(tournament) heads up question

3 general questions regarding heads up hand value, any answers greatly appreciated (especially since some math is required)


1) Say you and your opponent hold each 1000 chips. Mathematically, what is the minimum blind level you should just be shoving all in with:
a) A-2
b) K-2
(ie 50-100, 75-150 etc. Answers including M are acceptable)

2) Also, assuming your opponent will only call with better hands, what are the odds your opponent has a better hand when you hold:

i) A-2

or

ii) K-2

3) What equity do we have against the total calling ranges that have us beat for these two hands?? (Assuming they only call with better hands?)



Just a couple of questions that were going through my head today! thanks

There is a difference between the optimal level you should be shoving those hands, and the exploitive level. If villain is folding everything but AA, then you should obviously push with a much deeper stack than you would if he was calling his top 10% of hands.

Optimal play however (play which cannot be exploited by your opponent) has been solved for these hands. They can be found in the Nash Equilibrium Charts in The Mathematics of Poker.

If you do a google search for nash equilibrium charts, you'll find them on the first page of google.

http://www.holdemresources.net/hr/sngs/hune.html

I've yet to read Mathematics of poker, though its on my list. This chart is a good tool, thanks for the reply!

nice chart. so to clarify, if i have 87o and i have 14.7 BB is it even money for me to push if he calls everytime? is that what it's saying...

I hope so because thats what I got from it...

I'd be all up for someone explaining this chart.

I see what you guys are saying about the 87o, but doesn't this depend on the blinds somehow? I don't see how this chart is related to blinds at all...

yea if u have no chips just go all in a lot basically or if he plays badly u can go all in less and see flops but by no means do u have to

Quote:

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Originally Posted by Massimo

nice chart. so to clarify, if i have 87o and i have 14.7 BB is it even money for me to push if he calls everytime? is that what it's saying...

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No. 87o is 45/55 against ATC so if he calls every time then obv you should fold.

It's saying that shoving 87o is part of the Nash equilibrium. If both players are playing perfect poker, pushing 87o will be break-even for 14.7 BB, profitable for less than that, and unprofitable for greater than that. If your opponent is too loose or too tight then you should make the appropriate adjustments.

by playing "perfect poker" you mean only calling with better and folding worse?

No I mean he is playing perfectly vs. your shoving range and you are playing perfectly vs. his calling range. That's what Nash equilibrium is, both players know each other's ranges and are adjusting optimally. He has to fold stuff like T7o because it's losing to your range even though it's ahead of you this specific time.

2 As you have probably by more than K2, but I prefer to go with a few strong or good hands to go all-in-hand in hand