I found this scenario/subject interesting, so I thought I’d start a new thread with some additional information that may be useful when considering a large number of trials where each trial has a low probability of success.

I believe Don calculated correctly in his scenario below when he said that the probability of hitting the hand was 1/52 * 1/51 * 1/50 * 1/49 * 1/48 = 1/311,875,200. As discussed, at 200 hands per hour, it would take you approximately 178 years to play that many hands (311,875,200/24/365.25, accounting for leap years).

HOWEVER, a statement that it would take an ‘average’ of 178 years to hit your hand (and thus be released from Hell) is where it gets tricky/interesting (at least for aspiring math geeks, such as myself ). Actually the true probability is that after ~178 years, you still have about a 37% chance of not having hit your hand (presuming an honest machine that the Devil hasn't rigged against you). Given the House in this scenario, I'd plan on playing for longer .

What if instead the Devil said, "I'll give you as many attempts (hands) that you want, but you have to tell me in advance how many you're going to do. If you don't hit by the time you're through the number of trials you specify, I get your Eternal Soul to punish forever. HOWEVER, if you hit the hand before your number of trials is through, I get to poke you once with my pitchfork for every trial you have remaining before you can go free." How many trials would you choose to 1) give yourself comfort that you would hit your hand (and thus ultimately go free); but 2) not be so many that you have to endure the pokes from the pitchfork unnecessarily after you hit your hand?

If I say I'm going to play 178 years, at the end of that time I'll still have an almost 37% chance that I will be punished for eternity (which is presumably A LOT worse than pokes with the pitchfork, however many). However, if I say I'm going to play for 10,000 years I'll probably have to endure a lot of unnecessary pokes before my Eternal Soul is released for better things, even though I'll be pretty confident that I'd ultimately be released.

Given this new scenario, what is the ideal number of hands to play?

Answers (or at least the methodology for calculating it) to come in Part III, if anyone cares .

NOW we're gambling!

Brent J. Jensen
R-8007
orbis non sufficit