Baccarat Odds for 1 to 12 Decks

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.

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."

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.

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.

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

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.

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!

Here's what I get:

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%

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!