1. ## Dice game

Hello,

Consider a person wanting to play a game of dice. Whenever he wins a game he gets 1 dollar from his opponent. If he looses he gives his opponent a dollar.
He starts by rolling the dice 4 times hoping to get at least one 6. After a number of tries he thinks that his chances would be better if he rolls two dice 24 times hoping to get at least two 6.

The question is: from where could he have gotten the idea of changing the number rolls (and dice) so as to improve his chances of winning some money?

Thanx

2. ## Re: Dice game

Originally Posted by surjective
[snip]
The question is: from where could he have gotten the idea of changing the number rolls (and dice) so as to improve his chances of winning some money?

Thanx
Doubtless he is the author of a probability textbook. ;-)

3. ## Re: Dice game

Originally Posted by surjective
Hello,

Consider a person wanting to play a game of dice. Whenever he wins a game he gets 1 dollar from his opponent. If he looses he gives his opponent a dollar.
He starts by rolling the dice 4 times hoping to get at least one 6. After a number of tries he thinks that his chances would be better if he rolls two dice 24 times hoping to get at least two 6.

The question is: from where could he have gotten the idea of changing the number rolls (and dice) so as to improve his chances of winning some money?

Thanx
What have you done on this? What is the probability of getting "at least one 6 in four rolls"? In the second case, do the two 6s have to be on the same roll of a pair of dice or is it just two 6s in 48 rolls? Do you know how to find the probability of either of those?

4. ## Re: Dice game

Hello,

Hehehe You may be right but how should I present a satifying answer?

5. ## Re: Dice game

Hello,

I have calculated both probabilities using the binomial-method. The opposite of at least one six (in 4 rolls) is no six at all and the opposite of at least two six (in 24 rolls) is no two six at all. I have calculated the probabilities. But how does a satisfacotry answer come from that?

6. ## Re: Dice game

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