[M.B.E.]

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Okay. Somewhat late in a large multitable tournament, say a $5. I have 12,500 in chips with the average at 11,000. There are 240 people left and they are paying 20% of the field or 340 people. Blinds are 300/600 but going up in 2 minutes (so in this case you can say they are 400/800 by the end of two hands). My M right now is 12500/600=20.8,

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No. Your M right now is 12500/900 = 14 (assuming no antes).

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If you raise to 1800 and then make a continuation bet of 2400 on a flop of Q 4 2 and get pushed all in you just cost yourself 4200 chips plus the minimum of 1200 within a few hands. That's 5400 chips out of the 12500.

Isn't it just smart to push or "overbet" your M of 20 because of varying factors like blinds moving up, your position on the table (close to the escalating blinds) and a hand that is the top drawing hand?

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You're in the cutoff; what are the stacks of the players behind you? If (for example) one of them has you covered but the other two are less than 5000, then pushing is a good play.

But if all three players behind you have you covered, then pushing AK from the cutoff with a stack 20 times the big blind is a bad play.

Raising to 1800 is not that good either, for the reasons you mention.

If the players behind you are aggressive, and have you covered, limp here with AK and hope someone raises so you can then push. Otherwise, minraising to 1200 is not bad. If you get called, you can c-bet the flop and if you have to lay it down you won't have put a huge dent in your stack. If there are antes then you need to raise to more than 1200 but not a lot more; 1500 should be enough.