Gambler's Ruin

The problem
you: $100 · casino: $1,000,000 · $1 bet per fair flip$100you⇄$1,000,000casinobet $1 per coin flip · fair coin · play until someone is brokewhat's your probability of bankrupting the casino?

You walk into a casino with $100. The casino has $1,000,000. You bet $1 per round on a perfectly fair coin flip. You play until one of you is broke.

What's the probability that you bankrupt the casino?