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# Probability Game

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Whenever my roommates and I decide to go out to eat or something else, we play a game to decide who drives. There are 3 of us, and we each have a car. Here is how the game works: We each guess a number between 3 and 15, in turn and out loud, and you cannot pick the same number as a person before you. Then we put our hands behind our back and decide how many fingers to put out. You have to use at least 1 finger and at most 5 (use one hand). At the same time, we put our hands out and add the number of fingers. The person who drives is the person who guessed a number furthest away from the sum. For example, if we guess 3, 4, 5 and the sum of fingers was 10, the person who guessed 3 would drive. In case two people are the same distance away (for example, guesses 9, 11 are both 1 away from 10), the one who guessed higher will drive. Also, as a special case, if the sum equals the number you guessed, you drive. This problem is not totally random, since one player''s number uess is dependent on the people before him, and the number of fingers will be dependent on the number you guessed and the numbers the other players guessed. In one case, if the first person guessed 3, the next two people will guess 9 and 10, then each put out 5 fingers. It does not matter how many fingers the first person who guessed 3 puts out, the sum will be greater than 10 and the first person will have to drive. My question is, is there a scheme one of the players can use to minimize the chance of being the one to drive?

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The first thing that springs to mind is that the one in the middle is the safest, since the only way he can drive is if the total is exactly equal to his number. So you should try to be in the middle. Other than that, you should probably aim for a number near 10. Once the numbers are shout, it becomes a competition between the first one and the last one. The last one will try to maximize the number, so he is rather easy to predict. The one in the middle knows what to expect from the other two, so he is probably predictable, to some extent.

In the end, it all depends on which Yomi layer the other two players are playing, because there is no way to be sure to win, if your opponents aren't dumb.

Here lies the ultimate answer you seek: Yomi layer 3!

Cédric

[edited by - Cedric on July 8, 2003 8:15:04 PM]

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