Just in case your sleep might be disturbed by the Stanford study cited some posts above, on the dynamics of a flying coin, I anticipate you the conclusions of that said study: "For tossed coins, the classical assumptions of independence with probability 1/2 are pretty solid" (page 27).
It is a pleasure to confirm the correctness of your calculations.
Thank you very much, though, quite honestly, I was not really worried about it. Hopefully you did not spend (waste) your time on my account.
It is rather funny in that the last Global War scenario I was testing with Net Play, I had a real outlier with US Entry. I placed all 3 of the initial US markers against Germany/Italy.
After Germany declared war on Poland, the roll was a 1 which resulted in 2 markers drawn against Germany/Italy.
When the CW declared war on Germany in its first impulse, the roll was a 10, which meant no markers were removed against Germany/Italy
Finally, when the USSR occupied East Poland, the roll was a 9, which again meant no markers were removed against Germany/Italy
Germany, starting its second impulse, was looking at 5 US Entry markers. The odds of this are something like:
German DOW on Poland 80% 1 marker, 20% 2 markers
CW DOW on Germany - 90% remove 1 marker, 10% remove 0 markers
USSR occupies East Poland - 70% remove 1 marker, 30% remove 0 markers
20% * 10% * 30% = 0.6% or 6 chances in a 1,000.
The markers, IIRC, were something like 3,2,2,1,1 which yields 14 versus German/Italy and 5 against Japan.
Given this situation:
Should Germany curtail any aggressive actions for the balance of 1939, ie no Denmark or Belgium, and wait for the lower markers in 1940?
Should Italy start to watch its back? This seems to be an ideal setup for an early Commonwealth/French strike against it.
As discussed by previous posters, US Entry is a key driver in their decision process. Certainly the AI will need to do the same.
The test sequence did yield a bug in Net Play, so not a total waste of time.
< Message edited by Cad908 -- 7/22/2013 9:07:50 PM >