Baccarat Odds

I was recently in Las Vegas for COMDEX, and I enjoyed walking around the various casinos looking at all of the action. One of the most interesting games that I could see was Baccarat. In short, you place a bet on one of three exclusive outcomes---"bank," "player," or "tie"---before any cards are even played!

The game unfolds in a completely deterministic way as cards are drawn from the shoe, and one of the above three outcomes is selected. In other words, you place a bet, and everything goes on from there with no further intervention on your part.

I wrote a small Monte-Carlo program that plays fifty million hands of Baccarat with a shoe of eight decks.

Outcome	Probability	Return
Bank	B=45.86346%	0.95:1
Player	P=44.61371%	1:1
Tie	T=9.52283%	9:1

Now that we know the probability of the hands, as well as their returns, we can now calculate our losses per hand if we sit at the Baccarat table:

We bet	Loss per hand	Why?
Bank	1.04%	= 0.95B+(-1)P+0T
Player	1.24%	=(-1)B+1P+0T
Tie	4.77%	=(-1)B+(-1)P+9T

(Note that if we bet on "player" or "bank" and a tie takes place, we get to keep our money; this helps our odds tremendously.) Betting on "tie" is foolish even with 9:1 odds, and some casinos apparently offer 8:1 (and our loss per hand is stunning 14.29%).

So, it seems that one should only bet "bank" and lose money as slowly as possible. But don't lose everything---you need to have some money left to see a show like Mystere.

WARNING: READ SOME OTHER SOURCES ON THE MATHEMATICS OF BACCARAT TO BE SURE THAT THIS IS RIGHT! It seems that mathematicians and statisticians have done lots of work to study casino games, but I have not yet had a chance to read any of their works.

Kleanthes Koniaris, email.