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Topic: Game strategy?
Replies: 12   Last Post: Apr 3, 2005 7:33 AM

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Posts: 27
Registered: 1/29/05
Re: Game strategy?
Posted: Apr 2, 2005 2:35 PM
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On Sat, 2 Apr 2005 13:30:11 -0500, "Brian M. Scott"
<> wrote:

>On Sat, 02 Apr 2005 09:38:07 -0800, Bob <>
>wrote in <>
>in alt.math.undergrad:

>> On 1 Apr 2005 23:13:09 -0800, "Joseph A."
>> <> wrote:

>>> You have up to 3 rolls of an unbiased six-sided dice, and
>>> your aim is to obtain the highest result from a single
>>> roll of the dice. After the first and second rolls of
>>> the dice you can choose to stop (and accept the result),
>>> or you can choose to roll again. What is the optimal
>>> strategy and its expected payoff?

>> "optimal strategy" implies weighing pro and con for alternatives.
>No, the optimal strategy is the strategy with the highest
>expected value.

?? which means the same thing, as you show below.

>> What is the cost of doing one more roll? You have not
>> stated any cost,

>Although it isn't stated explicitly, it's clear that your
>final score is the *last* number that you roll,

I agree that seems likely (and thus I agree with your analysis below).
But I'm not so sure it is really clear from the statement of the
question; it certainly did not seem clear to the OP.

Most importantly, I think... we agree that determining the strategy
requires a clear understanding of the "rules". If the OP was not clear
what the game was, then it would not be possible to work out the
problem. Step 1 is to be sure what the game is, either because it is
stated, or because one makes an assumption.

>so the cost
>of rolling again is the probability of getting a result
>lower than your last roll.

yep. You are now doing what I suggested at the start, considering the
con of one approach.


>> so it would always be of advantage to
>> roll again (unless you already have a 6).

>This is obviously not true. Suppose that your first roll is
>a 1; clearly you cannot lose by rolling again. Suppose that
>you now roll a 5. If you roll a third time, the probability
>is 2/3 that you will end up with a lower score, 1/6 that you
>will end up with the same score, and 1/6 that you will
>improve your score; clearly you should not roll a third

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