Mathematical_Recreations-Kraitchik-2e

Probabilities 1~5
Finally, the probability of throwing a point and then of making
it is the product of the separate probabilities: for example,
(t)(%) = ft is the probability that the thrower will win by
throwing a 5 and making his point. In this way we arrive at
the following table of all possible results of one play:
Result of play
Probability
The thrower wins
by throwing a natural: 7 or 11
6+2 2 220
3"6= 9 = 990
by throwing and making 6 or 8
by throwing and making 5 or 9
5 5 25 125
2·-·--~-=-
36 5 + 6 198 990
444 88
2·-·--=- =990
364+6 45
by throwing and making 4 or 10 2.~._3_= ~ =~
363+6 18 990
in anyone of these ways
The thrower WBeil
by throwing craps: 2, 3, or 12
1 + 2 + 1 1 55
-
= 495
36 9
by throwing and losing 4 or 10 2.~._6_= 55
-
363+6 9 - 495
4 6 2 66
by throwing and losing 5 or 9 2·-·--- -
364 + 6 15 = 495
by throwing and losing
5 6 5 75
6 or 8 2·-·--- -
365+633 = 495
488 244
990 495
in anyone of these ways 251
495
From these results it appears that the thrower is at a slight
disadvantage, since the odds against him are 251 to 244.
This is interesting in the light of the almost universal feeling
among players (even honest ones) that they would rather
hold the dice. The game is made equitable if the dice