How Many Decks In Baccarat

How
  • Appendices
  • Baccarat Analysis
  • Miscellaneous

Introduction

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 Default Baccarat Strategy and When to Deviate. Let’s assume that we have an eight-deck game since that is the most common. The default strategy for Baccarat will be to place a bet on the banker’s hand while looking out for certain conditions that will indicate to us that we should switch to the player’s hand. Edge sorting has many characteristics of legal advantage play, making it comparable to card counting, shuffle tracking, sequencing, roulette wheel bias, and video poker (on +EV games). Here are steps on how to effectively use edge sorting in baccarat: Some card decks have small irregularities on the long-side edges.

The first thing to realize about baccarat is that most casinos allow very deep deck penetration. In most cases, the dealer makes it almost to the end of an eight-deck shoe. This deck penetration is significant when considering that you stand to win more money as a counter upon seeing additional cards. Deck007 was right about Commission Free Baccarat, because Asian gamble friends told me CFB is popular in Singapore. WOO show the 8 deck data here Commission Free Baccarat - 8 decks HE for B8 = 1.46%. I wonder what the house edges for 6 decks CFB is.

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

DecksPlayerBankerTieTotal
16,548,674,4326,737,232,6401,372,227,32814,658,134,400
2487,816,735,232501,543,728,128103,154,274,2401,092,514,737,600
35,837,305,562,4966,000,349,195,0081,238,768,922,81613,076,423,680,320
433,608,344,225,79234,543,624,867,8407,145,601,996,92875,297,571,090,560
5130,087,780,016,000133,700,037,548,80027,690,387,926,400291,478,205,491,200
6392,220,492,728,832403,095,751,234,56083,552,962,932,288878,869,206,895,680
7995,884,732,700,0321,023,469,376,328,440212,268,385,833,2802,231,622,494,861,750
82,230,518,282,592,2502,292,252,566,437,880475,627,426,473,2164,998,398,275,503,350
94,540,095,442,933,6304,665,676,262,757,120968,435,421,769,72810,174,207,127,460,500
108,570,454,841,408,0008,807,402,586,035,2001,828,629,499,384,00019,206,486,926,827,200
1115,222,978,065,896,80015,643,682,376,129,2003,248,754,169,011,64034,115,414,611,037,600
1225,714,619,121,272,80026,425,038,379,143,1005,488,795,281,294,72057,628,452,781,710,600

How Many Decks In Blackjack At Foxwoods

The next table shows the probability of each outcome by number of decks.

Decks

Probabilities

DecksPlayerBankerTie
10.4467604303041460.4596241551721620.093615414523693
20.4465081508224040.4590727345516410.094419114625955
30.4463992376815640.4588677563299300.094733005988506
40.4463403498815580.4587614762008000.094898173917642
50.4463036260181980.4586965166863450.094999857295457
60.4462785698388770.4586527188253240.095068711335799
70.4462603934998100.4586211954239350.095118411076256
80.4462466093435970.4585974226327630.095155968023641
90.4462357986284530.4585788557581380.095185345613408
100.4462270936928590.4585639539177370.095208952389404
110.4462199342865840.4585517296063540.095228336107061
120.4462139425931940.4585415207872720.095244536619534

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

DecksPlayerBankerTie
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
Decks

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

DecksWinLossTotal
1781,2481,326
23644,9925,356
385811,23212,090
41,56019,96821,528
52,47031,20033,670
63,58844,92848,516
74,91461,15266,066
86,44879,87286,320
98,190101,088109,278
1010,140124,800134,940
1112,298151,008163,306
1214,664179,712194,376

The next table shows the probability of winning and losing by number of decks.

Pair Bet Probabilities

DecksProb. WinProb. Loss
10.0588235294117650.941176470588235
20.0679611650485440.932038834951456
30.0709677419354840.929032258064516
40.0724637681159420.927536231884058
50.0733590733590730.926640926640927
60.0739549839228300.926045016077170
70.0743801652892560.925619834710744
80.0746987951807230.925301204819277
90.0749464668094220.925053533190578
100.0751445086705200.924855491329480
110.0753064798598950.924693520140105
120.0754414125200640.924558587479936

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

DecksExpected 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
Baccarat

How Many Decks In Baccarat

Written by: Michael Shackleford
Comments are closed.