Roll a Die

[debkumar]

Got this problem in Max Dama hand out. Could not figure out a solution.
"Roll a die repeatedly. Say that you stop when the sum goes above 63. What is the probability that the second to last value was X. Make a market on this probability. Ie what is your 90 percent confidence interval."

 

[leopardkk]

x=58 6/91
x=59 11/91
x=60 15/91
x=61 18/91
x=62 20/91
x=63 21/91

 

[debkumar]

Can you explain a little more?

 

[Shantanu Kumar]

I was wrong

 

[jovens]

T=Terminal, set P(T|62)= P(62)= x, then for value 61, P(T|61)=5/6P(61); 1/6P(61)=P(62), so P(T|61)=5x.
For value 60, P(T|60)= 4/6P(60); 2/6P(60) = P(61)+P(62) = x+6x=7x, so P(T|60)= 14x.
continue this process to get value up to P(T|57) in terms of x, then addind them equal to 1, solve for x, then we are done.