Craps House Edge and Odds

An In-Depth Look at the House Edge and Odds of Craps

Craps is one of the most popular dice games in the world, with a rich history that can be traced back to the Roman Empire. Its dynamic pace of play and wide range of betting options have made craps a staple at both online casinos and land-based gambling establishments.

Because craps relies heavily on chance and there is no way to control the outcome of a fair dice toss, many inexperienced players wrongly assume that it is an easy game to play. This is not necessarily true, as the sheer number of betting options can overwhelm any craps novice. While players cannot predict the outcome of the dice with certainty, they can make better-informed decisions by learning the different bet types and the possible dice combinations. Understanding the house edge, true odds, and payouts can help craps players compare wagers more effectively. With this in mind, our team has prepared the comprehensive guide below, which explains how odds and the house edge influence the game.

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Dice Combinations

House Edge

True Odds Calculations

Craps Bet Payouts

Understanding the House Edge

Gambling establishments do not generate profits because their personnel outplay customers. Instead, casino profits result from the built-in mathematical advantage the games provide over time. This advantage is referred to as the “house edge” and is something inexperienced players should understand before joining a craps table.

All casino games are tilted in favor of the house, which relies on its long-term mathematical advantage over players. The house edge is typically expressed as a percentage and represents the casino’s expected average profit from each wager. This does not mean that the casino profits from every individual bet. Instead, the percentage reflects the expected outcome over a large number of wagers.

As mentioned earlier, craps offers many different bets. More importantly, the house edge varies considerably between bet types. On some craps wagers, specifically odds bets, the house edge drops to zero, while on others, the house’s advantage reaches double digits. That is why knowledgeable players typically choose bets with a lower house edge, which can reduce their expected losses over time.

Let us demonstrate how the house edge works with an example. Pass Line bets have a relatively low house edge of 1.41%. This means that for every $100 wagered on the Pass Line over the long term, the casino expects to collect an average of $1.41. Individual players may win or lose during any given session, but the expected loss remains $1.41 per $100 wagered. Some players prefer to place Proposition bets because they offer higher payouts. However, this is not always a good idea, as the house edge for Proposition bets ranges from 5.56% to 16.67%.

Pass/Don’t Pass Line bets and Come/Don’t Come bets are generally considered smarter options, especially for inexperienced players. The casino’s advantage is smaller on these wagers, and their chances of winning are higher than those of many Proposition bets. As a result, these bets offer lower payouts and pay even money.

Players can take or lay odds behind qualifying line bets after the shooter establishes a point. Winning odds bets are paid at true odds. This causes the house edge on the odds portion of the wager to drop to 0%, making it the only craps bet on which the casino has no mathematical advantage. However, the original Pass, Don’t Pass, Come, or Don’t Come bet retains its standard house edge. The way winning bets are paid can also influence the casino’s advantage. When paying winning multiple-roll bets, the casino may round the sum down to the nearest whole betting unit.

Dice Combinations in Craps

To calculate the house edge on craps bets, players should become familiar with the possible dice combinations and the probability of rolling each total. Craps is played with two dice, and each die is a cube with six equal-sized sides. There are 11 possible totals from a two-die toss: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

The number of possible combinations is calculated by multiplying the number of sides on the two dice. Thus, 6 x 6 = 36, meaning there are 36 possible combinations, each producing one of the 11 totals listed above. You can see the dice combinations and their corresponding totals below.

It is easy to see that some totals have more possible combinations than others. There are more ways for the shooter to roll 7 than any other number, as shown by the diamond shape formed by the number of combinations. Since six dice combinations total 7, this number has the highest probability of being rolled. Players should consider this when deciding which bets to place at the craps table.

History of Craps

How to Play Craps

Craps Bet Types

Craps Strategy

How to Calculate the House Edge in Craps

As craps is a negative-expectation game, it is mathematically impossible for players to gain a long-term advantage over the house. The only exception is the odds portion of a bet when players take or lay odds. However, understanding the probability of rolling specific totals and the house edge on different bet types is essential, as it enables players to make better-informed betting decisions.

The two dice used in craps produce 11 possible totals, ranging from 2 to 12. There are 36 different ways for the shooter to roll these 11 totals. For example, a total of 3 can be rolled in two ways, meaning the probability of rolling this number is 2 in 36. Similarly, six different combinations add up to 7, so the probability of rolling this number is 6 in 36. The probability of rolling any other total can be calculated in the same way.

Once players understand how to calculate probability, they can proceed to calculate the house edge. An example can make this process clearer. The Craps 2 bet wins whenever a total of 2 appears on the next roll. In other words, there are 35 ways to lose and one way to win with this bet. If it wins, the payout is 30 to 1. Since there are only two possible results, a win or a loss, its expected value can be calculated as follows: (1/36) x 30 – (35/36) = -5/36 = -13.89%.

Other wagers, such as the Any Craps bet, have more winning combinations. The Any Craps bet pays 7 to 1 whenever 2, 3, or 12 is rolled. There is one combination for 2, two combinations for 3, and one combination for 12. Thus, there are four ways to win out of 36 possible combinations, so the probability of collecting a payout can be expressed as 4/36 = 1/9. This means that, on average, one out of every nine Any Craps bets will win, while the other eight will lose. The expected return for this bet can be expressed as follows: (4/36) x 7 – (32/36) = -4/36 = -1/9 = -11.11%.

As you can see, the house edge in craps varies considerably depending on the type of bet placed. For some wagers whose outcomes are determined by multiple dice rolls, calculating the built-in house advantage can be complex. Players who find these calculations difficult can instead memorize the house edge associated with each craps bet.

Understanding the True Odds

You may have noticed a discrepancy between the probability of winning specific bets and the way winnings are paid. This discrepancy is what gives the house its edge. The house maintains an advantage by paying less on winning bets than the true odds would dictate. For instance, Pass Line bets pay even money and have a house edge of 1.41%, which means players can expect to lose an average of $1.41 for every $100 wagered over the long term. The main exception is the free odds portion of a wager. When free odds are taken or laid, winnings on that portion are paid at true odds, so the house has no mathematical advantage on the odds bet itself.

You may wonder why players continue betting on craps when the game is tilted against them. The answer lies partly in distribution variance, which causes hot and cold streaks during repeated dice rolls. Short-term results can differ considerably from their expected mathematical distribution.

It is also important to remember that outcomes tend to approach their expected probabilities only over a large number of rolls. Many players remain at the craps table for relatively short periods. During these sessions, variance can result in either a profit or a loss. However, variance does not eliminate the house edge. Players should still choose their bets carefully, manage their bankroll properly, and understand the probabilities associated with different wagers.

• The Probability of Point Numbers in Craps

Players can use this table to compare the probability of winning Pass Odds and Don’t Pass Odds bets. They should remember that the probability favors the player only when laying a Don’t Pass Odds bet. When taking Pass Odds, the probability is against the player, although a winning wager receives a higher payout.

Crapless Craps is a variant of the casino classic worth considering. What makes this game stand out is that 2, 3, 11, and 12 can become point numbers during the come-out roll, along with 4, 5, 6, 8, 9, and 10. An essential detail is that players are paid at true odds when their odds bets win.

Still, choosing this craps variant might not be a player’s best option because the expected value of a $1 Pass Line bet is approximately 0.946176, making it significantly worse than the corresponding bet in regular craps. Players should also note that Don’t Pass bets are unavailable in such versions.

Independent Trials in Craps

One of the most important concepts for beginners to understand is that, much like roulette, craps is a game of independent trials. This means that the probability of rolling a specific dice combination does not change from one throw to the next. Even if 7 has appeared five times in a row or has not appeared for several rolls, the probability of rolling 7 on the next throw remains 16.67%.

Why do the odds remain the same in craps? Craps consists of independent events, meaning the outcome of the current roll does not depend on what happened during previous rolls. The dice have no memory. Even if a combination has appeared several times in a row or has not appeared for a while, the probability of rolling it on the next throw remains unchanged. In this respect, craps is similar to roulette, where previous spins have no effect on current or future spins of the wheel.

If a fair coin is flipped 10,000 times, its two possible outcomes are expected to occur roughly equally often, although the exact totals can vary. If one flip produces heads, the probability of getting heads on the next flip remains 50%. Each new coin flip is independent, meaning heads and tails remain equally likely.

Suppose you stake $1 on tails for each of 10,000 flips. If tails appears exactly 5,000 times and the bet pays even money, you will earn $5,000 from winning bets and lose $5,000 on the remaining bets, leaving you at the break-even point. As explained earlier, casinos generally do not pay all bets according to their true odds. Instead, they offer payouts that are slightly lower to preserve the house advantage. This is possible because casino payouts are slightly lower than true-odds payouts. If the house pays $0.95 in profit instead of $1 for each winning coin-flip bet, it retains the remaining $0.05. When the wager loses, the house collects the full $1 stake.

Now imagine betting on all 10,000 coin flips, which requires risking $10,000 in total. If exactly 5,000 bets win, the winning wagers generate $4,750 in profit, while the other 5,000 wagers lose $5,000. The result is a net loss of $250 because of the built-in house advantage.

Now let us return to craps. Because fair dice should produce random results, players cannot predict which possible outcome will appear next. The probability of rolling each combination remains the same on every throw. This would not be the case with biased dice. The same principle applies to online craps games, where outcomes are determined by a random number generator.

At this point, you may be wondering what you can do to minimize your expected losses and get the most out of your craps betting session. Because craps is a game of independent trials, no strategy or dice-throwing technique can change the mathematical probabilities. Players can, however, avoid bets with particularly high house edges. A Pass Line bet is one available alternative because its house edge is only 1.41%. Players can reduce the overall house edge further by placing odds behind qualifying bets.

The Payouts of Craps Bets

The large number of wagers available at a craps table can confuse inexperienced players. Because the probability of rolling specific totals varies, the payouts for different craps bets also differ. Pass/Don’t Pass Line and Come/Don’t Come bets pay even money because their chances of winning are higher than those of many other wagers. Proposition bets have lower chances of winning, so they offer higher payouts. The table below lists the payouts and house edges for the main bets in craps.