I played this hand at a home game on Saturday. My gut feeling is that my opponent made a good call but to know for sure I have to get my thinking cap on and work it out. That’s what we’re going to do here.
We were playing our usual game: a £20 tournament with rebuys for the first hour becoming a freeze out after that (six handed.) We were down to 4 players and the blinds were getting big (at 300/600) when this hand cropped up. I was in the big blind and the stack sizes were:
Dave B: 8000
Dave C: 10500 (SB)
Me: 8500 (BB)
The action went call, call, call, or alternatively “limp, limp and complete.”
Lee was under the gun and plays a lot of hands. He likes to call as well, so it needs to be a big bet to get him out of there if you’re thinking of 3-betting. I suppose you could say he is a passive player (or even a “faackin’ calling station” in the words of Dave C :) ). Dave B plays a sensible game and would definitely have something respectable – I thought he might have a small suited ace like A-6s, or suited connectors, or a small pair. Dave C in the small blind could have anything. It costs him 300 to complete in the small blind to get a shot at a 2400 pot so of course he will come along for the ride. He knows the odds.
Well, with all that weakness in front it looked perfect for an all in steal. So that’s exactly what I did, smashing all in over the top and declaring war on all you weak limpers or something similar. I had A-10o which I reckoned was the best hand, but I really didn’t want a call because I would be pretty much dead if I lost.
Well after I went all in it got interesting. Pretty quickly Lee and Dave B folded. It was good that Dave B folded because he could have had something as strong as, say 77, which I didn’t want a call from. But then it got to Dave C. He asked me questions…..lots of questions. I just thought this was irrelevant because I “knew” he wouldn’t call. Even after two minutes I was sure he wouldn’t call. I mean what hand would call an all in but wouldn’t raise the limpers?
K-Qs, that’s what sort of a hand.
And he did indeed look me up! To my shock, he called. But I think that might have been something to do the fact he’d done a whole bottle of red. Between quiz questions on my hand he even told me he had K-Qs and that he was thinking of calling. Pretty sure you’re not allowed to reveal your cards in the WSOP but it’s allowed in our game.
I reckon I always lose these confrontations when they have two middle cards (A-10o is a 56% – 44% fav over KQs)….. but not this time! An ace came on the flop and another on the turn so it wasn’t even a sweaty one.
But I got the inkling it was a good call. I couldn’t say it was a “bad call” at any rate, definitely not. So let’s work it out.
Looking at it from his point of view, of course he didn’t know I had A-10. He would have had to have made some guesses as to what I had. He would have also known I could shove with a wide range because it was such a great stealing opportunity. He knows the score. So let’s say “any ace” goes into the mix and any two broadway cards, because I could easily do that.
Something he didn’t say at the time, but that I thought massively relevant, was that I could have been doing this with a small pair. People always overplay their small pairs, don’t they? They don’t want to see a flop with 55 or 88, let alone play it multiway. So a small pair would have made perfect sense. K-Qs is virtually even money against the likes of 44 or 55 and I would have been really sweating after two minutes under the cross examination if that’s what I’d been holding.
I could have also been stealing with any two cards. It’s not impossible. So perhaps add in a random 10% chance that I was shoving any old crap. Adding in another 17 of the 169 combos gives us a very wide range indeed – 37.25% of all hand combos I could be shoving here. And I guess that is what tipped the balance in favour of a call.
K-Qs would be a 54.8% favourite against that little lot over a big enough sample.
Looking at the pots odds between the actual hands, he had to invest another 7900 to win the 18200 pot. That’s 1.3-1 odds and he needed to be 43.4% for it to be a fair call. He was pretty much bang on the money in that respect, being a 56-44 shot.
But against my whole range of hands, the call was a great one according to the pot odds. 54.8% when you only need to be 43.4% according to the pot odds is just fantastic. But pot odd, schmott odds. Pot odds isn’t the right way to look at a tournament decision. As we well know by now, ICM is the correct way to look at tournament decisions.
For an ICM calculation we need to know the payouts. (We actually did a chop when we got down to heads up but we weren’t to know that during the hand.) Payouts would have been something along the lines of £220 for 1st, £100 for 2nd and £20 for 3rd. At the start of the hand with stacks of 7k, 8k, 10.5k and 8.5k our stacks were worth the following values according to the ICM:
Lee: £72.7 (7000 chips)
Dave B: £81.3 (8000 chips)
Dave C: £100.5 (10500 chips)
Me: £85.5 (8500 chips)
Which sums to £340 as it ought to. What we are going to do now is compare whether it was better to fold to my all in or call it. We can work out the ICM for each case – 1) folding 2) calling & losing and 3) calling and winning. And then can decide what % of winning the hand he needed to have in order for the call to show a profit.
If he just FOLDS the ICM situation would be as follows:
Lee: £ 67.6 (6400 chips)
Dave B: £76.5 (7400 chips)
Dave C: £ 96.5 (9900 chips)
Me: £ 99.4 (10300)
If he CALLS AND WINS the ICMs now look as follows (based on new stack sizes of 6400, 7400, 19700 and 0):
Lee: £84.4 (6400 chips)
Dave B: £93.6 (7400 chips)
Dave C: £162.1 (19700 chips)
Me: £0 (0 chips)
If he CALLS AND LOSES the ICMs would look like this:
Lee: £76.7 (6400 chips)
Dave B: £86.0 (7400 chips)
Dave C: £26.2 (2000 chips)
Me: £151.1 (18200 chips)
So folding = £ 96.5. Calling and WINNING = £162.1 and Calling and LOSING = £26.2. Remember, these are the monetary values of your chip stack according to the ICM.
Knowing that the probability of winning the hand = (1 – the probability of losing) the hand we can set up an equation which tells us what probability is required to make the expected value (EV) of calling positive. Positive EV is the gambler’s holy grail after all.
For EV > 0
P (162.1) + ((1-P)*(26.2)) > 96.5
162.1P + 26.2 – 26.2P > 96.5
135.9P > 70.3
P > 0.52
In English, if the chances of winning the hand were 52% or better then it is a call which will show a profit.
As we know now – A-10o is actually 56-44% favourite over KQs so 44% is a long way from the required 52%. But that would be to judge in hindsight. It’s easy when you know what the cards are.
Dave was unlucky really. I could have easily been holding a lot worse than A-10o. We saw earlier that it was reasonable to suspect I was shoving 37% of hands. And if he thinks I am shoving 37% of my hands then in the long run KQs should indeed get the job done 52% of the time and more. Indeed, KQs would win 52% of the time if was shoving my top 30% of hands.
I think it was a good call.
Success in the long run comes down to a player’s ability to estimate his opponent’s range of hands. Especially when it comes to all in decisions. It’s not about saying “I think he had AK” or some other exact specific hand. You need to assemble a whole range of hands he mihjt be holding and then make your decision.
One final point. The all in call, after completing from the small blind no less, achieves something else. It tells me “you’d better think about it next time sunshine. You know I might just call.”