I hear you. Yet, what I'm trying to express seems to make some intuitive sense, and I'd appreciate help in spotting whatever might be wrong with it.

Think of it in game theoretic terms: you have 10 points to can allocate between games A and B. Game A is a winner-take-all scenario, and your opponent has allocated 1000 points; the payoff is P. Game B is a percentage-return scenario; the payoff to each player is proportional to the amount they allocated (perhaps in much smaller proportion). In game A as in game B, your allocation may be aggregated with that of other players, but you are uncertain of how many are playing.

It seems to me that, depending on P and on your probability assignments for how many other players you're likely to be cooperating with in game A, it can be rational to choose to pass up game A altogether.

(Having expressed it that way, it seems somewhat similar to the "should I vote" question, as in "I should only vote if it's likely that my vote is the one that will tip the scales.")