A very well argued response, and while I have no doubt that you are mathematically correct, I beg to differ to some extent.
Final table play can be incredibly polarized depending on luck with the cards. You tend to get into a game of rock-paper-scissors where any hand could be your last as an effective force in the tournament.
That is why pros often cut a deal when large amounts of money are involved, or run all-ins two times to increase the possibility of a split pot.
Imagine a tournament that pays 4 places. First prize is $1,000,000 and then there is another million split between 2nd, 3rd, and 4th.
But there are 5 players left in, one of whom will go home empty handed while the others all receive life-changing money. The stacks are all roughly equal in size. There are 150,000 chips in play and the average stack is 30,000 chips and the blinds are 1500/3000, so the average stack is 10 BB.
Obviously it will be to the advantage of all the players to say “let’s do a deal. Lets split the second million 5 ways, so everyone gets life changing money, and then divvy up the other million proportionally among the four winners according to their final place.”
Otherwise there is every chance that on the next hand a player with AA will call a shove from a player with 22, lose, and end up out of the money–and no one wants to be that player!
But you can’t do that on RP, so the most interesting question becomes “what is the best way to get into a position where I am heads up against another opponent, and I start with the largest stack and have him covered?”
Working backwards from that, one sees that the best way to get into that position is probably to be the person who eliminates the third place finisher, and the best way to get into position to eliminate the third place finisher is to eliminate the fourth place finisher, and so on, which is where the rock-paper-scissors analogy comes into play. Is it better to let other players knock each other out so that you can be promoted in the money, or to knock them out yourself, but run the risk of being eliminated yourself when they get lucky and you don’t?
(Just the other day I had an amazing finish where I lost a big pot and was left with only about enough chips for 2 antes on the bubble, and on the very next hand two players with stacks of several thousand chips both busted out and I finished in third place out of 4 paid places. Obviously this would never have happened in a real money game!).
In the hand where I had JJ in the SB above, by limping in, I kept open the option of seeing whether the BB would shove preflop, and the option of seeing the flop before deciding how to continue. At this point I could certainly afford to fold JJ if the two small stacks went all-in against each other and effectively merged their stacks or I could call if the flop looked favorable to my cause. As it was, I had the perfect flop and the element of deception in the preflop limp meant that they could not suspect that I had JJ.
These are the kind of hands that bust logjams and get you closer to that position where you are heads up and have the largest stack.