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Henry J.

asked • 01/02/20

Roll of the dice simulation

I have 3 dice and a $1 wager. I roll the first dice. Whatever the result, I want to roll the second dice such that it is lower than the first. So, if I roll a 3 on the first dice, I want to roll a 1 or a 2 on the second dice. If I'm successful, I get a 50% return on my money. So if I wagered $1, I get $1.50 back. I can stop there or continue with the third dice which I also want to roll lower than the first. If I'm successful, I double my wager, so my $1 becomes $2. If I'm unsuccessful on either the second or third roll, I lose my $1 wager. What are the mathematically expressions for combinations (ie "choose") that show all probabilities for this simulation.

1 Expert Answer


Henry J.

OK, I will fix by making the condition that the player MUST roll the third dice unless of course he/she has already lost. So, player rolls a 1 first, game is over* since he can't roll lower than a 1 on subsequent roll. Players rolls a 2? His next roll is a 1, he may NOT stop and must roll the third dice hoping of course for another 1. Hopefully that will make it easier to solve. *One final condition to make it more interesting for the player: If player rolls all three dice the same (1,1,1; 2,2,2; etc.), he quadruples his money (300%). This way, there is still hope if second dice is same number as first; he just needs to hope third roll is also the same. Thanx.


David G.

Thanks, Henry. You are right that adding the condition that the player must always make all three rolls simplifies things. Perhaps you could edit your original problem, so the complete version is in one place. That would be helpful to other solvers. Thanks.


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