Playing the final three of a tournament is a special situation that requires special tactics. My feeling is that it is best to try to grind down the other two opponents slowly so that eventually they will be forced into going all in against each other, and one will be eliminated.
Usually there is a good jump in prize money from third to second place, so this is a good thing to do.
If you are the big stack, you can expect that you will have the best hand preflop one third of the time, or 33%, so what you want to do is to raise preflop from the button a little more frequently, like 40% to 45% of the time, since opponents are only going to call from the blinds and risk losing all their chips with (probably) top 20% or better hands.
If they call from the blinds with an unpaired hand and miss the flop, they will be in a very perilous situation. If you are on the button and the flop comes Ace high, opponent will hardly ever check to you if they have an Ace, so you can continuation bet with some confidence, and then if they shove back at you fold if you don’t have a good draw.
In fact, if you raise from the button and one of the blinds has a super hand like AK, AQ, or any pair 9 or higher, they are very likely to shove back at you, at which point you can decide how to proceed. It is less likely that a BB will flat call a 2BB raise with AK, then flop an A or K and check back the flop. They will want to get their chips in, and take the pot there, and prevent you from drawing out on them.
Here is a typical last 3 hand:
Note that had villain raised preflop, I would surely have folded and he would have saved himself a lot of trouble. I did not think he had made a flush, as he would probably have bet the flop with the flush draw, and then shoved on the turn. His betting pattern suggested that he had something, but didn’t want to put all his chips at risk. I might have extracted more chips on the river here.
On the hand that follows I had K T offsuit.
At these blind levels the villains simply cannot afford to be folding too many hands and are going to be forced to confront each other all-in very soon. This is one of those three men in a lifeboat situations, where the only hope of survival is that one of the two smaller stacks launches a hostile merger bid against the other.
We go round again and I have a pair of 4s.
Now things are desperate, and here comes the merger:
Bingo!
5 more hands and it is all over when Villain realizes he might as well shove with anything or see his stack reduced to rubble:
As a second stack in the final three, it seems to me that you want to engineer situations where the other two opponents confront each other, if possible, but that you should try to steal more from the large stack, who is probably raising preflop with crap and can afford to fold, rather from the other smaller stack who may be more likely to shove back at you if desperate and holding any two reasonable cards.
As the smallest stack, you need to be super-aggressive, because either you must win pots, or you will soon be blinded out or your stack so reduced that you become impotent and remain under pressure even if you manage to pick up one or two sets of blinds. You can attack the second stack, as he probably will not shove back at you without a decent hand.
As a really small stack, you may want to shove the flop with a flush draw if you are in the BB and a villain limps in, as he may fold rather than give you the chance to double up at his expense.
Ultimately you need a bit of luck, but by being aware of the stack dynamics you may avoid gross errors.