okay, now I have a little more time to talk about this and elaborate. So lemme try to give a couple of examples. Assume we're in the first hand of a 9-handed STT, blinds at t15-t30, starting stacks of t1500. We're in BB, and the action folds to villain in the SB who will go all-in in each example. Keep in mind that ICM does not take into account things like player skill, the benefits of having a big stack, etc., so these are not 100% accurate in terms of what our calculated $EV actually is. But they are close enough to what we need them for in this exercise.
So, to steal a scenario similar to the one in the book, let's say we have AhKh. Before we make our decision, villain flips his cards face up, and he has 2c2s. Here are our win odds:
ProPokerTools Hold'em Simulation
1,712,304 trials (Exhaustive)
(852,207 wins, 10,775 ties)
(849,322 wins, 10,775 ties)
This is effectively a 50/50 race. As for our here (http://www.holdemresources.net/hr/sngs/icmcalculator.html)). So to calculate the total equity of this play, we use the equation:
$EV = 50.08*(0.2028-0.1111) + 49.92*(0-0.1111) = -0.009 $EV
So our equity is negative, albeit not by a lot. Folding here is then the "optimal play".
Now let's say in a new scenario, villain turns over AsQh. Now our chip equity looks like this:
ProPokerTools Hold'em Simulation (http://propokertools.com/simulations/show?g=he&h1=AhKh&h2=AsQh)
1,712,304 trials (Exhaustive)
(1,249,340 wins, 77,295 ties)
(385,669 wins, 77,295 ties)
Using the same method as above, we can figure out the $EV of this decision:
$EV = 75.22*(0.2028-0.1111) + 24.78*(0-0.1111) = .042 $EV
So here, calling is correct by a pretty wide margin.
Now the question is, how much equity do we need to break even in terms of tournament equity? We can do this by setting our equation equal to zero and solving for x, the percentage of the time we win.
$EV = 0 = x*(0.2028-0.1111) + (1-x)*(0-.1111)
--> x = 0.5478
This means if we are have more than 54.78% win odds against a villain's range, then we can profitably call the all-in bet.
So if we can put a villain on a range of cards that he'd be shoving with in this spot, and our hand is about 55% against that range, we should call. Obviously, we won't always know exactly what the villain would have. Assigning a range will be based on whatever reads we have from that opponent. If they're shoving on the first hand of an SNG, we can probably assume they're pretty bad. This means two things: 1) they're probably pushing with a wider range; and 2) our tournament equity, or $EV, is probably greater than the 0.111 that we assigned initially. Basically, calling forces us to risks more chips, so there is more value in just surviving the early stages than if we
were playing against all good players and we had less of an edge. However, I would say in general we should still call if our range is ahead of his, like 60% or so.
It's up to you to determine what you should be stacking with early in an SNG against each villain. Hopefully this will help you do that a little. Also, bear in mind, in this example, we are facing an all-in shove that gives us 1.04:1 pot odds. I would say it is much more common in an SNG for villain to raise to something like t90, you 3-bet to t300, and then villain shoves all-in. Now, you are calling t1200 to win t1800, which is 1.5:1 pot odds, so your calling range should be a little wider than it would be in these contrived examples.