Question about a simple game

[Namir]

I need to apologize for my big math mistake. The equation relating the number of iterations and the threshold is wrong because I deduced it by taking the sum AND NOT the difference between two subsequent random numbers.

After correcting my VBA code in Excel, I recalculated the number of iterations and looked at the correlation. I came with results close to Albert's results!! Good call Albert.

I noticed that for T <=8 the following GENERAL relation seems to hold:

I = 7*T^2.5

For T > 8, a quadratic fit between I and T does better:

I = 50*T^2-300*T+450

The above two equations are based on averaging the correlation coefficients.

The above results cast doubt in my mind that there is a theoretical background for relating the number of iterations with the threshold. I feel that the statistics involved go beayond the stats for the difference between two random numbers.

Namir