Saturday, 13 July 2013

Thinking outside the box

ICM at its finest

Hand Played on Pokerstars
Seat 3: Big Stack (5767 in chips)
Seat 4: Mid Stack (2932 in chips)
Seat 6: Hero (301 in chips)
Big Stack: posts the ante 25
Mid stack: posts the ante 25
Hero: posts the ante 25
Big Stack: posts small blind 100
Mid stack: posts big blind 200
*** HOLE CARDS ***
Dealt to Hero [Ad 5s]
Hero: calls 200
Big Stack: raises 5542 to 5742 and is all-in
Mid Stack: calls 2707 and is all-in
Hero: folds
Uncalled bet (2835) returned to Big Stack
*** FLOP *** [3c 5h 2c]
*** TURN *** [3c 5h 2c] [6s]
*** RIVER *** [3c 5h 2c 6s] [Qc]
*** SHOW DOWN ***
Big Stack: shows [7c 5c] (a flush, Queen high)
Mid Stack: shows [8d 8s] (a pair of Eights)
Big Stack collected 6089 from pot
Mid Stack finished the tournament in 3rd place
Seat 6: Hero (button) folded before Flop
Hero coasts into the money J
This hand should act as a key reminder of the importance of ICM for new or upcoming SNG players.

I’ve just lost an all-in and find myself cripple stacked on the button, and glance down at A-5o, easy shove right? Well, it would be if you weren’t too clued up on the concept of ICM and I’m fairly certain at least 99% of players would shove here. On the other hand, I believe it to be the second best play. We are 1.5bbs deep so it’s pretty clear we have no fold equity against either opponent – that’s to say we won’t be able to get either player to fold if we shove all-in, especially the BB who will have a profitable call with 100% of cards regardless of our range pretty much.

What does this mean?
This means limping becomes the preferred option because if we limp and both the stacks end up all-in pre-flop, we can then fold in hope that the big stack eliminates the mid-stack and we coast into the money since a 6max SNG pays the top two finishes. This gives us a much better shot at making money overall since if we were to shove and end up in a 3 way all-in we would have to beat both opponent’s hands to stay in the tournament since we’re the short stack and that will be difficult with A-5o in a 3 way all-in. And even so, if we triple up, we will still only have 4bbs and will definitely be in need of more future double-ups to get back into the match before thinking about making money, so our best shot at making money in the long run will be to limp-fold and leave our stack super crippled.

There’s two counter arguments to this strategy that may make some of you sceptical:

1.    It’s even worse for our equity when the mid-stack wins the all-in since our stack becomes super crippled and we’ll almost definitely bust.
2.    Usually the mid-stacks range for getting it in will usually be much stronger.

The latter isn’t necessarily true if the mid-stack has no grasp of ICM, but for most part, assuming the mid-stack isn’t a complete idiot they should win more of the time meaning we’ll go on to bust more of the time and therefore not make money as often.
So let’s take a look at the numbers to see if we can make some sense of it all:

·        Equity of our stack pre-flop = 4.83%
·        Equity of our stack if we limp-fold and big stack wins = 35.25%
·        Equity of our stack if we limp-fold and mid stack wins = 1.30%
·        Equity of our stack if we limp-call and lose = 0%
So, as we’re very really low on chips the equity of our hand before the cards are dealt is 4.83%. If we limp-fold and the mid-stack wins, we’ll be left with 76 chips and our equity will drop to 1.30% - not so great! Needless to say, if we limp-call off and lose we’ll eliminate in 3rd place and our equity will be equal to 0%. However, as you can see, if we limp-fold and the big stack wins, we’ll coast into the money and given that a 6max SNG rewards 2nd place 35% of the prize pool, our equity will take a staggering rise from 4.83% from when the cards were dealt pre-flop to 35.25% - that’s massive!

Indeed, if the mid-stack is solid and has a really skinny range for getting it in here then the majority of times they will win and we will be left with that stack resembling 1.30% in equity. However, we only lose 3.53% in equity when this happens (4.83% – 1.30%) and when comparing this to the times the big stack wins, our equity increases by 30.42% (35.25% – 4.83%) and that's guaranteed money. And remember, even if the mid-stacks range is much tighter than the big stack’s when the cash goes in, suck-outs can always happen too!

So the conclusion is even if the mid-stack will win the majority of the time, limp-folding is still the preferred option since the equity we gain is so huge the times the big stack wins, and on top of this, since we’re so short our equity is that negligible that we aren’t losing a lot by folding – we only drop 3.53% in equity, and the times we do commit to the hand and win the 3 way all-in (if we were to limp-call off), our equity is still considerably low since we’ll still only have 903 chips and we’ll almost certainly require future double-ups to make money.
As it was, both stacks got it in and luckily for me the big stack managed to beat the mid-stack and I coasted into the money with that 76 chip stack. Lucky for me indeed, but sometimes you just gotta make your own luck!

Live long and prosper

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