence of cards of these values led to a Player, Banker or Tie result. They are sorted in descending order of effect by card value. Some of the results are intuitive, others may surprise. Column 3: Player Win % Compared to Other Wagers compares the effect the card value has on a wager as compared to the other wagers, in this instance, Banker and Tie. Column 4: Player Win % by Card Value compares that card value’s effect as compared to all other card values for that particular wager. Player Card Value: Permutations Player Win % Compared to Other Wagers Player Win % by Card Value 4 1,036,330,148,130,820 44.9220% 7.7436% 0 1,035,362,791,243,780 44.8801% 7.7363% J 1,035,362,791,243,780 44.8801% 7.7363% Q 1,035,362,791,243,780 44.8801% 7.7363% K 1,035,362,791,243,780 44.8801% 7.7363% 1 1,034,132,990,550,020 44.8268% 7.7272% 3 1,032,891,882,528,770
All right folks. First off, please understand that having a 1st-card advantage means that the player has somehow found out what the first card of the as-yet undealed coup is. This is at worst cheating or at best, if the dealer or procedures are weak, advantage play. 1st-card advantage is essentially a study of all the possible card permutations that start with Ace through to King that result in a Player, Banker or Tie result from the remaining cards in the shoe. The 2 tables below show that knowing that the 1st card is a 1-5 or 10-K, would give a small advantage on the Banker wager. Knowledge of the 1st card being 6-9 would give an increasing advantage on the Player wager, with knowing a 1st card as being 9 giving a 21% advantage on the Player wager. Below is a table that shows the probabilities before the start of the shoe: Card Value: Player Win Banker Win Tie
In simulating different conditions of a Baccarat shoe, the following instances were observed: Wager refers to the wager type studied – Pairs, Wins on Natural 9s (WN9) and Wins on Natural 8s (WN8). Win % Probability indicates the percentage probability of that result occurring. Expectation, based on 11:1 for Pairs and 8:1 for Wins on Natural 8s and 9s, shows the expectation (player’s edge) of the respective wagers with the state of the shoe on the right. 1 – K indicates how many cards of that value have been dealt. Wager Win % Probability Expectation 1 2 3 4 5 6 7 8 9 0 J Q K Pairs 8.66% 3.9% 5 23 23 23 23 23 23 23 23 23 23 23 23 Pairs 25.02% 200.2% 5 5 30 30 30 30 30 30 30 30 30 30 30 WN9 14.27% 28.4% 25 25 25 25 25 25 25 25 5 5 5 5 5 WN8 13.21% 18.9% 25
Why does a Banker win on 6 pay half? If you have ever wondered about this, you are not alone. This table shows the Probability and House Edge for Baccarat (where Banker wins pay 0.95:1). Notice the House Edge on Banker (in bold): Wager Permutations Probability Break-Even House Edge Player 2,230,518,282,592,260 0.4462466093 1.02768 0.012351 Banker 2,292,252,566,437,890 0.4585974226 0.97307 0.010579 Tie 475,627,426,473,216 0.09516 9.50906 0.143596 Total 4,998,398,275,503,360 The House Edge means, theoretically in the long-term, for every dollar wagered, a player is expected to lose 1.05 cents. This is a table with the House Edge on Baccarat, comparing what the House Edge would be if Banker were paid half on wins of 1 to 9: Banker Win On: Permutations Probability Banker Win on Any Other Result Player Win Difference House Edge 1 24,291,119,898,624 0.004859781 2,267,961,446,539,260 2,230,518,282,592,260 – 49,588,723,896,320.0 -0.009920923 2 44,681,581,871,104 0.00893918 2,247,570,984,566,780
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This analysis spreadsheet is meant for Baccarat. This spreadsheet computes all the possible permutations of a Player, Banker, Tie or
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