You are offered to bet on a dice throw. This dice has 6 faces (1, 2, 3, 4, 5, 6). You put 1€ on the table.

Question

Which bet would you go for? Detail the reasoning behind your betting choice. What would be your second best option?

A If it falls on either 1, 2 , 3 , 4 , 5 you get 1,10€

B if it falls on 1 you get 9€

C if it falls on either 1 3 4 you get 2,60€

D If it falls on either 1 or 4 you get 3,70€

Answer 1

Hi James,

Calculate the expected reward in all scenarios:

A) you get 1.1 with 5/6 probability and 0 with 1/6 probability. Expected reward is 1.1*5/6 + 0*1/6 = 0.916666

B) you get 9 with 1/6 probability and 0 with 5/6 probability. Expected reward is 9*1/6 + 0*5/6 = 1.5

C) you get 2.6 with 1/2 probability and 0 with 1/2 probability. Expected reward is 2.6*1/2 + 0*1/2 = 1.3

D) you get 3.7 with 1/3 probability and 0 with 2/3 probability. Expected reward is 3.7*1/3 + 0*2/3 = 1.233333

To maximize expected reward, I would go for B. Second option would be C.

This strategy is based on maximizing expected reward, and doesn't take into account the variance of the reward.