What you describe is captured in the probability concept called "expected value".

The expected value is just the probability of an outcome multiplied with its value.

And as you note, there are two kinds of players. Those that:

Type 1) Attempt to get the maximum expected value, and are willing to end up with 0.
Type 2) Are unwilling to end up with 0 and avoid it in exchange for a lower chance at the maximum prize.

This is the heart of the game "Deal or no deal". It's fascinating to see where the player switches from type 1 to type 2, or watch the permanent type 1's go down in flames.

In that game, there is no strategy. You have no idea which suitcase to pick at all times.

The entire strategy has to do with managing expected value, given where you are, versus where you want to be.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)