$125 live SnG, trying to calculate EV for my all-in move

[filimaica]

Live SnG, blinds are 50/100, 5 players remaining. Here are their estimated chip counts (total 15,000 in play):

UTG/CO + 1 = 1200
CO = 2000
Button (Me) = 1200
SB = 4000
BB = 6600

The blinds were going up in 3-4 hands. Starting pot is 150. UTG limps in. CO limps in. I pick up and I push all-in. Before I ask for help on calculating EV, here are the parameters.

-UTG and I were even in chips. A few hands earlier, he spoke to the table about "his mistake of limping UTG". When he limped here, I didn't have a tricky read on him. He could have raised. I put him on a limping range of 33-77, A2s+, A7o+, K9+, QT+. But this range was put together in hindsight. In that moment, I didn't read any strength.

-CO limped with pretty bad cards, especially suited combos. His previous showdown was a measly Q7s, after he had limped from the button. I wasn't afraid of him.

1) The pot was 350 when I pushed. What's my EV on this move?
2) How do I go about calculating this EV?
3) UTG ended up calling w/ 55. I imagined this hand to be in his limping range, but not necessarily his "calling" range. For the sake of calculation, are "limping range" and "calling range" the same?

Thanks for the input y'all.

P.S. How do people use images on these forums that let card combinations look like actual cards? Instead of Kc Jh, , how do I make these look like the card images that others use?

[nsidestrate]

[nsidestrate]

Your question is a lot more complex than you realize. The EV of a particular move is based on a number of factors. In this specific case, you have three questions to answer:

1) What are the odds that neither player will call and you will win the pot uncontested?
2) What are the odds that only one of them will call you?
3) What are the odds that both of them will call you?
4) If they call you, what are the hand ranges that they will call you with?

Let's simplify the question a bit so that you can see the general method. Let's just pretend that you are certain that the CO will fold 100% of the time. This is unrealistic, but it will make the calculation a bit easier to work out.

We'll start with your assumptions of his limping range. You next have to calculate which of those hands he will call with. For the sake of discussion, lets say that his calling range is 33-77, A7s+, AJ+ KTs/KJs/KQs/KQ. Your assigned limping range is 18.3% of his hands and my assigned calling range is 8.9% of his hands. If this was correct, he would call you 48.6% of the time and fold 51.4% of the time.

These ranges are likely to be wrong, but it isn't important right now. He probably doesn't limp strong hands like AK/AQ and he might limp TT/99/88/22 as well, but once you learn the method, you can play with the numbers yourself.

Based on the range we have assigned for him, you will win 37.5% of the time he calls and he will win 62.5% of the time he calls.

So we have the following scenarios:

51.4% of the time you win 350 chips when he folds
18.2% of the time he calls you and you win 1,350 chips
30.4% of the time you lose 1,200 chips

To calculate the net EV of this you use the following formula:
(.514 * 350) + (.182 * 1350) + (.304 * -1200) = 60.8

This means that your average expected gain is 61 chips.

All of the calculations done above were done using PokerStove, which is a great tool for assessing your hand strength against a range of the other player's hands.

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I would be remiss if I didn't point out that this is not even the entirety of what you should look at. A lot of work has been done with something called the ICM (Independent Chip Model) which computes your percentage chance of finishing in the money based on your chip stack. The analysis you are working on here is called the cEV (chip expected value) method and most of us have determined that the ICM model is much more useful for SnG situations. You can get started reading about the ICM in this post on the subject