Giving a short stacked opponent a perfect all-in vs forcing them to over-commit

Question

I just finished Every Hand Revealed by Gus Hansen and in it he is talking about a short-stacked opponent and says:

I should probably watch out so I don't give him too many perfect all-in moves before the flop. It is imperative to manipulate the size of my pre-flop raises so that [he] either has to over-commit his chip stack for a small gain or else he will simply have to see a flop.

Can someone explain the math behind this type of move and how to calculate the cut off bet between giving your short stacked opponent a perfect all-in and forcing them to over-commit?

Edit: March 6th, 2012

The following example (adapted from the book) is what alerts Hansen to make the above quoted statement.

Table is 7 handed
Blinds and Antes: 15/30/5
Seat 1: Gus Hansen with 4,800
BB: Villain with 450

The Button opens with a raise (amount not specified) and Villain pushes all-in. I'm assuming Hansen's concern is for when he is on the Button and Villain is now in Seat 4. How much should he raise to make moving all-in a bad move for Villain?

Answer 1

If your opponent has 10 000 in chips and the blinds are 200/400 your normal raise would be something around 1000 - 1350 which means that it's with the blinds something around 20% of your opponent's stack. He can go All in now and win your bet + blinds which is not much but can lose a lot (everything) if he gets called by you (or even reraised all in). If he for example would have only 5 000 in chips now this becomes almost 40% which means he is getting almost 2.5:1 odds for his money. If he has any kind of decent hand (any Group 1-3 hand from sklanksy chart) he can go all in because it's profitable for him.

The bottom line is. If your raise will be a bigger portion of your opponents stack he will be priced in to go all in because he can win a lot of chips with a decent hand. If the bet is still too small to give him the right odds for an all in then he will basically bleed away his chips if he keeps calling.

This was my understanding from this while I was reading the book. Correct me if I am wrong. :)

Answer 2

Short stacked opponents are looking for opportunities to go all in, almost BY DEFINITION.

That is, they are looking for "double or nothing" situations whereby they can either "double up" or "go home" immediately, probably to a more profitable game.

For instance, if the size of the pot is 50% of the person's stack, he can push 100% of his money to win 50% if not called, or 200% of his money, if he is called, and he wins.

It is in the interest of the big stack NOT to give the short stack these potentially profitable situations, keep the pots small, and let the law of averages "bleed out" the short stack, through blinds. So you want to create a situation where their BLINDS "overcommit." And the way to do that is to keep them "undercommitted" on other hands.