Craps

History

Craps developed from Hazard, which was a very similar gambling game, popular from the time of the Middle Ages. The young men in Chaucer's 'The Pardoner's Tale' (14th century), who set out to 'deal with' Death, after one of their comrades died, and who met him in circumstances they did not expect, were, we are told, given up to 'such folly as riotous living, Hazard, brothels and taverns'. Hazard continued to be very popular with gamblers throughout the 17th and 18th centuries. It was through Hazard that William Crockford made his fortune, and founded the gaming club that still bears his name in London, England. Born in 1775, the son of a London fishmonger, he at first followed his father's trade. He soon abandoned fish for gambling, however, and became a bookmaker, race-horse owner, and a partner in a gaming house (he is reported to have won £100,000 in 24 hours). In 1827 he opened his new gaming house, whose splendour dazzled contemporaries, and where the highest and most fashionable of London society gathered to take supper, and pass the night with wit and Hazard. Hazard was also common in New Orleans around 1800, where the rules were simplified to produce Craps, as it is played today.

Craps in a casino is played on a table like that shown in Figure 1.

Figure 1

There are many different styles of layout, but that in the illustration is typical, and will serve to describe the bets. Seated at the centre of the table (at the top in the diagram) will be the boxman, who controls the game and keeps watch on all transactions. Opposite him will be the stickman who handles the dice and looks after the betting on the centre section of the table. On each side of the boxman will be a dealer, who looks after all bets at his end of the table. The gamblers stand round the table to the left and right of the stickman, and use the casino's chips, which will usually vary in colour with the denomination.

The player who throws the dice is the shooter. He rolls the dice across the table so that they hit a backboard (which surrounds the table) before coming to rest. The first roll is known as his 'come-out' roll. The totals 7 and 11 are 'naturals', and, should either be thrown, the shooter wins immediately. The totals 2, 3 and 12 are 'craps', and mean that the shooter loses. Should any other total appear, it becomes the shooter's 'point', and the dealers at each end of the table place a marker in the box containing that number. The shooter then continues to roll the dice in an attempt to throw his point before he throws a 7. If he throws his point, he wins; if he throws a 7 he loses. Other totals do not count. A 7 therefore is a natural and a winner on the come-out roll, but a loser thereafter. Should the shooter win, the dice are said to 'pass', and a bet on this is called a 'right' bet. It is possible to bet that the dice 'don't pass' or 'miss out', and this is a 'wrong' bet.

On this simple base is built a complex betting structure. The game, however, remains one of chance only, and its main attraction to games players lies in examining the probabilities concerning the outcome of throwing two dice, and comparing them with the various odds offered against the bets allowed.

Total	Possible combinations										Number of ways			Odds against
2													1	35-1
3													2	17-1
4													3	11-1
5													4	8-1
6													5	31-5
7													6	5-1
8													5	31-5
9													4	8-1
10													3	11-1
11													2	17-1
12													1	35-1

Table 1 shows the 36 ways a pair of dice may fall, and lists the true odds against any total appearing. There are eight ways in which a shooter may come out with a natural 7 or 11, so that in the long run twice in every nine rolls the shooter will win immediately. There is a total of four ways in which the come-out roll may be a crap 2, 3 or 12, a loser for the shooter on one roll in nine. On the remaining six rolls in every nine, the shooter will make a point, and his chance of winning will vary with his point. To discover the shooter's overall chance of winning, a total of 1980 rolls must be considered to avoid fractions. Table 2 summarises these rolls.

Shooter's Probability of Passing

Thus, in the long run, of every 1980 come out rolls, the shooter will win 976 and lose 1004, and, since the bank offers even money for a pass bet, it will enjoy an advantage over the shooter of 1·414 per cent.

Using Table 2, it is possible to calculate the bank's percentage advantage in all the craps bets it will allow.

The bets and advantages are as follows:

Win, Do, Pass or Front Line. This is a bet that the shooter will pass, and the stake is placed on the space marked 'line' on the table. This line might on other tables be marked 'pass line' or 'win'. The odds offered are even money. As calculated above, the bank's advantage is 1·414 per cent.

Lose, Don't, Don't Pass or Back Line. This is a bet that the shooter will lose, and the stakes are placed on the 'Don't Pass' space. The odds are again even money. As there are more ways in which the shooter can lose than win, the bank must adjust the bet to retain its advantage. The 'Don't Pass' line in the illustration above states the adjustment: 'Bar 6 6'. This means that, if the shooter comes out with a double-6, 'don't pass' bets are void, and await a further throw. A double-6 will occur 55 times in the total of 1980 rolls listed in the table above, and, if these are barred, the shooter can lose only 949 times, while still winning 976 times, so the 'don't pass' bettor finds that the casino keeps its advantage, although it is slightly less, 1·403 per cent. Some casinos bar double-1 rather than double-6, and their advantage remains the same. Others bar 1, 2, which occurs twice as often as double-1 or double-6, and their advantage rises to 4·385 per cent.

