Let's strike it rich at the casino!, Simple roulette probability compuation Options

[hyzmarca]

It is really a case where the mathematically expected winnings do not match the most probable winnings.

In all likelihood, you'll win $2 or $0 $1 (75% chance). My calculator tells my that the Log2 of 1,000,000,000 is 29.8973528539868. The first value over 1,000,000,000 that you can win is 2^30 = 1,073,741,824 the probability of you reaching a score of 30 is 1/2^30 or 1/1073741824.

In other words, your probability of winning an amount of money or more (given that it is an integer power of 2) is equal 1/(that amount). Someone who would pay billions per play for this is a moron. This is a point where the math is wrong and common sense is right, which isn't often, and thus is often called a paradox.

It isn't a paradox so much as the fact that the mathematical formula used to determine expected value can't handle divergence, and thus a different formula is needed for determining the expected value of potentially divergent system.

However, given infinite possible itterations and the ability to quit when one is ahead, then you will always come out ahead, eventually. The problem is that you can't play infinite itterations unless you also have an infinite bankroll.

Thus, if you have infinite money then you'll have infinite money.

[Kagetenshi]

You'll never win $0 according to the question as posed, as the payoff if you immediately come up tails is $1 :)

~J

[Moon-Hawk]