The decision of whether or not to call all-in overbets in MTTs has given me quite a big of trouble recently. Four different situations that have come up recently have all given me some problems. I'm going to post them one at a time in hopes of generating some good discussions.

Situation #1) Early in a tournament, a maniac at the table is pushing all-in preflop every hand.

This is a fairly common situation in low buy-in SNGs and MTTs, and I'm sure you've encountered it before. Assume the tournament has just started and the blinds are very small

Several questions come to mind. Please discuss! (For the sake of discussion, assume the maniac is going all in without looking at his cards)

1) What range of hands would you call with if you were in the big blind and everyone else folded to you after the maniac raised all in UTG?

(This is the simplest one, and it's basically a math question and a question of how willing you are to gamble and take advantage of probable 60-70% edges when the blinds are very small)

2) How much smaller would the range be if you were on his left and the rest of the table had yet to act?

(Obviously it has to be MUCH smaller since the rest of the table knows what the maniac is doing and if you only play against his hand, you'll wind up with the 2nd best hand in a 3-way showdown)

3) What about if you were on the button and it was folded to you after the maniac pushed UTG?

(Again, the range would have to be smaller than in #1, but obviously much larger than in #2)

4) What if the maniac pushed in 4th position after UTG and UTG+1 limped and you were in 5th position?

(This one would scare me because the EP players might be limping with monsters expecting the maniac to raise. But the "monsters" might not actually be all that strong, just strong relative to the infinite range of the maniac)

5) How would the tournament structure affect these decisions? Would you be more likely to gamble in a MTT with 1000 players than you would in a 180-person SNG or in a STT? Would you be more likely to call in a speed tournament and less likely to call in a deep stack?

I'll post #2 later this weekend, after we get some good discussion going on this one. The other three posts will be more interesting since this one is pretty simple and is more about probabilities than anything else.