Minimum hand to raise HU vs almost all-in player

[fatdave]

Assume you are on Party, with its escalating blinds. You are heads up against a tight-weak player that has frequently folded to your preflop raises, and is now extremely short stack.

The blinds are 250/500. After posting the BB, he has 750 left, and you have 6750. Despite his having folded the last several hands, and despite the fact that he is very tight and weak, on this particular hand, he will call with any 2 cards if you put him all in.

Knowing, this what range of hands will you raise with, knowing that he will call with any two?

The reason I ask is because if you fold, he will have $1500, but if you raise him all-in and he calls and wins, he will have $2500.

Knowing all this... what is the minimum 2 cards you will have before you raise him all in?

My "normal" heads-up range pre-flop raising range includes AA-22, any ace, any king, QJ-Q8, JT-J7, connectors (suited or not) T9-56.... and any two if they have been folding a lot but still have a decent enough stack to fold a little bit more.

What should I add in this situation?

[lastchance]

You're putting in 500 for the chance to win 1000 more.

Do the math. Hint: 32o is 32% against any 2.

[well]

Assuming your winning probability (PW) equals your chip fraction I get the following:

If you fold your hand, you'll have a PW of 81.25%
If you raise your hand, you'll have a PW of 100%*EQ+(1-EQ)*68.75%
Here EQ denotes the equity of your hand over a random hand, since your opponent calls with any hand.

So to raise with a hand, you'll need an EQ greater than or equal to .4
The hands that do not meet this criterion are 72s, 63s-62s, 53s-52s, 43s-42s, 32s, 92o, 84o-82o, 74o-72o, 65o-62o, 54o-52o, 43o-42o and 32o.

If the short stack were to fold, he would have a PW of 9.375%
If he calls, it would be EQ*31.25%
So the short stack is correct to call all hands with EQ>=.3 over the set of hands you will raise with.
There are no hands that fail to meet this criterion, so your read on the weak player is that he will play this hand perfectly.

Note that this calculation does not take into account your edge over the opponent if you and him would have (say) an equal amount of chips after a few more hands.

Hope it's all clear,

Regards.