Pantsonfire;160691 wroteThe number one thing in scenarios like this is whether it is better for the all-in player to be eliminated or whether the chips in the pot are more important to try to win.
I would suggest that in most cases, the chips are more important to you than the player being eliminated. Proving this is more complicated than I wish to attempt in this brief post but I'm certain most experienced tournament players will agree with this.
I'll try to give one example. Say there is a dry side pot with three players one all-in for 3bbs and you and another call. It is a 10.5bb pot. If you have something like 20bbs, this pot is important to you. The flop brings you an A high flush draw. I would certainly bet at this pot in hopes of knocking out something like top pair. And fortunately, most players would figure top pair was no good here given my bet into a dry side pot. My chance to win the pot now would be greatly increased and I might even be ahead of all-in guy with my A high.
Actually, a lot of good tournament players might be better off not agreeing with my opinion and I might just stop saying stuff like this.
I ran into a situation where I had to bet to win both of the pots. I forced the other guy out on the river, but I hit a full house on the flop, so I had to try to extract as many chips as I could.
From my point of view at the moment, there are situations where both can apply.
I was playing the other day and hit a pair on the flop. It wasn't a big pair, but another guy was all in with very few chips. There were 4 of us total, and all of us saw the flop. I was first to act with a pair of 9's or something like that. I had 9-T suited I think, small blind. So, I checked. The guy on the button decides to raise, so the other two of us fold. He was bluffing and the dude that was all in had nothing. He had a good hand with AK, but he didn't hit anything on the flop.
So, in this situation, I believe the best move is to not bluff others off of their hands in order to get the guy out.
Like I said, I can think of good examples of both. I was also playing yesterday and another guy pushed me off of my hand early when I had AQ suited. I hit nothing on the flop, but a T came up. There were 3 of us in this hand. One guy was all in - he bet a bit more than I wanted to call to be all in, but I took the chance to get him out, and I had a lot of chips - and the other guy called him with me. The flop comes out and I'm last to act. The other guy raised almost twice the pot size. I just couldn't call that, so I folded. The turn and river ended up being JK to give me the straight. He had nothing and the all-in guy ended up with a pair of Jacks.
So, yeah, I can see why checking down to the river works sometimes. So, if there is a large chance you are going to win, you should consider pushing the other guy out of the pot, to increase your chances, but if you don't have anything, don't bluff. That's how I see it now. No bluffing when other players are all-in.
EDIT:
On the other hand, if you have nothing and you sense weakness, you might want to push the other guy out of the bot incase it comes down to a 'who has the highest card' type of situation. Or, you might hit your pair on the turn or river to win. Pushing as many people out of the pot as possible will increase your odds. You could look at it that way too.