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Exact Winning Side and Total in Baccarat

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Introduction

Some baccarat games offer side bets on the exact winning side (or tie) and the winning (or tieing total) total. The image below shows an example of such bets as seen on an electronic table game at the 2024 Global Gaming Expo.

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Analysis

The following table shows the number of combinations of all 28 possible combinations of winning side and total (including ties).

Total Player Win Banker Win Tie
9 613,074,020,540,416 586,850,279,002,112 55,146,054,060,032
8 555,823,197,134,848 529,914,458,673,152 54,879,416,675,072
7 408,043,979,470,848 384,279,324,919,808 101,717,538,899,968
6 312,658,895,192,064 269,232,304,455,680 96,170,001,308,416
5 122,838,277,197,824 216,715,928,915,968 39,684,046,743,808
4 86,165,771,096,064 163,359,790,133,248 36,294,133,463,040
3 62,946,423,310,336 72,927,778,568,192 22,250,510,129,408
2 44,328,525,111,296 44,681,581,871,104 20,006,606,104,576
1 24,639,193,538,560 24,291,119,898,624 20,499,217,668,352
0 0 0 28,979,901,420,544
Total 2,230,518,282,592,260 2,292,252,566,437,890 475,627,426,473,216

The next table shows the probability of the 28 possible outcomes listed above.

Total Player Win Banker Win Tie
9 0.122654 0.117408 0.011033
8 0.111200 0.106017 0.010979
7 0.081635 0.076880 0.020350
6 0.062552 0.053864 0.019240
5 0.024576 0.043357 0.007939
4 0.017239 0.032682 0.007261
3 0.012593 0.014590 0.004452
2 0.008869 0.008939 0.004003
1 0.004929 0.004860 0.004101
0 0.000000 0.000000 0.005798
Total 0.446247 0.458597 0.095156

The next table shows the fair odds on a "to one" basis for all 28 bets above. In other words, these are what a bet should pay to have zero house advantage.

Total Player Win Banker Win Tie
9 7.15 7.52 89.64
8 7.99 8.43 90.08
7 11.25 12.01 48.14
6 14.99 17.57 50.97
5 39.69 22.06 124.95
4 57.01 29.60 136.72
3 78.41 67.54 223.64
2 111.76 110.87 248.84
1 201.86 204.77 242.83
0     171.48

The next table shows the actual pays based on the image shown above.

Total Player Win Banker Win Tie
9 6 7 77
8 7 7.5 77
7 10 10.5 41
6 13 15 44
5 34 19 107
4 49 26 117
3 67 58 190
2 95 95 212
1 172 174 207
0     146

The next table shows the house advantage based on the pay table above.

Total Player Win Banker Win Tie
9 14.14% 6.07% 13.94%
8 11.04% 9.89% 14.36%
7 10.20% 11.59% 14.53%
6 12.43% 13.82% 13.42%
5 13.99% 13.29% 14.25%
4 13.81% 11.76% 14.32%
3 14.37% 13.92% 14.98%
2 14.86% 14.18% 14.74%
1 14.72% 14.95% 14.70%
0     14.77%

For any other pays, I will let you do that math for yourself. I will present two different formulas to get the house advantage.

Key:
F = Fair odds (on "to one" basis)
A = Actual odds (on "to one" basis)
P = Probability of winning

  • Method 1 — 1 - (A+1)×P
  • Method 2 — (F-A)/(F+1)

Note that method 2 doesn't require knowing P explicitly.

Let's look at the case of a winning Player total of 9, for example. In this case the variables equal:

Key:
F = 7.153009
A = 6
P = 0.122654

  • Method 1 — 1 - (6+1)×0.122654 = 14.14%
  • Method 2 — (7.153009-6)/(7.153009+1) = 14.14%

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