Solved by Thomas W. Millett

solution: world series

this probably isn't the cleanest solution, but...

a dynamic-programming type solution is:

(1) Create a 5x5 matrix P.

So, P[i,j] holds your pile of money when the yanks have won i games and the mets have won j games.

initialize P[4,j] := 20 for j from 0 to 3 initialize P[i,4] := 0 for i from 0 to 3

fill P in bottom-right to top left by averaging bottom and right adjacent cells:

P[i,j] := (P[i+1,j]+P[i,j+1]) / 2

(2) Make another 5x5 matrix, B, which represets your bet at any-time.

So, B[i,j] represents your bet when the yanks have won i games and the Mets j games.

fill this top-left to bottom right by:

B[i,j] = P[i+1,j] - P[i,j]

(3) Look in matrix B for your bet at any time.

The final matricies are: