The idea is that if the coin flip goes in the player’s favor, they win double their bet. After winning, they can either collect their winnings, or risk them all on another coin flip to have a chance at doubling them. The initial bet is fixed at, let’s say $1.

Mathematically, this seems like a fair game. The expected value of each individual round is zero for both house and player.

Intuitively, though, I can’t shake the notion that the player will tend to keep flipping until they lose. In theory, it isn’t the wrong decision to keep flipping since the expected value of the flip doesn’t change, but it feels like it is.

Any insight?