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→Divergence of new build for Attack - AC of -2 vs critical immune foe
This results in the following total probabilities for the 5 outcomes: -1: 113/200, 0: 69/4000, 1: 13119/40000, 2: 171/20000, 3: 3249/40000. In 40000ths they are -1: 22600, 0: 690, 1: 13119, 2: 342, 3: 3249. The average drift each step is (-22600+0*690+13119+2*342+3*3249)/40000, or 950/40000, or 19/800. This is a random walk with bias or wind, the bias is away from zero in the same direction as the initial condition, and the step sizes don't increase. Therefore the average number of time steps until zero-crossing diverges. I need to find or write a proof of this obvious and simple property for walks with more than just a left or right step, failing that I'll work out the whole darned stochastic process. -[[User:Cedges|Cedges]] 03:34, June 21, 2010 (UTC)
:I'm not up to date on Markov processes; the result that the time steps until zero-crossings diverge is good enough for me. Provided the result is written down somewhere (so it is obvious), I find the above more than sufficient. Thanks for satisfying this! You should copy/paste this into the page (with perhaps a citation for the walks with more than two steps) to lay to rest any arguments from randoms who come and look at it. [[User:Surgo|Surgo]] 14:05, June 21, 2010 (UTC)
