Yep, it’s my 1k post. Ahh, but how many of my posts were wasted doing mundane ICM calculations for lazy 2+2ers? Well, consider this the last time I am doing your ICM homework for you...

Software
PokerStove
ICM Calculator

Hand 1 – The Basics
Poker is all about maximizing your Expected Value (EV). In order to calculate EV, you determine the value of every possible outcome, multiply each value by the probability of that outcome happening, and then add all of those numbers together. I will call the value of an outcome it's equity (EQ).

Possible Outomes for Hand 1 (ignoring ties):

• Call and win - with equity EQ_win, probability P_win
• Call and lose - with equity EQ_lose, probability P_lose
• Fold - with equity EQ_fold

We want to know whether calling is better than folding, so we take the EV of calling relative to folding.

Equation 1
EV = EV(call) – EV(fold)
EV = ( P_win*EQ_win + P_lose*EQ_lose ) – ( EQ_fold )

Type the stack sizes for each outcome into the ICM calculator to determine equities:



Put UTG on a range (I used ~30%), and PokerStove to find P_win and P_lose:



EV = P_win*EQ_win + P_lose*EQ_lose – EQ_fold
EV = 0.64438*44.735% + 0.35562*9.493% – 32.440%
EV = -0.24%

Repeating this calculation for every hand, or for every villain range would be tedious. We just want to know which hands are +EV. After some maths (set EV>0, P_lose = 1-P_win, re-arrange), we get a magical equation...

Equation 2
P_win > ( EQ_fold – EQ_lose ) / (EQ_win – EQ_lose)

This gives the required P_win value needed to make a call +EV.

For Hand 1:
P_win > ( 32.440% - 9.493% ) / ( 44.735% - 9.493% ) = 22.947 / 35.242
P_win > 65.11%


Hand 2 – 3bet Preflop (6max)

For some reason sng wiz doesn’t do 3bet situations, so it’s good to know how to do them the old fashioned way.

This is stars 6max so the payouts are 65/35. Plug the stacks into the ICM calculator for each outcome. When you lose you are busto, so EQ_lose = 0. Here are the others:



Equation 2:
P_win > ( EQ_fold – EQ_lose ) / (EQ_win – EQ_lose)

EQ_lose = 0, so this becomes:

P_win > EQ_fold / EQ_win
P_win > 16.054 / 31.085 = 51.65%

So you need at least 51.65% equity to call a shove.

( Equation 1 also simplifies to: EV = P_win*EQ_win – EQ_fold )


Hand 3 – ZOMG ICM Postflop?

OK, this time you can work out the stack sizes yourself (50/30/20 payout). I get:

EQ_win = 24.896%
EQ_lose = 5.044%
EQ_fold = 11.781%

P_win > ( EQ_fold – EQ_lose ) / (EQ_win – EQ_lose)
P_win > ( 11.781% - 5.044% ) / ( 24.896% - 5.044% ) = 6.737 / 19.852
P_win > 33.94%

You need ~34% equity to call this shove.


Hand 4 – The Multiway Pot

EV = EV(call) – EV(fold)
EV = ( P_win*P_BTN_win_side*EQ_BTN_win_side + P_win*P_SB_win_side*EQ_SB_win_side ) - ( P_BTN_win*EQ_BTN_win + P_SB_win*EQ_SB_win )

.... Just kidding! Even I’m too lazy to do that, here’s a dodgy way to run these spots in sng wiz:

• Create a custom structure where the BB is the amount you have raised.
• Set the SB to the amount of the rest of the dead money in the pot.
• Put yourself in the BB, and a player who folds in the SB.
• Adjust stacks as necessary

And there you go:



Thanks STTF
Obv there are (still) lots of cool 2+2ers around STTF, I’m not going to list them all. But thanks AMT, Kevin8423, DevinLake, and Little John. Back when I was a noob and first found these forums you were the posters who’s advice I knew I could trust.

Hopefully some of you ICM noobs learnt something from this post.

Nicely structured post. Knew most of it already, but still good to refresh.

Nice1!!! I Love these equitations..ICM calculations etc.

ha-ha excellent math post . What is your profession , education ?

