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o measure the effect of, the presence of a great number of other contestants. Yet it is easy to illustrate the matter.
Thus, suppose a player casts a die single against one other. If the first has cast four the odds are in favor of his not being beaten; for there are only two casts which will beat him and four which will not. The chance that he will not be beaten by a single opponent is thus 4/6ths or 2/3. If there is another opponent, the chance that he individually will not cast better than 4,
is also 2/3. But the chance that neither will throw better than 4 is obtained by multiplying 2/3 by 2/3. It is therefore 4/9; or the odds are 5 to 4 in, favor of one or other beating the cast of the first thrower. If there are three others, in like manner the chance that not one of the three will throw better than 4 is obtained by multiplying 2/3 by 2/3 by 2/3. It is therefore 8/27; or the odds are 19 to 8 in favor of the first thrower's cast ,of 4 being beaten. And so with every increase in the number of other throwers, the chance of the first thrower's cast being beaten is increased. So that if the first thrower casts 4, and is offered his share of the stakes before the next throw is made, the offer is a bad one if there is but one opponent, a good one if 1 there are two, and a very good one if there are more than two.
In like manner, the same hand which it would be Safe to stand on (as a rule) at poker against two or three opponents, maybe a very unsafe hand to stand on against five or six.
Then the player has to consider the pretty chance-problems involved in drawing.
Suppose, for instance, your original hand contains a pair--the other three cards being all unlike: should you stand out ? or should you draw ? (to purchase right to which you must stand in); or should you stand in without drawing ? Again, if you draw, how many of the three loose cards should you throw out ? and what are your chances of improving your hand ?
Here you have to consider first whether you will
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