First of all, I'm assuming that money is involved here. If so, then ideally, to a certain extent anyway, it should depend on the competition in each pool.
If, for,example, I knew that in one pool everyone was just flipping coins, and there was a chance that people would be picking 16s to beat 1s, or 15s to beat 2s, I would go with what I felt was my best shot.
But that's probably not the case. So I would make different picks for each of the pools I was in, putting what I felt was my best in the pool that was worth the most, and so on.
I would do it that way based on the following logic:
If I'm in 4 different pools, and use the same picks for each, then I will either win all 4, or win none. If I use 4 different picks, I have no chance to win all 4, but I have a much better chance of winning one out of the four.
Per dollar invested, I believe that my expected value would be greater doing it that way.
It's the same as if I played the daily number in a state lottery game. If I bought 4 tickets on the same number, I would win four times the amount of the prize if that number came in. But if I played 4 different numbers, I'd have a four times greater chance of winning one quarter of that amount.
Given that the payoffs in these things are so large, I'd rather have the four times greater chance of winning the smaller amount.
