Have you seen this paradox anywhere before?

Hello everyone!

I've had this problem bugging me for the last couple of days. I don't think I've seen it anywhere on the internet before or heard anyone else talk about it. It seems related to the "just one more" paradox (https://youtu.be/_FuuYSM7yOo?si=Awh9akV2RohkYuIR), but it's not the same.

Here's how it goes:

You are offered the chance to play a game. Each round, there are two possible outcomes:

Outcome A (75% chance):

You double your money. You must now choose whether to continue playing or take the money you have earned and stop.

Outcome B (25% chance):

You lose all of the money that you have bet and can no longer continue playing.

So the question is, at what point should you stop and take your money? Each round you are more likely to win money than to lose, so there will never come a point where stopping has a greater expected value than continuing. However, if you only follow this logic, you will keep playing until you eventually lose your money, which obviously is not a favorable outcome. So that's the paradox: simply following the strategy that the math seems to indicate gives the best outcome will actually end up with the worst one.

For example, from the outset you can tell that you have a 75% chance of winning the first round, a ~56% chance of winning both the first and the second, and a ~42% chance of winning the first, the second, and the third. This would seem to indicate that you should play two rounds and then stop. But after playing two rounds, you still have a 75% chance of winning round three, so now it seems like you should continue.

P.S.:

For the sake of clarification, assume that you can only play this game once. In other words, if you choose to stop, or are forced to stop at any point, you can't simply bet money and play again.