[BruceZ]

961/[ 1 + 2*(10/37) + 3*(10/37)^2 + 4*(10/37)^3) ] = 523 flips.

That should be:

961 / [ 1 + (10/37) + (10/37)^2 + (10/37)^3 +... ]

= 961*(1 - 10/37) = 701