# Dice game

• Aug 11th 2012, 05:00 PM
surjective
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
• Aug 12th 2012, 04:47 AM
awkward
Re: Dice game
Quote:

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. ;-)
• Aug 12th 2012, 05:38 AM
HallsofIvy
Re: Dice game
Quote:

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?
• Aug 12th 2012, 05:39 AM
surjective
Re: Dice game
Hello,

Hehehe :) You may be right but how should I present a satifying answer?
• Aug 12th 2012, 05:41 AM
surjective
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?
• Aug 15th 2012, 08:42 PM