Hypothetical Rebuy Tournament

[Double Ice]

Mr Weak Tight is obviously wrong about people not rebuying intially. His other arguments are solid arguments, and he is not getting credit for them.

Lets talk about his argument, which is an appeal to chip equity. In the beginning, you have 2 buyins, and a double-buyin is free. Obviously the correct play is to shove because you can't lose anything. Notice that here, the 2 buyin "compensation" for losing is your whole stack. When you have more chips, say 20 buyins, the effect is not as pronounced. Say everyone on the table has 20 buyins. If someone loses an all in, they only get compensated 2 buyins, which is 1/10th a stack. If players are push/folding optimally, then in terms of chip equity, it is not correct to shove/call shoves with every hand, because some really weak hands don't do well enough even versus a random hand, among other considerations. So it is true that relatively early (not "one million chips" as someone mentioned, but closer to 10 or so buyins) players, if all playing optimally (Nash eq.) should be tightening up, if they wanted to make only +cev moves. [Obviously if everyone knew for sure that everyone else was shoving blind no matter what, then it is "optimal" to shove every hand no matter what number of chips.]

There is one interesting thing to note in these arguments.
We usually have a general idea in our head that 200,000 chips now is worth the same amount as 200,000 chips later. In fact, the chips decrease in value for obvious reasons. This makes "sitting" on chips worth less, because as time passes, the chips are depreciating in value. Obviously in the early stages of an MTT, chip value is linear (that is, twice as many chips is twice the equity), so that is an argument for not taking -cev spots in a vacuum.

Anyways, because of these considerations, the situation is more complex, and certain moves that are -cev in a vaccum, might be good (knocking players out so they will rebuy-shove more, allowing you +cev spots because you can select a tighter range, while they have no choice but to shove any cards)

In conclusion it is really hard to say what exactly optimal play in maniac rebuys is, and it really depends on the players.