I have set up a stall where you may play a fabulous game.
 
Presented before you are 4 unusual 6-sided dice:
 

A Big Red die:
has the numbers 5, 5, 5, 5, 1 and 1 on its sides

A Large Yellow die:
has the numbers 6, 6, 2, 2, 2 and 2 on its sides

A Medium Green die:
has the numbers 6, 4, 4, 2, 2 and 1 on its sides

A Small Blue die:
has the numbers 3, 3, 3, 3, 3 and 1 on its sides
 
I inform those that are unaware that the average value they would roll with each of the 4 dice are (roughly) 3.66, 3.33, 3.17 and 2.67 respectively. All dice are fair and players find it impossible to cheat when rolling them.
 
I request a $1 payment from you to play. You may choose any one die. Then I may choose any of the remaining dice. We then roll. If you roll more than or the same as me, I return your original $1 stake and a bonus $1 prize. If I score more than you, I keep your stake and you win nothing.
 
What would be your strategy if you wanted to walk away from my stall with the most amount of money possible?
 
(Thanks go to an old university professor would showed us something similar, which instantly intrigued me, in a Probability lecture)

If I were to choose three larger dice, leaving you with only the blue die, there is no way you could match me since my smallest roll would be a 4 and your highest would be a 3.

Am I correct in assuming the statement should read "You may choose any one die. Then I may choose any one of the remaining dice."?

Posted by TomM on 2002-07-24 02:15:01