Games 3: Baccarat – An Analysis

In this article, we shall go over the various components of baccarat:

1. Effect of individual cards on probability
2. Effect of different card combinations in a coup

Effect of individual cards on probability

The following 3 line-charts show the effect of removing each value of card on the probabilities on the next hand of the Banker, Player and Tie. You will notice that different card values have different effects on the probability of the next hand.

Running a regression analysis on each line, the following respective 3 bar-charts indicate the quantifiable effects on probability.

Banker

These charts show that removing 4s and 2s have the largest positive effect on the probability of a Banker result, while removing 8s and 9s have the largest negative effect on the probability of a Banker result.

Player

These charts show that removing 6s and 7s have the largest positive effect on the probability of a Player result, while removing 8s and 4s have the largest negative effect on the probability of a Player result.

Tie

These charts show that removing 8s and 9s have the largest positive effect on the probability of a Tie result, while removing 6s and 7s have the largest negative effect on the probability of a Tie result.

Effect of different card combinations in a coup

The reason for these differences can be traced directly to the composition of each possible coup. From combinatorics, we know that each hand in baccarat is formed from 6 cards. While there are 4 and 5-card coups, mathematically, the total number of possible outcomes from a 6-card game is necessarily calculated using 6 cards by default.

This is how we get the total possible outcomes in baccarat: 416! / (410! x 6!)

! means a factorial. This means 416 x 415 x 414 x 413 x 412 x 411 = 4,998,398,275,503,360 possible 6-card coups in baccarat.

The number of permutations of each coup is calculated by multiplying the number of total remaining cards of each value by the subsequent card.

For example, a hand consisting of 6 cards of different values from a new shoe would be (not counting the burn procedure, for simplicity) 32 x 32 x 32 x 32 x 32 x 32 or 32^6. A hand of consisting of 2 same value cards and 4 different value cards would be 32 x 31 x 32 x 32 x 32 x 32 or 32!/30! x 32^4.

This would mean that results which consist of an overall higher occurrence of 6 different value cards would have a higher probability of occurring. The following chart elaborates on this.

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Good luck!