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Wizard
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Wizard
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December 27th, 2016 at 3:45:19 PM permalink
Lately I've been asked for the odds in baccarat for unusual numbers of decks. I think they are doing a 12-deck shoe somewhere in Singapore but I think I've heard of other numbers being used somewhere. Baccarat math is pretty easy so I threw together this page -- Baccarat Odds for 1 to 12 Decks. Please have a look and let me know what you think. As always, I welcome questions, comments, and especially suggestions.

The question for the poll is which statements do you agree with? Multiple votes allowed.
It's not whether you win or lose; it's whether or not you had a good bet.
ThatDonGuy
ThatDonGuy
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December 27th, 2016 at 4:39:55 PM permalink
Side note: Seinfeld may have stolen the joke from BBC's Brain of Britain radio series. In the early 1990s, somebody was asked the question, "The Three Tenors performed in Rome the night before the 1990 World Cup final; who are they?", and the contestant replied, "I know two of them, but have no idea who the third one is."
JB
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JB
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December 27th, 2016 at 4:49:15 PM permalink
I'm not sure Microsoft deserves the blame for the 15-digit limit. These are ultimately the limits of the IEEE-754 double-precision floating-point format (the "double" data type in C/C++/C#). However, given Microsoft's expertise, they could have implemented a greater precision for Excel. They did for C#, although operations on doubles are faster since they are performed by the CPU/FPU.
Wizard
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Wizard
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December 27th, 2016 at 5:00:56 PM permalink
Quote: JB

I'm not sure Microsoft deserves the blame for the 15-digit limit. These are ultimately the limits of the IEEE-754 double-precision floating-point format (the "double" data type in C/C++/C#). However, given Microsoft's expertise, they could have implemented a greater precision for Excel. They did for C#, although operations on doubles are faster since they are performed by the CPU/FPU.



In Visual Studio C++ you can declare an __int64 variable, which has obviously hold 64 bits instead of the usual 32. If declared as unsigned, it can reach values up to 18.4 quintillion, or 19-20 significant digits. I've heard Mathematica has accuracy to millions of decimal places.
It's not whether you win or lose; it's whether or not you had a good bet.
JB
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JB
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December 27th, 2016 at 5:18:57 PM permalink
My baccarat program uses 64-bit integers. If you're interested, here are the "pure" numbers for the ones that encountered the 15-digit limitation. For 10 decks, the numbers you have are already accurate.

Decks Player Banker Tie Total
7 995,884,732,700,032 1,023,469,376,328,448 212,268,385,833,280 2,231,622,494,861,760
8 2,230,518,282,592,256 2,292,252,566,437,888 475,627,426,473,216 4,998,398,275,503,360
9 4,540,095,442,933,632 4,665,676,262,757,120 968,435,421,769,728 10,174,207,127,460,480
11 15,222,978,065,896,832 15,643,682,376,129,280 3,248,754,169,011,648 34,115,414,611,037,760
12 25,714,619,121,272,832 26,425,038,379,143,168 5,488,795,281,294,720 57,628,452,781,710,720
Wizard
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Wizard
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December 27th, 2016 at 6:13:39 PM permalink
Mine does too. However, when copying and pasting into Excel, you lose everything after 15 or 16 digits. I could copy and paste the exact numbers into the HTML but I'm hoping Bill Gates will stumble on the page and then see to it the necessary improvements are made.
It's not whether you win or lose; it's whether or not you had a good bet.
greenberry26
greenberry26
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September 27th, 2019 at 9:29:56 AM permalink
Hi, sorry to activate this thread. I've seen your page on the odds for 1 to 12 decks, however, I am interested in the number of combinations per Banker or Player result (e.g. how many combinations are there where the Banker wins on 6 in a 10-deck shoe?). I am particularly interested in a 10-deck shoe. I'm guessing this is an easy computation for you, so hoping you have this stored somewhere. Thanks!
ThatDonGuy
ThatDonGuy
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September 27th, 2019 at 6:41:43 PM permalink
Here's what I get:

Player wins with 194,780,865,497,600
Player wins with 2170,472,431,654,400
Player wins with 3241,940,928,643,200
Player wins with 4331,273,378,771,200
Player wins with 5472,005,527,200,000
Player wins with 61,201,685,065,446,400
Player wins with 71,567,353,547,491,200
Player wins with 82,136,206,001,932,800
Player wins with 92,354,737,094,771,200
Bank wins with 193,430,787,264,000
Bank wins with 2171,863,109,990,400
Bank wins with 3280,263,170,428,800
Bank wins with 4627,932,444,051,200
Bank wins with 5832,427,227,372,800
Bank wins with 61,034,753,540,582,400
Bank wins with 71,476,066,627,996,800
Bank wins with 82,036,595,696,595,200
Bank wins with 92,254,069,981,753,600
0-0 tie111,707,735,539,200
1-1 tie78,765,726,769,600
2-2 tie76,959,284,304,000
3-3 tie85,486,205,284,800
4-4 tie139,569,561,609,600
5-5 tie152,433,381,867,200
6-6 tie369,912,808,987,200
7-7 tie390,759,532,380,800
8-8 tie211,152,814,804,800
9-9 tie211,882,447,836,800



I have the feeling the one number you are really interested in is:
If a Banker win with 6 is a push, the house edge on Banker is 4.153835%
greenberry26
greenberry26
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September 28th, 2019 at 5:37:28 PM permalink
This is awesome, thanks!

Actually, interested in each of the individual outcomes as there are different variants in my region, such as Super Six and Baccarat 27.

If you would have the counts for Player and Banker naturals, that would be great too!

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