My program

ICM Explorer does a lot of the calculations needed to decide whether to push or to fold. It uses the Independent Chip Model (ICM), a commonly used tournament equity model to evaluate the possible results of the hand.

The easiest decisions are whether to call all-in when you are last to act and there is only one other player in the pot. Use the "Call Push?" button in ICM Explorer. For example, with 4 equal stacks of 3375 on the bubble of a 50-30-20 SNG with blinds of 200/400, if the SB pushes and you are in the big blind, this is the result from ICM Explorer:

Fold: 2975 chips, 0.2303, SD: $16.36

Win: 6750 chips, 0.3833

Lose: 0 chips, 0

Tie: 3375 chips, 0.25

**Equity needed: 60.07%**
Chip odds: 44.07%

Risk premium: 16%

Chips gained by marginal call: 1079.7.

Ties count as 65.22% of a win.

SD of marginal call: $18.9.

You can ignore the standard deviation (SD) information, and the chips won by a marginal call. The most relevant result is that you want 60.07% equity against the pusher's range to call. Although you are getting pot odds of about 5:4, you are really risking about 1.5 times as much as the reward, so you need to be about a 3:2 favorite for calling to gain equity.

You have to figure out your opponent's rage to determine which hands have 60% equity. That's not just mathematics.

When you are deciding whether to push, you can use the "Semi-bluff?" button in ICM Explorer. If you set how often you will get called, you can see how much equity you need when you are called. If you set your equity when called, you can see how many calls are acceptable. If you set both, you can see how much equity pushing gains or loses over folding.

Possible multiway situations are more complicated. There are Nash equilibrium calculators such as ICM Trainer and HoldemResources.net which use numerical approximations to estimate the game-theoretically optimal strategy, and if you can predict how your opponents deviate then you can use SNG Wizard to estimate what range to push and how much pushing a particular hand gains or loses.