Answer From Below



The kneejerk reaction is that itwouldn't matter how many coin tosses the Devil gave you, the odds are fifty/fifty--i.e., it's either heads or tails. This is not true. According to the scenario, you will only need for heads to come up once regardless of the number of tosses, so the formula would in fact be:



1 - (probability for heads never coming up)

= 1 - (0.5^n)



where n is the number of trial tosses.



Now, while it sounds like the torture described would drive you insane immediately and you should take the offer on the first day, if you waited until the 13th day, you would have a 1/50,000 chance of losing. If you wanted to get the chances better than 1 in a million, you would have to hold out another week. It all depends on your utility for pain. The first day, after all, is the only day you can escape eternal torment completely.