The Probability of Winning in Craps - What are the odds?

Craps is like a lot of casino games in that it is very useful to understand basic mathematics in order to play it. Mathematics equates to probabilities, and there is nothing about seeking out "hot shooters" at the table that has any real sound mathematical basis. Could the shooters themselves even explain logically what has made them so hot?

How about the "law of averages"? Allegedly that's very strong. It's supposed to mean that if a ten was rolled, then a five, then a nine, that series of rolls might somehow increase the possibility that a 7 will be rolled next, because it's "due."

This sounds like it makes a lot of sense, but the world of numbers doesn't really work that way.

If you want to talk about pure mathematics, just because a number has been rolled, it doesn't mean there is less of a percentage chance that it is going to be rolled next time. In fact, when you hear that "the dice have no memory" you need to believe it, because there is a lot of validity to it.

When we talk about math, craps games operate on the basis of "independent trials," which means that the occurrence of one event has no bearing on the probability that any subsequent event will result. The odds are 5 to 1 that if someone picks up a pair of dice they're going to roll a 7, and it's going to be 5 to 1 every time those dice are thrown, no matter how many times a seven comes out. Each and every event is separate.

There is indeed a major difference between playing craps and playing blackjack in the casino. When cards get removed from the deck in blackjack, they are generally removed from play (in cases where automatic shufflers are used, of course).

Certainly that has a bearing on which cards can come up next. That's a principle on which card counting is based, because this is the kind of activity that changes the odds each time a card is dealt. In craps, keep in mind that you are not removing any possibilities from play, so consequently the odds don't change. The odds on all the bets are the same, every time.

For purposes of our discussion today, this is pertinent, because for one thing, it doesn't really matter where you enter the game; if you have learned anything about craps you will know the odds on each of the bets. What anyone else is doing at the table doesn't change what the probability of your bet winning is going to be.

Also, coming to this understanding really makes the game simpler for you, because you don't have to be concerned with learning craps strategies for deriving an "edge" over the casino; this may be bad news for some of you, but because of the probabilities that exist in the game, that edge doesn't exist and can't be overcome by certain playing and betting techniques. Each of the available craps wagers carries an advantage to the house that is basically built-in; if you want to only place bets in which you are giving up less than 2% to the house, you can do that regardless of what is going on around you.

This is the case whether you believe the law of averages has an effect on the probability of certain rolls or not.