Consider the chance of winning at least 100 times. It's 1 over 2^100, and you win at least 2^100. So the small chance and the big reward "balance out", kind of.
But the reward is not limited there. Once you reach each and every "balance point", the next step is 50% chance for doubling the reward. If you currently have X, the value of continuing to play is 1.5X. This is independent of how big X is, or how unlikely you have made it this far (sorta a reverse Gambler's Fallacy). And it's why the expected value is infinite.
But the reward is not limited there. Once you reach each and every "balance point", the next step is 50% chance for doubling the reward. If you currently have X, the value of continuing to play is 1.5X. This is independent of how big X is, or how unlikely you have made it this far (sorta a reverse Gambler's Fallacy). And it's why the expected value is infinite.