Did we have the probability discussion/explanation in this thread? I can't remember.

Anyway, you all taught this non-math-included creative writing major about the coin flips/doors thing.

Flip a coin (no tricksies) and I have a 50% chance of heads.

Only a 25% chance of heads twice in a row.

Is that right? I think that's right.

I was just wondering, can that be (theoretically) exploited to make money? In a theoretical situation where someone is willing to bet on a coin flip (I'm sure this exists), couldn't I flip a coin in advance, see which result I get, and then always bet on the opposite, given I know that the next time I flip a coin, I only have a 25% chance of hitting the same side?

It'd be a long game, but the odds would always be in my favor, so you'd have to expect to be making money in the long run. To increase the odds, I could keep flipping coins until I do get two in a row, and then make the wager against the third occurrence.

It's clearly dishonest since the person betting against me doesn't know that I've already flipped a coin, but it seems like a highly exploitable move.

(This is assuming the probability rule applies to the flipper. If it applies to the coin itself, I guess it would be harder to do in quantity, given you'd have to track which coins you flips and what result each coin has preloaded.)