One player is presented with n cards. The cards have a number value on it (money value). The player can turn the cards one after an other and can say stop and any point. The payoff is the last card that was turned over. I remember the solution involved turning over 1/e*100 % of the cards and then doing something similar (I don't remember the exact details) to stopping after the next one (or last) that is above the average.
The crux of the game is that the player at first doesn't know anything about the range of values written on the cards. For all they know, this could be 1€, 2€, 1000€ etc.
I remember this paper (and its solution) being discussed in a youtube video. Unfortunately, I don't remember more.