Odd Baccarat
Posted By admin On 02/04/22Introduction
Odds of Baccarat vs. At 1.06% for the Banker’s hand and 1.24% on the Player’s hand, the house edge in Baccarat is low – only Blackjack’s is lower at 0.5% – and better for players than Roulette, where the house edge is 5.26%. Baccarat has one of the lowest house edges of all casino games, hence why it is so popular with fictional characters like James Bond and high rollers across the globe. Of the three common bets, the Banker has the lowest house edge of just 1.06%. As our charts highlight, the Tie bet offers the worst house edge of all.
I've been getting asked a lot about the odds in baccarat for unusual numbers of decks. To hopefully cover all my bases, this page shall show the number of combinations, probability of winning, and expected return, for every number of decks from 1 to 12.
Combinations
The following table shows the number of combinations for all three possible outcomes by the number of decks. The combinations in this page get pretty huge. Unfortunately, Excel displays only 15 significant digits, so please don't write to me that I'm wrong after 15 digits. Instead, please blame Microsoft.
Combinations
| Decks | Player | Banker | Tie | Total |
|---|---|---|---|---|
| 1 | 6,548,674,432 | 6,737,232,640 | 1,372,227,328 | 14,658,134,400 |
| 2 | 487,816,735,232 | 501,543,728,128 | 103,154,274,240 | 1,092,514,737,600 |
| 3 | 5,837,305,562,496 | 6,000,349,195,008 | 1,238,768,922,816 | 13,076,423,680,320 |
| 4 | 33,608,344,225,792 | 34,543,624,867,840 | 7,145,601,996,928 | 75,297,571,090,560 |
| 5 | 130,087,780,016,000 | 133,700,037,548,800 | 27,690,387,926,400 | 291,478,205,491,200 |
| 6 | 392,220,492,728,832 | 403,095,751,234,560 | 83,552,962,932,288 | 878,869,206,895,680 |
| 7 | 995,884,732,700,032 | 1,023,469,376,328,440 | 212,268,385,833,280 | 2,231,622,494,861,750 |
| 8 | 2,230,518,282,592,250 | 2,292,252,566,437,880 | 475,627,426,473,216 | 4,998,398,275,503,350 |
| 9 | 4,540,095,442,933,630 | 4,665,676,262,757,120 | 968,435,421,769,728 | 10,174,207,127,460,500 |
| 10 | 8,570,454,841,408,000 | 8,807,402,586,035,200 | 1,828,629,499,384,000 | 19,206,486,926,827,200 |
| 11 | 15,222,978,065,896,800 | 15,643,682,376,129,200 | 3,248,754,169,011,640 | 34,115,414,611,037,600 |
| 12 | 25,714,619,121,272,800 | 26,425,038,379,143,100 | 5,488,795,281,294,720 | 57,628,452,781,710,600 |
The next table shows the probability of each outcome by number of decks.
Probabilities
| Decks | Player | Banker | Tie |
|---|---|---|---|
| 1 | 0.446760430304146 | 0.459624155172162 | 0.093615414523693 |
| 2 | 0.446508150822404 | 0.459072734551641 | 0.094419114625955 |
| 3 | 0.446399237681564 | 0.458867756329930 | 0.094733005988506 |
| 4 | 0.446340349881558 | 0.458761476200800 | 0.094898173917642 |
| 5 | 0.446303626018198 | 0.458696516686345 | 0.094999857295457 |
| 6 | 0.446278569838877 | 0.458652718825324 | 0.095068711335799 |
| 7 | 0.446260393499810 | 0.458621195423935 | 0.095118411076256 |
| 8 | 0.446246609343597 | 0.458597422632763 | 0.095155968023641 |
| 9 | 0.446235798628453 | 0.458578855758138 | 0.095185345613408 |
| 10 | 0.446227093692859 | 0.458563953917737 | 0.095208952389404 |
| 11 | 0.446219934286584 | 0.458551729606354 | 0.095228336107061 |
| 12 | 0.446213942593194 | 0.458541520787272 | 0.095244536619534 |
The next table shows the expected return of each outcome by number of decks. Note how as the number of decks increase, the expected value of the Player and Tie bets increase and the Banker bet decreases.
Expected Returns
| Decks | Player | Banker | Tie |
|---|---|---|---|
| 1 | -0.012863724868016 | -0.010117482890592 | -0.157461269286765 |
| 2 | -0.012564583729237 | -0.010389052998346 | -0.150227968366401 |
| 3 | -0.012468518648366 | -0.010474869168131 | -0.147402946103443 |
| 4 | -0.012421126319243 | -0.010516947490797 | -0.145916434741219 |
| 5 | -0.012392890668147 | -0.010541935166171 | -0.145001284340884 |
| 6 | -0.012374148986447 | -0.010558486954819 | -0.144381597977809 |
| 7 | -0.012360801924125 | -0.010570257847072 | -0.143934300313697 |
| 8 | -0.012350813289166 | -0.010579057842472 | -0.143596287787236 |
| 9 | -0.012343057129685 | -0.010585885658222 | -0.143331889479325 |
| 10 | -0.012336860224877 | -0.010591337471010 | -0.143119428495365 |
| 11 | -0.012331795319770 | -0.010595791160548 | -0.142944975036449 |
| 12 | -0.012327578194079 | -0.010599497845285 | -0.142799170424194 |
Pair Bets
The next set of tables are for the Player Pair and Banker Pair bets. The expected value table is based on the usual win of 11 to 1. This next table shows the number of combination of winning and losing by number of decks.
