Your goal is to accrue a total of $100. Here are the constraints / rules:

• You can choose one of three denominations: $1, $10, $100. Whichever one you pick, you have to stick with.
• If you choose $1, you will be given $1 with probability 99.9%; if you choose $10, you will be given $10 with probability 99%; if you choose $100, you will be given $100 with probability 90%.
• On each turn, you receive the chosen denomination with the given probability. If you miss, then the game is over and you receive nothing. If you didn’t miss, you keep the denomination and the game continues with a new turn. If you have $100, you win and the game is over.

Which option do you take? Do you think it’s more likely to get 100 consecutive $1 payouts, or 10 consecutive $10 payouts, or the single $100 payout?

The puzzle is solvable with basic probability theory. But before you attempt to solve it with whatever your technique, test your intuition and take a guess.