Mathematics of baccarat

The mathematical percentages of each chance's victory vary, albeit slightly, depending on the number of decks considered; let's remember that the most common games are played with 6 and 8 decks.e decks used in Baccarat (Punto Banco) are generally 6 or 8.

 

Decks Bank Player Tie
       
Infinite 45.8428% 44.6147% 9.5426%
8 decks 45.8597% 44.6247% 9.5156%
6 decks 45.8653% 44.6276% 9.5069%
4 decks 45.8761% 44.6340% 9.4898%
2 decks 45.9073% 44.6508% 9.4419%
1 deck 45.9624% 44.6760% 9.3615%

 

 

The following table illustrates the percentages with which the bank and the player achieve various scores and, for each score, the corresponding expected win rate:

 

Score     Bank Distribution       Bank
Win Rate 		  Player Distribution   Player
Win Rate
               
0 8.9%   0.0%   9.4%   0.0%
1 6.9%   7.2%   7.5%   6.6%
2 6.9%   12.9%   7.4%   12.0%
3 7.3%   20.1%   7.5%   16.9%
4 9.3%   35.0%   7.4%   23.1%
5 10.1%   43.1%   7.5%   33.0%
6 11.2%   44.5%   13.5%   47.0%
7 12.8%   59.9%   13.4%   61.0%
8 12.8%   82.8%   13.3%   83.5%
9 12.8%   91.4%   13.4%   91.7%

 

The following table illustrates the house edge for various combinations and different payout and commission variants. We remind you that, except for particular cases (promotions, bonuses, etc.), the commission is 5%, and the Tie is paid 9:1.

Currently, the only casino that applies a 4% commission is "The D" in Las Vegas, Downtown (in the High Limit room). In 1989, however, the Sahara reduced the commission to 0% for bets not exceeding $100. Naturally, the promotion didn't last long (today, the Sahara no longer exists).

 

Decks Bank (5%) Bank (4%) Player Tie (9:1) Tie (8:1)
           
Infinite 10640% 0.6056% 12281% 457,44 141170%
8 decks 10579% 0.5993% 12351% 484,4 143596%
6 decks 10558% 0.5972% 12374% 493,13 144382%
4 decks 10517% 0.5929% 12421% 510,18 145916%
2 decks 10389% 0.5789% 12556% 558,09 150280%
1 deck 10117% 0.5521% 12864% 638,46 157461%

 

 

 

How would the bank's advantage vary with further changes in commission? The following table answers this question (a negative HA value indicates that the player has the advantage):

 

6 decks

Commission  House Advantage
3%   0.1386%
2%  -0.3201%
1%    -0.7787%
0%  -1.2374%

 

8 decks

Commission  House Advantage
3%    0.1408%
2%  -0.3178%
1%  -0.7764%
0%  -1.2350%