RAFFLING.
In a raffle for prizes of any kind, each player has three throws with three dice. The rules already given for throwing dice from a box must be followed, the scorer placing the dice in the box before each throw, and lifting the box after it. The total of the three throws is recorded opposite the name of each player, and the highest throw wins. The odds against throwing a certain number or higher are shown in the margin.
| IT IS ABOUT | AGAINST THROWING | ||
|---|---|---|---|
| Even | 32 or more | ||
| 9 | to | 7 | 33 ” |
| 11 | to | 6 | 34 ” |
| 28 | to | 11 | 35 ” |
| 3 | to | 1 | 36 ” |
| 5 | to | 1 | 37 ” |
| 7 | to | 1 | 38 ” |
| 10 | to | 1 | 39 ” |
| 16 | to | 1 | 40 ” |
| 24 | to | 1 | 41 ” |
| 39 | to | 1 | 42 ” |
| 66 | to | 1 | 43 ” |
| 116 | to | 1 | 44 ” |
| 215 | to | 1 | 45 ” |
| 422 | to | 1 | 46 ” |
| 886 | to | 1 | 47 ” |
| 2016 | to | 1 | 48 ” |
| 5032 | to | 1 | 49 ” |
| 14093 | to | 1 | 50 ” |
| 45809 | to | 1 | 51 ” |
| 183229 | to | 1 | 52 ” |
| 1007768 | to | 1 | 53 ” |
| 10077695 | to | 1 | 54 |
Suppose the prize in a raffle is a horse which would be worth a hundred dollars to you. The highest throw so far is 42, and there are only twenty more chances to be thrown. It is 2 to 1 that 42 is not beaten or equalled because it is 39 to 1 that 42 is not thrown, and there are only 20 more chances to throw it. If 45 had been thrown, and there were still 21 chances to be thrown, you would be safe in paying liberally for the 45 chance. The great mistake that people make in buying or selling chances on throws already made in raffles is in thinking that because a certain number has not been thrown, that therefore it is likely to be. If there are 116 chances, they argue that 44 or better should be thrown, because that number or higher should come once in 116 times. This is quite right at the beginning of the raffle, but it is not right to assume that because 100 of the 116 chances have been thrown without reaching 44, that the odds are only 15 to 1 that 44 will not be thrown in the remaining 16 chances. The odds are still 116 to 1 against 44, just as they were before the raffle began. If you are going back to take into account the previous throws of the dice, you should know the 100 throws that were made with those dice before the raffle began.
CRAP SHOOTING.
This game is a simple form of Hazard, and when played “on the square,” is one of the fairest of all games, the percentage in favour of either side being very small. It is rapidly replacing Faro as the gambling game of America.
Any number of persons may play, and any one may be the caster for the first throw. Two dice are used. The players bet a certain amount of money, and the caster covers it, or as much of it as he can. If the caster does not take all the bets offered, players may back him against the other players. The bets made, the caster shoots. If the total of the two dice on the first throw is seven or eleven, it is called a nick, or natural, and the caster immediately wins the stakes. If the first throw is two, three or twelve, it is a crap, and the caster immediately loses. If the caster throws any number, 4, 5, 6, 8, 9, or 10, that number is his point, and he must continue throwing until he throws the same number again, in which case he wins; or throws a seven, in which case he loses.
Two dice may come up in thirty-six different ways, each of which will produce one or more of eleven possible throws, running from 2 to 12. The most common throw is seven, because there are six ways that the two dice may come that will make seven; 6-1, 5-2, 4-3, 3-4, 2-5 and 1-6. The most uncommon are two and twelve, because there is only one way for each of them to come; double aces or double sixes. The numbers of different ways in which each throw may come are as follows:—
| 7 | may come | 6 different ways. |
| 6 or 8 | may come | 5 different ways. |
| 5 or 9 | may come | 4 different ways. |
| 4 or 10 | may come | 3 different ways. |
| 3 or 11 | may come | 2 different ways. |
| 2 or 12 | can come | 1 way only. |
When the caster makes his first throw, he has 8 chances out of 36 to get 7 or 11, which will win for him; and 4 chances out of 36 to throw 2, 3 or 12, which will lose for him. It does not follow from this that the odds are 2 to 1 in favour of the caster, because there are only 12 throws out of the 36 possible that will bring any “action” on the bets; so that the odds are 2 to 1 that the first throw will not settle the bets either way. After the first throw, the caster’s chances vary according to his point. If his point was six, he would have 5 chances out of 36 to throw it again, while the players would have 6 chances out of 36 to get a seven. If the player’s point is four or ten, the odds will be 6 to 3 against him; because there are only three ways to get his point, while there are six ways to get a seven.