What is Dice Probability
The dice odds are what make these games worth playing. However, the trick is learning how to calculate when the chance is in your favor and when it isn't. Often, players are under the mistaken impression that they need extremely high odds in craps and other games to make money. That obviously isn't the case as evidenced by the fact that casinos make money on a game with just a 0.7% house edge.
Calculating Craps Odds
Craps odds are simply the ratio of winning rolls to the total number of remaining possible outcomes. So, the chance of getting any number using a normal die is 5 to 1. That means that if you bet on any number coming up and are paid 4 to 1 then you are at a disadvantage, when playing at casinos this is known as the house edge. However, the craps odds are some of the best in the casino and if you are able to play close to optimal strategy you stand to win more than you lose.
The dice probability for any roll of a single six sided die is easy to work out since there are only six possible outcomes. However, anytime you add another die the outcome is multiplied by an additional six making the dice odds a bit trickier to calculate. So, if you have two dice then the possible outcome jumps to 36 and a game with three dice gives you an unbelievable 216 outcomes. If you want to see the odds of a certain total coming up you have to determine how many possible combinations will give you that total and subtract that amount from the total possible outcomes. The number of combinations vs. the number of outcomes gives you the odds.
Just to illustrate we'll calculate the craps odds of getting a total of 7 when throwing two dice. There are six combinations that will equal 7 when you have two dice. They are a 1&6, 2&5, 3&4, 4&3, 5&2 and 6&1. Since there are 36 possible outcomes with two dice our odds of getting a total of seven is 30 to 6, since 36 possible outcomes minus 6 ways to get a seven equals 30. This is then simplified as odds of 5:1.
Contrary to popular belief the odds in craps of getting a certain result are always the same on each time the dice are thrown. Just because you've rolled a double six the last five times in a row doesn't change the dice probability. While it seems less likely to see a long run of the same numbers coming up it does happen. The odds will work out to their proper ratio over time and casinos know this. That's why they pay the way they do for certain combinations. The law of averages does apply and while you might not always be at the casino long enough to see that it doesn't make it any less true.