Pair Bets Combinations
Wizard Of Odds Baccarat
| Decks | Win | Loss | Total |
|---|---|---|---|
| 1 | 78 | 1,248 | 1,326 |
| 2 | 364 | 4,992 | 5,356 |
| 3 | 858 | 11,232 | 12,090 |
| 4 | 1,560 | 19,968 | 21,528 |
| 5 | 2,470 | 31,200 | 33,670 |
| 6 | 3,588 | 44,928 | 48,516 |
| 7 | 4,914 | 61,152 | 66,066 |
| 8 | 6,448 | 79,872 | 86,320 |
| 9 | 8,190 | 101,088 | 109,278 |
| 10 | 10,140 | 124,800 | 134,940 |
| 11 | 12,298 | 151,008 | 163,306 |
| 12 | 14,664 | 179,712 | 194,376 |
The next table shows the probability of winning and losing by number of decks.
Pair Bet Probabilities
| Decks | Prob. Win | Prob. Loss |
|---|---|---|
| 1 | 0.058823529411765 | 0.941176470588235 |
| 2 | 0.067961165048544 | 0.932038834951456 |
| 3 | 0.070967741935484 | 0.929032258064516 |
| 4 | 0.072463768115942 | 0.927536231884058 |
| 5 | 0.073359073359073 | 0.926640926640927 |
| 6 | 0.073954983922830 | 0.926045016077170 |
| 7 | 0.074380165289256 | 0.925619834710744 |
| 8 | 0.074698795180723 | 0.925301204819277 |
| 9 | 0.074946466809422 | 0.925053533190578 |
| 10 | 0.075144508670520 | 0.924855491329480 |
| 11 | 0.075306479859895 | 0.924693520140105 |
| 12 | 0.075441412520064 | 0.924558587479936 |
The next table shows the expected return by number of decks. As you can see, as the number of decks increase, so does the expected value. This should be obvious, because as the number of decks increases, the effect of removal becomes less significant.
Pair Bet Expected Returns
| Decks | Expected Return |
|---|---|
| 1 | -0.294117647058823 |
| 2 | -0.184466019417476 |
| 3 | -0.148387096774194 |
| 4 | -0.130434782608696 |
| 5 | -0.119691119691120 |
| 6 | -0.112540192926045 |
| 7 | -0.107438016528926 |
| 8 | -0.103614457831325 |
| 9 | -0.100642398286938 |
| 10 | -0.098265895953757 |
| 11 | -0.096322241681261 |
| 12 | -0.094703049759230 |
Written by: Michael Shackleford
Home > Casino Game Odds > Baccarat
Baccarat is a casino game that offers relatively good odds for players. Playing the game is fairly simple because there are only three different wagering options, and each hand is played according to a fixed set of rules. Read more to learn which bet offes the best odds - you may be surprised.
Article Highlights:
Types of Bets Betting Odds
casino: Red Flush Baccarat is popular with players because of its simple betting options, fast gameplay, and favorable odds. |
Types Of Bets
To the first-time player, baccarat may seem like an intimidating game reserved only for those sophisticated enough to understand its nuances. While it is a popular game amongst high stakes players, it actually is quite simple to play. A player is responsible for making only one decision, whether to put their chips in the table area marked 'Player', 'Banker', or 'Tie'.
Odd Baccarat Pieces
Betting Odds
| Bet | House Edge |
| Player | |
| Banker | 1.17% |
| Tie |
The rules of play in baccarat have been carefully constructed to produce a small, yet measurable advantage for the house for both player and banker bets, and a steep jump in advantage for tie bets. Complex calculations are used to determine that the banker will win 50.68% of all non-tie hands and the player 49.32%. Using 100 credits worth of bets against these percentages shows that you can expect to lose 50.68 and win 49.32. The difference between the two is 1.36, hence a 1.36 house edge against the 'player' bet.
So why then does the banker bet offer no real house advantage if it wins more than half of the time (50.68%)? Well, casinos are definitely aware of this advantage. If they allowed the game to be played while giving up an edge to players, they wouldn't make any money. Casinos have taken this odds discrepancy into account, and made adjustments to tilt the advantage back into their favor by way of a 5% commission on winning banker bets.
The banker bet odds can be calculated as follows: let's say you are wagering 100 credits. Taking into account the 5% commission on winning banker bets, you will win 0.95 credits for every one credit wagered. Expecting to win 50.68% of the time, multiply 0.95 by 50.68 and you get 48.15. You still can expect to lose 49.32, and the difference is 1.17, resulting in a 1.17% house advantage.
Tie bets happen approximately 9.55% of the time, meaning the true odds of a tie bet are 9.47 to 1. Dividing 9.55 into 100 gives us 10.47 and taking into account the fact that you will receive your original wager back, the proper odds are 9.47 to 1. So, winning a tie bet should have you winding up with 10.47 credits, but instead you wind up with 9. Dividing the difference, 1.47, into 10.47 gives the house a 14.4% advantage. You might be tempted by the 8 to 1 payout, but the odds on this bet are unfavorable compared to the banker and player bets. Logic dictates that despite the 5% commission attached to winning the banker bet, it still offers the most favorable odds in baccarat, and over time you can expect to lose less by utilising this option.
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