How are baccarat odds calculated? Counting Banker 45.86% from 8 decks and 416 cards

2026-10-04

Almost every baccarat article quotes Banker 45.86%, Player 44.62% and Tie 9.52%. These numbers do not come from someone watching tables for a long time. They come from counting every card combination without missing one. We followed those steps for the 8-deck shoe used in Evolution live baccarat at the Stake (stake.com) casino.

Step 1: group the cards by points

Suits do not matter in baccarat, only points. 10, J, Q and K are all worth 0. Grouping 416 cards by points gives:

0 points      128 cards (10, J, Q, K x 32 each)
1 to 9 points 32 cards each

The chance that the first card is worth 0 is 128/416 = 30.8%. Once you know how many cards each point value has, the rest is multiplication and addition.

Step 2: count every first four cards

Player and Banker each get two cards, in 416 x 415 x 414 x 413 orders, about 29.5 billion. Each removed card lowers the count of what is left, and that is included. At this stage the chance of a Player natural (8 or 9) is 18.94%, and the chance of a two-card total of 0 is 14.74%. Counting points is explained in how to count baccarat points.

Step 3: branch on the third card rule

Without a natural, Player draws on 5 or less, and Banker decides by its own total and Player's third card. For each case the fifth and sixth cards are attached, again divided by the cards left. Spelling out every order up to six cards gives about 5 quadrillion sequences, but grouped by points a computer finishes in a few seconds. The rule table is in the baccarat third card rule.

Results and real records

Banker   45.86%
Player   44.62%
Tie       9.52%
Ties removed: Banker 50.68% · Player 49.32%

Counting only the clean shoes among the real shoes collected by Hiddenpick R&D, the Banker share is 50.68%, the same as the calculation. Theory and records agreeing also means the cards are shuffled and dealt by the rules. Why calling the next hand is so hard is covered in the truth about baccarat prediction software.

Summary

Group by points   0 points 128 cards, 1 to 9 points 32 each
First four cards  about 29.5 billion orders
Up to six cards   about 5 quadrillion (seconds when grouped)
Result            Banker 45.86 · Player 44.62 · Tie 9.52
Real records      clean shoes Banker 50.68% (ties removed), same as theory

Hiddenpick is a Windows program that runs Evolution live baccarat on Stake (stake.com) for you, following the rules you set. How much the numbers move with the number of decks is in 1 deck versus 8 decks.