Come. This is a bet made when the shooter has already established his point. It is the same as a 'pass' bet, except that the shooter's next roll will be considered as his come-out roll. The stake is placed in the box marked 'come'. If the shooter's next roll is a natural, the 'come' bettor wins immediately. Similarly he loses if the next roll is a crap. Alternatively, the next roll might establish a point for the 'come' bettor, in which case the dealer will move the stake to the appropriate point box. The bet is then the same as a 'pass' bet, except that the shooter and the 'come' bettor will have different points, and will win or lose at different times in the sequence of rolls. The odds offered are even money. The bank's advantage is, as for 'pass' bets, 1·414 per cent.

Don't Come. This bet is the opposite of a 'come' bet, made when the shooter has established his point. As with a 'don't pass' bet, the double-6 is barred (or the double-1 or 1, 2 as explained earlier). The 'don't come' stake is placed in the box marked 'don't come', and moved by the dealer to the blank square below the appropriate point square, when the shooter has made a new point for the 'don't come' bettor. The odds offered are evens. The casino's advantage is 1·403 per cent (or 4·385 per cent if the 1, 2 is barred).

Big Six and Big Eight. These are bets that a 6 or an 8 will appear before a 7, and the stakes are placed in the appropriate box. Reference to Table 1 shows that a 7 will be thrown six times to every five for a 6 or an 8. The odds offered are even money, so the bank enjoys an advantage of 9·091 per cent.

Field. This is a bet that any of a group of numbers will appear on the next roll. The stake is placed on the space marked 'Field' on the table. The group of numbers on the table in Figure 1 is 2, 3, 4, 9, 10, 11, 12. Table 1 shows that one of this group will appear 16 times in 36. The odds offered are even money, but to give the bettor a fairer bet, the double-6 and double-1 are paid double, i.e. at odds of 2-1. This means that the bettor on the field can expect a return of 34 chips for every 36 staked, an advantage to the bank of 5·556 per cent. The field varies, and some casinos will offer the 5 instead of the 4 in the field, but will not pay double on the double-1 and double-6. The bank's advantage remains the same.

Hardway. This is a bet that 4, 6, 8 or 10 will be made the hard way, i.e. by means of a double, before it is made any other way, or before a 7 is thrown. The bets are placed in the appropriate place in the centre of the table, where it will be seen that the bank offers 8 for 1 (7 to 1)on hardway 4s and 10s, and 10 for 1 on hardway 6s and 8s. Since there are eleven ways in which a 6 or 7 can be thrown, and only one is a double-3, the correct odds for a hardway 6 are 10-1. In offering 10 for 1, the bank thereby takes an advantage of 9·091 per cent, and takes the same for hardway 8s. The bank's percentage on hardway 4s and 10s is 11·111 per cent.

Place or Box Numbers. These are bets that a chosen number will be thrown before a 7. Stakes are placed on the line above or below the respective point number. On 4 and 10 the bank pays odds of 9-5. Reference to Table 1 shows the correct odds to be 2-1; so, the bank's advantage is 6·667 per cent. On 5 and 9 the bank pays 7-5, its advantage being 4·000 per cent. On 6 and 8 the bank pays either 7-6, in which case its advantage is 1·515 per cent, or even money, in which case its advantage is 9·091 per cent. Note that, if the casino offers odds of 7-6 on 'place' 6 and 8 bets, it is pointless backing Big Six and Big Eight at even money, where the bank enjoys nearly six times the advantage.

Buy or Lay Bets. A 'buy' bet is similar to a 'place' bet in that the player bets that a point number will appear before 7. The difference is that on the 'buy' bet the casino will pay winners at the correct odds: for points 4 and 10 at 2-1, for 5 and 9 at 3-2, and for 6 and 8 at 6-5. It will, however, exact a commission of 5 per cent of the stake. Since the minimum commission will be the minimum stake, the gambler must stake 20 times the minimum, or pay a higher percentage commission. The casino's advantage on these bets is 4·762 per cent. Reference to the percentages for 'place' bets shows that the player does better to buy bets on 4 and 10 and to place them on 5, 6, 8 and 9. 'Lay' bets are the opposite of 'buy' bets, i.e. the player bets that 7 appears before the point. The true odds are paid: for points 4 and 10 at 1-2, for 5 and 9 at 2-3, and for 6 and 8 at 5-6. The 5 per cent commission is, this time, exacted on the winnings rather than the stake, i.e. 1 chip commission will be levied on a stake of 40 on points 4 and 10, 30 on points 5 and 9, and 24 on points 6 and 8, since each of the bets will win 20 chips. The casino's advantage is respectively 2·439 per cent, 3·226 per cent and 4·000 per cent. The bets are made by the player placing his stake on the table, and calling the point he wants. The dealer removes the house commission (called 'vigorish') from the stake, and places the stake in the correct box.

