Odds for Dice Outcomes in Craps

When someone discusses craps odds, they’re discussing one of two things—the odds of rolling a certain number, or the payout for a particular bet. Odds are one way of describing a probability, but they’re also a way of describing how much a bet pays.

This page explains both types of craps odds. We refer to payout odds as the number that a bet pays off, and true odds as the probability that a given outcome will appear. The difference between the true odds and the payout odds is the house edge, which is the number that explains how the casinos stay so probable.

The Basics of Probability

Probability is that branch of mathematics that deals with the likelihood of something happening (or not happening). An event’s probability is always a number between 0 and 1, but that number can be expressed in multiple ways.

A simple example of a probability is a coin flip. The probability of the result being heads is 0.5, because half the time, that’s what will happen. 0.5 can be expressed also as 50%, ½, or 1 to 1.

That last expression of the probability is the one we’re most concerned with on this page, because that’s an expression of the odds.

The equation for calculating a probability is to divide the number of ways something can happen by the number of total ways it could happen. When rolling dice, you can calculate the odds of rolling a 1 by dividing 1 by 6. There are 6 possible outcomes, but the one you want to know is the chance of rolling a 1.

1/6 can also be expressed as 0.167 or 16.7% or 5 to 1. When expressing a probability as odds, you compare the number of ways something won’t happen with the number of ways something can happen. There’s only 1 way to roll a 1 on a single die, but there are 5 ways to roll something else, so the odds are 5 to 1.

When you’re calculating multiple probabilities, you add the probabilities together when you want to know the odds of event A OR event B happening. You multiple them by each other when you want to know the odds of event A AND event B happening.

For example, if you want to calculate the probability of rolling a total of 2 on 2 dice, you would multiply the probabilities of rolling a 1 on the first die by the probability of rolling a 1 on the second die. 1/6 X 1/6 = 1/36, which can be represented as odds of 35 to 1. (You’re calculating the odds of rolling a 1 on die A AND the odds of rolling a 1 on die B.)

On the other hand, if you wanted to know the probability of rolling a 1 on either of the two dice, you’d ADD the two probabilities together, and you’d get a result of 1/6 + 1/6, or 2/6, which can be reduce to 1/3. That would be expressed in odds as 2 to 1.

True Odds

When you discuss the odds of something happening, you’re discussing the true odds, or the probability, that something will happen. The difference between the true odds and the payout odds is what creates an edge for the casino. Casinos wouldn’t make a profit if they paid bets off at their true odds; they’d only break even. And like any other business, casinos exist to make a profit.

Payout Odds

So every bet in a casino pays out at less than true odds, except for one, which we’ll discuss later. For example, if you make a bet on something that has a 3 to 1 chance of happening, and the casino pays out at 2 to 1 on that bet, the casino will make a profit in the long run.

Suppose in a mathematically perfect simulation that you place four bets of $1 each on something that has a probability of occurring of 3 to 1. You would win once and lose three times. If you lose $1 on your three losses, and you win $2 on your single win, how much money did you net? You lost $1.

For every dollar that you wagered in that scenario, you lost an average of 25 cents.

That’s the house edge in a nutshell.

The House Edge

The house edge is usually expressed as a percentage of each bet that you can expect to lose over the long run. In the example above, the house edge was 25%, which is huge.

The house edge on most casino games is between 1% and 10%, but in craps, you’ll find some of the best bets and some of the worst bets in the casino.

The Best Odds in Craps

The best bets at the craps table are the ones with the lowest house edge, and luckily, those are also the simplest bets you can make. These bets include the pass bet, the don’t pass bet, the come bet, the don’t come bet, taking odds, and laying odds.

The house edge on the pass bet and the come bet is 1.41%, which means that for every $100 you wager, you should expect to lose, in the long run, an average of $1.41.

The house edge on the don’t pass and the don’t come bet is 1.36%, which means that for every $100 you wager, you should expect to lose, in the long run, an average of $1.36.

When you take odds or lay odds, your bet pays out at true odds. This means the house edge is 0, making this the best bet in the casino. The only catch is that in order to take or lay odds, you have to make a pass or don’t pass bet first.

The Worst Odds in Craps

The worst bets at the craps table are the complicated bets. They have the highest house edge, and when we say the house edge is high, we mean that it’s staggering.

The craps table features countless proposition bets of varying complexity, but here are a few examples of bets with bad odds in craps.

The Big 6 and Big 8 bets offer a house edge of 9.09%. That’s absurd when you consider that you can place the same bet as a “place bet” and only face a house edge of, at most, 6.67%.

Hardway bets also offer lousy odds. The house edge is either 9.09% or 11.11%, depending on which hard total you’re wagering on.

The Any Seven bet is another doozy. The house edge on this one is a whopping 16.67%.

Any time you find a game with bets with a house edge that ranges between 1.36% and 16.67%, you should educate yourself about which bets are offer the best odds and which ones offer the worst odds.