A fun exercise

[EverettKings]

You're playing heads up hold em. Both you and your opponent both have $1000 and each post a blind of $1. You are first to act and can only go all in or fold. You only get to play one hand. Your opponent will only call you with aces.

What do you push?

[Tom1975]

You should only play pocket Aces, everything else is -EV

[pzhon]

[ QUOTE ]
You're playing heads up hold em. Both you and your opponent both have $1000 and each post a blind of $1. You are first to act and can only go all in or fold. You only get to play one hand. Your opponent will only call you with aces.

What do you push?

[/ QUOTE ]
If you push with a hand without an ace, you pick up the pot of $2 about 203/204 of the time, and get called about 1/204 of the time. When you get called, the best situation would be that you have 65s and get back an average of $450 for your $999 investment, a loss of $549. Your net loss is about $0.70 if you push with the best possible hand without an ace, so you should fold anything without an ace.

If you push with a hand with an ace, you are blocking your opponent from having AA. You only get called about 1/408 of the time. You need to lose at most about $815 of your $999 investment to justify pushing with an ace. You need to win at least $184 from the pot of $2000, so you need to win at least 9.2% against AA.

Any suited ace wins at least 11.5% (A9s is the worst) against AA, so you should push with any suited ace.

Any offsuit ace wins at most 8.2% (ATo is the best) against AA, so you should fold any offsuit ace.

You should also push with AA.

[EverettKings]

Pzhon got it without breaking a sweat. I was tinkering with a computer program that I wrote and found those results to be very interesting.

As a follow up, now say he calls with aces and kings. What do you push now?

Everett