Pagan, you were right!  All that I needed to do was switch it to your first for loop and outcomes the answer!!!

Thank you so much, I was really frustrated with it!

Manny

Ok thanks for the reply.  f[N+1] was working fine. 

The problem was that I needed to obtain f[N] from f[N+1].  Then obtain f[N-1] from f[N], ....., f[1] from f[2], using the formula:

f [i] [j] := b*( p* f [i+1] [j+1] + (1-p)* f [i+1] [j] ),where j is an integer less than or equal to i.

So that only f[N+1] works with max while f [k] doesn't when k<N+1.

So it is sort of like going backwards!

Any further advice?

Manny