Craps

In brief

Craps is a casino game played with two dice. One player, the "shooter", throws the dice, and everyone at the table bets on the outcome of those throws, against the house. Only the sum of the two dice counts. The game has many bets, with very different house edges: from the odds bet, on which the house has no edge at all, to some one-roll bets, with house edges among the highest in the room.

The table and the shooter

A craps table is long, with high rails, and the betting layout is repeated at both ends. The game is run by a crew of dealers: one moves the dice with a long stick and calls the results, the others collect and pay the bets. The role of shooter passes from one player to the next, usually clockwise. The shooter picks two dice from those offered and, in most venues, must throw them so that they reach the far wall of the table, so that the throw stays random.

The sums of two dice

Two dice give 36 equally likely combinations. The sums, however, are not equally likely, because some can be made in more ways than others: 7 comes from six combinations (1 and 6, 2 and 5, 3 and 4, each in both orders), while 2 and 12 come from only one.

Seven is the most frequent sum, with a probability of 16.67%. Almost all the mathematics of the game starts from this table.

The come-out roll and the point

A round starts with the come-out roll:

• 7 or 11: pass line bets win at once (a "natural");
• 2, 3 or 12: pass line bets lose ("craps");
• 4, 5, 6, 8, 9 or 10: the sum becomes the "point", which the dealer marks on the table with a puck.

Once the point is set, the shooter keeps rolling until one of two things happens: the point comes again and the pass line wins, or a 7 comes and the pass line loses. The other sums do not decide the pass line in this phase. When a 7 comes after the point is set (a "seven-out"), the shooter's turn ends and the dice pass to the next player. Otherwise the shooter keeps the dice, and once the pass line is decided, a new come-out roll follows.

Pass line and don't pass

The pass line is the basic bet, paid 1 to 1. Its chance of winning is 49.29% and the house edge is 1.41%. On the come-out roll the bet is favoured: it wins with 7 and 11 and loses only with 2, 3 and 12, which are rarer. Once the point is set, the situation reverses, because 7 is more likely than any point. With a point of 4, for example, only three combinations win, against the six of the 7. The two phases almost balance, but not completely, and the overall chance stays a little under one half.

Don't pass is the opposite bet. On the come-out roll it wins with 2 and 3, loses with 7 and 11, and a 12 is a push: the stake stays on the table, neither won nor lost. In some venues the push number is 2 instead of 12. After the point is set, don't pass wins if a 7 comes before the point. The house edge is 1.36%. The push on 12 is exactly what keeps the edge on the house side: without it, don't pass would be the perfect mirror of the pass line and would favour the player.

Come and don't come

The come bet works like the pass line, but is placed after the point has been set. For this bet the next roll acts as a come-out roll: 7 or 11 wins, 2, 3 or 12 loses, and any other sum becomes the bet's own point, and the dealer moves the bet to that number's box. Don't come is its mirror, under the don't pass rules. The house edges are the same as on the pass line and don't pass respectively.

The odds bet, paid at true odds

Once the point is set, a player with a pass line bet may place an extra bet behind it, called odds. It wins if the point comes before a 7 and is paid exactly according to the probabilities:

• 2 to 1 on points 4 and 10 (three combinations, against the six of the 7);
• 3 to 2 on points 5 and 9 (four combinations, against six);
• 6 to 5 on points 6 and 8 (five combinations, against six).

Because the payout matches the ratio of combinations exactly, the house edge on the odds bet is 0.00%. It is one of very few casino bets with no edge for the house. There is also a reverse form for players on the don't side ("laying odds"), paid at the inverse ratio. The odds bet can only be placed together with a pass line, don't pass, come or don't come bet, and each venue sets how large it may be, as a multiple of the main bet.

The odds bet lowers the house edge measured on the total staked, but it does not lower the average loss in money. That loss comes entirely from the main bet, which keeps its edge of 1.41%. Added to the table, the odds bet only widens the spread of results.

Place bets

A place bet goes on one of the numbers 4, 5, 6, 8, 9 or 10 and wins if that number comes before a 7. Unlike the pass line, it does not depend on the come-out roll and can usually be placed or taken down almost at any time. The payouts are below true odds: 9 to 5 on 4 and 10, 7 to 5 on 5 and 9, 7 to 6 on 6 and 8. On 6 and 8 the house edge is 1.52%; on 5 and 9 it is higher, and on 4 and 10 higher still. Because of the 7 to 6 payout, stakes on 6 and 8 are usually placed in multiples of 6. In many venues place bets are not working on the come-out roll unless the player asks otherwise.

Field

The field is a one-roll bet: it wins if the next sum is 2, 3, 4, 9, 10, 11 or 12 and loses with 5, 6, 7 or 8. It pays 1 to 1, and 2 and 12 pay 2 to 1. Some venues pay 3 to 1 on one of them, which lowers the house edge. The winning sums are more numerous, but the losing ones, grouped around 7, can be made from more combinations than all the winning ones together, as the table above shows. With 2 to 1 payouts, the house edge is 5.56%.

Proposition bets

The proposition bets sit in the centre of the table and are handled by the stick dealer. Most are decided on a single roll. "Any seven" wins if the next roll is a 7 and pays 4 to 1. Its chance is 16.67%, and the payout is well below true odds, so the house edge reaches 16.67%.

The same area holds bets on 2, 3 or 12 ("any craps"), on a single sum such as 11 or 12, and the "hardways": a 4, 6, 8 or 10 made as a double (for example 3 and 3 for a 6) before a 7 or before the same sum made another way. Hardways are not necessarily decided in one roll. The house edges on these bets are generally high. On some layouts the payouts are written as "5 for 1", which includes the returned stake and means the same as "4 to 1".

The house edge at a glance

At the same table and with the same dice, the bets carry very different house edges. The dice and the probabilities are the same for everyone; the difference comes from the sums each bet picks and from its payout. Combining several bets does not cancel the edge of any of them: the player's average loss is the sum of the average losses of each bet. Apart from the odds bet, the edge stays with the house on every bet. The principle is explained in the article on the house edge and RTP.

Dice have no memory

Each roll is independent of the previous ones. A shooter who has made several points is not "on a streak", and after a long run without a 7, the chance of a 7 on the next roll is still 16.67%. The idea that a result "is due" after a long absence is a well-known error of reasoning, described in the article on the gambler's fallacy. Schemes that raise the stake after losses do not change the house edge either, as the article on betting systems shows.

Terms

• House edge: the share of each stake the house keeps on average.
• RTP: the share of stakes that returns to players on average.
• Variance: how widely results are spread around the average.