Recently, A friend of mine tell me something about "Baccarat"a hot game of gambling.and he want to know some way to play it that can win more money. and he guess that math can help to do this. But I don't know anything about this, and I don't know the difficulty level. Where can I find some material about the reasearch of Baccarat from the math viewpoint...? Thanks very much
closed as off topic by Pete L. Clark, Qiaochu Yuan, S. Carnahan♦, Anton Geraschenko Jan 16 '10 at 15:09
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6$\begingroup$ As in all casino games, the expected value of baccarat is negative. This means that the best strategy is never to play: any other strategy will result in a loss of money in the longrun. This is not an appropriate MO question, as only highschool level mathematics is involved. $\endgroup$ – Pete L. Clark Jan 16 '10 at 5:43
Counting cards is possible, but extremely ineffective in baccarat.
In blackjack with n decks, you might model the game as starting out with a house advantage of 0.5%1% while each card might affect the house advantage by + 0.5%/m, where m≤n is the number of 52 card decks left in the shoe. So, it's not terribly unlikely that you reach a situation in which the deck is in your favor, although casinos try to shuffle before too many cards are dealt. If you try to monitor the deck's composition and bet more when it is in your favor, then you are counting cards, and you can obtain an advantage. Favorable decks are common enough that you can win at blackjack (until the casino notices and bars you) while varying your bet size by a relatively small amount, e.g., a factor of 4, although this depends on many other specifics such as how far into the decks are dealt before the decks are shuffled.
The problem with baccarat is that card removal has a much lower effect on the house edge. This means you would often have no advantage at any point in the shoe, and you would wait for a vary small advantage. I don't think anyone does it seriously, unlike blackjack.
See The Wizard of Odds on counting in baccarat which contains this comment:
"I hope this section shows that for all practical purposes baccarat is not a countable game. For more information on a similar experiment I would recomment The Theory of Blackjack by Peter A. Griffin. Although the book is mainly devoted to blackjack he has part of a chapter titled 'Can Baccarat Be Beaten?' on pages 216 to 223. Griffin concludes by saying that even in Atlantic City, with a more liberal shuffle point than Las Vegas, the player betting $1000 in positive expectation hands can expect to profit 70 cents an hour."
This assumes you are making no bets, but are keeping perfect count, and then jump in with the occasional $1000 bets on 1 hand out of 500.

2$\begingroup$ I'm not sure we should encourage this kind of question with an answer, but I'll see what others have to say. $\endgroup$ – Pete L. Clark Jan 16 '10 at 7:02

$\begingroup$ I'm indifferent to whether the question is found to be off topic or too simple. However, I think most mathematicians are not aware of how simple the model can be for counting cards, and there can be some interesting mathematics involved in analyzing its effectiveness. $\endgroup$ – Douglas Zare Jan 16 '10 at 7:22

$\begingroup$ I'm somewhere between the two comments: I think that there is some interesting mathematics involved in analyzing gambling strategies (there's interesting mathematics involved in many things) but I'm not sure this question is the sort of one to bring it out. The question also feels a bit like Stone Soup ( en.wikipedia.org/wiki/Stone_soup ) although that's just my personal taste $\endgroup$ – Yemon Choi Jan 16 '10 at 14:51