Other Bets. There are various other bets or combinations of bets possible at craps. A few are shown on the table in Figure 1. Most are 'one-roll action' bets, and are settled on the result of one roll. For instance, a gambler can back 7 to appear on the next throw. The odds are 5 for 1, and the bank's advantage 16·667 per cent. Odds of 30 for 1 are offered for double-1 and double-6, with the same advantage to the bank. Odds of 15 for 1 are offered for 3 and 11, the advantage still being 16·667 per cent. All craps are offered at 8 for 1, an advantage to the bank of 11·111 per cent.

Free or Odds Bets. When the shooter has a point, casinos allow players who have bet on 'pass', 'don't pass', 'come' or 'don't come' to double their bets, and the second half of the bet is paid at the correct odds. Thus 'pass' or 'come' bettors will get 2-1 on points 4 and 10, 'don't pass' or 'don't come' bettors will get 1-2. The odds offered on 5 and 9 will be 3-2 and 2-3 respectively, and on 6 and 8, 6-5 and 5-6. For example, a 'come' bettor with a point of 6 and a stake of five chips will be allowed a free or odds bet of five chips on 6, to be paid at odds of 6-5. As the casino will not deal in fractions of a chip, the stake on this particular free bet must always be in multiples of five, and the player will be allowed to round his stake up or down to the nearest multiple of five. If his stake is only one or two chips he will not be allowed a free bet at all. The casino allows the free bet to speed up the action, and takes no commission on it. Thus the player should always accept it for the maximum stake allowed, and correspondingly reduce the bank's advantage on the total bet. Free bet stakes are not placed flat on the table, but overlap the edge of the original stake.

The bank's overall advantage on the bet can be calculated by reference to Table 2. Of the 1980 rolls summarised, the bank returns to the pass line bettor 976 x 2 chips (assuming one chip per bet), or 1952 chips. The table shows that 1320 of the 1980 rolls will result in a point, and, if the 'pass' bettor takes the free bet each time, he will stake a further 1320 chips, and, since the bets are paid at the correct odds, can expect 1320 chips back in return. Thus, if he always accepts the free bets, his total stakes on the 1980 rolls will be 1980+1320, or 3300 chips, from which in the long run he will expect 1952+1320 back, or 3272. So he will expect to lose only 28 chips in 3300, a casino advantage of only 0~848 per cent. Don't pass bettors will do even better, with an advantage to the bank of only 0·832 per cent. This is the lowest advantage the casino takes in crap games, except for some casinos in Reno, where free bets are allowed of double the original stake. A player making full use of these bets will reduce the casino's advantage to 0·606 per cent on 'pass' or 'come' bets, and 0·595 per cent on 'don't pass' or 'don't come' bets.

Craps is still the most popular casino game in Nevada, USA, and is increasingly played at home. To cater for this demand, modern miniature Craps tables, manufactured in plastic in the orient, are sold in many Nevada resorts. The small circular compartment into which the two dice are dropped is so constructed that their weight triggers an electrical contact with a small motor powered by three torch batteries. The base of the compartment revolves rapidly, and the dice are thrown out against the side of the table. Bets are not placed on the table as in the full-sized casino game, but on a separate board, to prevent the chips being scattered by the dice.

Craps played privately is a much simpler game than casino craps. The only essential equipment is a pair of dice, although a blanket or carpet might be used to roll them on, and a backboard for the dice to rebound from is advisable. Because of the lack of a staking table, the bets are fewer and simpler.

The first shooter places a sum of money before him as his 'centre' bet, and the other players are invited to 'fade' it. The shooter is betting that he will win; the other players put up an amount equal to his stake to bet that he will lose. It is an even money bet. As in the casino game, the shooter wins if he throws a natural 7 or 11, loses if he throws a crap 2, 3 or 12, and continues to roll if he establishes a point.

Meanwhile, the other players bet among themselves on whether the shooter passes or not. 'Come' and 'don't come' bets are also made. Once a shooter has thrown his point, he and other players may bet that he will or will not make it. The correct odds are paid, i.e. 6-5 that he will make 6 or 8, 3-2 that he will make 5 or 9, and 2-1 that he will make 4 or 10. Sometimes even money is bet on the shooter making a point of 6 or 8, but this is incorrect, and gives the 'wrong' bettor a tremendous advantage. Hardway bets are common. If the shooter's point is 4 or 10, 8-1 are the odds against making it the hard way. It is 10-1 against making a hardway 6 or 8. The players may make other bets among themselves, but those already mentioned are the commonest.

The shooter keeps the dice while winning; as soon as he misses out he passes the dice to the next player in rotation.

Craps is a game of chance, and skilful play consists only of knowing the proper odds and probabilities for each bet, and making bets that are arithmetically sound. In private crap games the 'wrong' bettor generally has an advantage of 1·414 per cent, a significant advantage over a long period. In casino games, a sound bet is merely one with a small advantage to the casino. The player will therefore avoid, for example, Big Six, Big Eight and hardway bets. 'Wrong' bettors face a slightly smaller disadvantage than 'right' bettors. If the free or odds bets are made whenever possible, the casino's advantage can be kept below 1 per cent.

From 'The Illustrated Book of Table Games' ISBN 0 600 34870 9
© The Hamlyn Publishing Group Ltd 1975

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