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Tables to Improve Your Game

Posted By: Nack Ballard
Date: Tuesday, 16 March 2010, at 12:17 a.m.

In Response To: Tables to Improve Your Game (Joe Russell)

When the odds of success average 1/x, you generally become a favorite somewhere between .6*x and .7*x. When x reaches three digits .7*X is a good approximation. In the case of an ace and a six being required, you are a favorite to roll it in 3.77 rolls, which is x*.633.

Thanks, Joe. I appreciate the reference shortcut.

However... the 3.77 rolls sounds fewer than I remember (for the number of rolls to become a favorite to escape a prime needing a 1 and 6), so I did the calculation by hand, for reconciliation:

Roll 1 = 2/36
Roll 2 = [(9*11) + (25*2)] / 36^2
Roll 3 = [2(9*25*11) + (25^2*2)] / 36^3
Roll 4 = [3(9*25^2*11) + (25^3*2)] / 36^4
Roll 5 = [4(9*25^3*11) + (25^4*2)] / 36^5

Roll 1 == 5.5556%, cum. = 5.5556%
Roll 2 = 11.4969%, cum = 17.0525%
Roll 3 = 13.2887%, cum = 30.3412%
Roll 4 = 12.9121%, cum = 43.2533%
Roll 5 = 11.5250%, cum = 54.7783%

The cumulative ("cum") chances of escaping in five rolls does not surpass 50% until the fifth roll (with the crossover around 4.6). Can someone see if I went wrong somewhere?

Nack

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