Anyway, enough intro... here is our situation:

4 players left, 3 get paid 50/30/20 pool and even chip stacks of 2500. Before posting the blinds of 200 / 100 each player has a dollar equity of $25... (keep it simple eh?).

Now, based on the calling range of your opponents and a handy ICM calculator you estimate that you have a +$ev push that is worth $2... here is how the mathematics works:

- Compare your equity of folding (thats $25) with:

Your gain when your opponents fold (based on their ranges) * probability of them folding

**and**your winning chances when called (again using the entire range) * probability of them calling.

So, if they fold 90% of the time and call the rest, yet you win 40% of the time when called you can compare the probable gain with the risked equity... at the end we convert it all into $ equity using that handy ICM calculator... that, in a nutshell is how it works. If your equity from shoving is > than your equity of folding then you will win money over time by shoving... easy.

Now for the PG Theorem... in its short and sweet (and red) form.

"

**ICM Models under-estimate the dollar equity value of folding**"

Here is why. Bubbles do not go on for ever, at some point 2 players will fight it out and one will be busted. When this happens your equity will go up - you made the money without risking any chips.

So, what percentage of the time would this scenario need to happen to see a marked effect on your $ev fold. We will go from one extreme to the other....

50 hand bubble: 2% of the time (on average) 2 of your opponents fight it out

20 hand bubble: 5% of the time...

10 hand bubble: 10% of the time...

So what happens to our $ev fold for the different length of bubble

50 Hands... 2% of the time we gain $5.83 in equity for free thats +11c on $ev fold

20 Hands... 5% of the time we gain $5.83 in equity for free thats +29c on $ev fold

10 Hands... 10% ... thats +58c

This is where the wild opponents come in... at the lower level SNGs bubbles are rarely more than 20 hands long, particularly where the blinds are getting high. Coupled with this the 'default' setting that is common for ICM calcs is 0.5%, if we under-estimate $ev fold it may be possible to make a -$ev push into a wild field thinking that it is +$ev.

Of course, the effects of the blinds, stack sizes (including relative stack sizes and their position) are all more important than the PG theorem.... but then again - every cent helps!

GL at the tables, Mark

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