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Tables to Improve Your Game

Posted By: Bob Koca
Date: Tuesday, 16 March 2010, at 4:59 a.m.

In Response To: Tables to Improve Your Game (Bob Koca)

Got it. As the success probability becomes smaller the geometric distribution is better and better approximated by an exponential distribution with cumulative function F(x) = 1 - e^(-theta x) Setting F(x) = .5 and solving gives x = ln(.5)/ -theta. The theoretical value is -ln(.5)which is about .693147181

The same setup works for whatever %age you want (but if %age is close to 0 or 1 the p must be very small for the approximation to kick in). For example suppose p = 1/10000. How many trials are needed to have a 10% chance of at least one success? Setting up and solving the equation gives -ln(.9) which is about .10536. So about 1054 trials would be needed.

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