Coming from a Criminal Justice major, this hurts my head.

great post man, i've always valued your advice highly and I feel you are one of the best posters as far as strategy goes in this forum

makes the 2.5k post i had planned seem so trivial now. i might wait for 3k ;p

ty and gl with everything poker related

Nice post, you definitely seem to know a lot about this and it's good to know how to do it by hand. It inspires me to go through and solve a few problems with pen and paper (and pokerstove) the way I used to do it before good ol sngwiz.

Nice post. Congratulations on reaching the 1k mark.

Nice post! I particularly like the "Hand 3 – ZOMG ICM Postflop?" hand as it's pretty rare here that people think about postflop like this (probably because SNGPT, SNGWiz, etc won't let you do it automatically). Knowing you need 34% equity to call the push makes the decision just as easy calling with draws.

Juk

Yay maths! Solid, informative post, as usual. Thanks and GL.

My brain hurts

Good post. Would read again.

As usual, an excellent post. Looking forward to the next 1K.

..

I tried to dumb it down as much as I could.

Bonus points for anyone who identifies a Hero/Villain, Hand 3 should be obvious...

I'm doing a physics major, but my brain got fried after too much studying so I am taking the next 8 months off.

Congrats on 1k. Will read this soon as I plan on starting to play poker again within the month, and I will then bless you with much poker insight. Oh yeah, just don't drop out.

I'm glad i stumbled accross your post as I'm having difficulty understanding how these calculations have any relevance to a given hand as you are playing it. do you need to learn by rote certain situations that crop up regularly or are you expected to work each situation out in real time? (on-line site time limits seem to exclude this and if you're live in a casino?)
an example of my confusion is example 3. having raised his flop bet and then watching him run over you for all his stack, do you think your aces are good? if not, does it matter what your equity is? also, if you are not dead on with his possible range, how worthwhile are the equity figures anyway, some must be so borderline that you're a coin-flip anyway?
I appreciate the example of not calling the raise in example 1, the book i've read by K.Moshman explains that point well but i'm having difficullty seeing the point in the post flop examples.

any help greatly received

Very good post Ifldpcktns. I like the Hand 4, it's a SNGWiz trick I didn't know, ty.

You don't post a lot but everytime it's good quality and argumentation.

Very nice post!

Can you follow up more on how this...

Hand 3 – ZOMG ICM Postflop?

Falls into hand reading, defining the range here is critical yes?

thanks a lot and gl

Yep, hand reading is always essential, and is often (like in this case) the limiting factor to making correct decisions. I'm not really trying to argue how these hands should be played (I chose this hand because it is AMT pwning with AQo preflop), I'm just showing how the maths is done. The maths tells us we can call if villains range contains any dominated ace, {99,66,AJs,A9s,A6s,AJo,A9o,A6o} (35.9% equity).

These examples are just to show you how to analyze a hand post-game. Like I said before I'm not trying to show 4 examples where I have determined the correct play, I chose 4 interesting hands that have been discussed on 2+2. But if you repeat these calculations for hands you are unsure about, you will improve your intuition at the tables. This will work best in common spots, like say you have ~15 bbs 6-handed and make a 3x raise preflop and someone 3bets you all-in, if you have done enough of these calculations in the past you will have an instinctive feel for what your calling range should be vs any given shoving range.

FWIW villain in Hand 1 is Bigjoe, so I would snap-call and type "MY BUBBLE" into the chat, I bet Moshman doesn't teach that in his book.

Hehe, I remember the post now! It was the one where he called and Bigjoe told him "it was a -$300 call" and ended up with a big discussion on the long-term EV of spitecalling Bigjoe to stop him pushing ATC in spots like this.

Juk

I agree. Looking forward to another 1k posts.

thanks for the shout out, pktones. good luck with poker, it's been a pleasure having you around here as a strat poster and I hope you continue to indulge in poker study with us.

holla!

edit: orly?

So are you suggesting a fold in hand1?

if you do i have to disagree with that, that spot for that guy is worth taking a risky ATC shove that is -ev for this exact hand but once he gets chiplead he gets into mass +ev ATC shove zone where youll have to be folding everything, and you really can't let that happen with AK. And since AK hadly changes its 65% win chance against various ranges i think its a must call spot.