I saw this hand last April and it really caught my attention. After being knocked out of a tournament I’d left the screen open on my PC and happened to look over just as the final hand was played. This are the scenes that unfolded. I took a screen print of the hand history and saved it as a word document. I gave it the title “Funny shove – Funny call” and I resolved to look at it in more detail later on.
Being as it was the final hand there were naturally just two players left. One had 25k and the other had 65k. The 25k stack shoved and the 65k stack called in an instant, with absolutely no thought whatsoever. Showdown!
25k stack: 3-2s….whoopsie.
65k stack: J-8o.…..!!!!???
No-one made anything, the jolly old J-8 offsuit won with Jack high and he took first place.
It’s that age old problem. It’s fine to move all in with a filthy hand…..unless you get called! I’m joking of course. The play is either fine or it isn’t fine. It doesn’t become good or bad depending on the result but you know what I mean. When they fold you get away with it but when you are called you’ve been exposed. Hand in the cookie jar, trousers down and all that.
Anyway, I did look at the hand in further detail and what I found really surprised me even though I’ve been playing poker for seven thousand years. The shove itself is not a bad play!
Not a bad play – how so? How silly do you end up looking when your pathetic 3-2s gets called? This really is not intuitive stuff and it requires an explanation. There’s a bit of maths here but stick with it because I can actually prove the point to you. Basically I asked myself the following question: “If I was in the shoes of the player with 3-2s, how often would I expect this all in move to be called?”
I came up with a figure of 25%. He could expect to get called one time in four and the other three times his opponent would fold. And this is the conclusion that surprised me: if that assumption is true – ie if your opponent will call you 25% of the time – then it is not a bad decision to shove all in.
25% of hands means something like: 66+,A2s+,K6s+,Q8s+,J8s+,T8s+,A7o+,K9o+,QTo+,JTo
Do we think this is fair? I reckon so. Our 3-2 suited man probably wouldn’t expect to get called by the likes of T8s or JTo but then again he might expect to get called by some hands which aren’t in the list, particularly any pair or any ace. We only go as far as A-7o but A-2o through to A-6o could also call. So take a few out hands and put a few in and 25% is roughly OK.
Now our 3-2s man wasn’t to know he was going to get called by a hand as weak as J-8o (which would amount to a calling range of at least 43%) but my point is that he was entitled to think 25% was all he would get called with and on that basis, his shove was absolutely fine.
To prove this we get into the realms of the ICM, or the “Independent Chip Model”.
ICM puts a monetary value on your chip stack which is important because as we all know, poker chips and money are not the same thing. If we know what our chip stack is worth right now – and we also know what it will be worth after a hand has played out, we are in a position to compare the two scenarios and answer that vital question “will this play show me a profit?”
If you really want to understand exactly how ICM works I’ve added the best explanation of ICM I ever found on the internet at the end of this piece*. That explains it beautifully but you don’t have to read it. You could just take it on trust that ICM assigns pretty accurate monetary values to chip stacks.
OK – back to our “ridiculous” hand with the 3-2s and J-8o. There were 61 players in the tournament and we were down to the last two. 1st place paid $192 and 2nd place paid $132. The exact chip stacks and monetary values assigned by ICM were:
25,832 (ICM = $148.94)
65, 668 (ICM =$175.06)
Now let’s look at it from the point of view of 3-2s man. We are only looking at shoving or folding here to make things simple – ie we won’t consider small raises. That being the case, these are his options.
He can FOLD and move on. If he does this he’ll have 1000 less chips, ie 24, 832 (ICM = $148.28). So folding gives us a monetary value, calculated with the ICM, of $148.28. Remember this figure because it is the figure we will use as a comparison to shoving all in.
Folding = $148.28
Or he can SHOVE all in. When he does this one of three things will happen.
1 – his opponent will fold and he will win the blinds (stack is 27 832 and his ICM = $150.25)
2 – his opponent will call and he will win the hand (stack is 51664 and his ICM = $165.88)
3 – his opponent will call he will lose the hand (stack = 0, he comes 2nd and gets $132 no need for ICM)
So we know what the potential results are. What we now need to know is what are the chances of each outcome occurring should he decide to shove. This boils down to one question: how often will he get called if he does shove?
We’ve already agreed on 25% but the longer answer is that we just don’t know. Of course we don’t know because we don’t know what our opponent is holding and even if we did we still couldn’t guarantee he would call with those cards. But we can always estimate. The ability to estimate well is what makes the good players good. They will ask themselves “Is he loose or tight? What’s he been doing so far? Have I tested his patience lately and is he itching to call?”
With a calling frequency of 25% let’s get back to those three things that can happen:
1 – opponent will fold 75% of the time and he will win the blinds (ICM of $150.25)
25% of the time his opponent will call. Of this 25%……..
We feed into a hand calculator
2 – opponent will call and 3-2s will win! 33.43% of the time 3-2s will have an ICM of $165.88
3 – opponent will call and 3-2s will lose. 66.57% of the time 3-2s will be eliminated with $132
We now have all the information we need to work out the expected value of shoving. When we’ve done that we’ll compare it to the EV of calling and see what the better option was. For each shoving outcome we multiply the probability times the result.
Our EV is shoving is the sum of: (0.75*$150.25) + (0.25*0.6657*$132) + (0.25*0.3343*$165.88)
112.6875+ 21.968+13.863 = $148.52
Shoving all in = $148.52
If we shove we can expect a monetary value of $148.52
If we fold we will have a monetary value of $148.28
The numbers are almost identical, but shoving 3-2s all in is ever so slightly preferable. So there you have it: shoving all in is as good an option as folding, assuming our man will fold 25% of the time. That’s nuts. I reckon 90% of players, if not more, would just fold the 3-2s in that spot even though that option is indistinguishable from shoving all in.
OK, you’re probably thinking “but his opponent called with J-8o. That’s not 25% of hands”
And you’d be right. But in some respects, calling with J-8o is every bit as ludicrous as shoving with 3-2s. Would you call with J-8o? I wouldn’t.
If you ranked all 169 starting hands against a random hand, J-8o would be the 79th best. 43.9% of all hands are better than J-8o. So the chap calling was pretty darned wide – a good bit wider than 25%. Like I say, I saved the document as “Funny shove – Funny call” so my initial reaction was that it was a perverse call.
Don’t get me wrong. I’m not saying 3-2s is an automatic push here. All I’m saying is that it’s as good as folding if we assume you’re only getting called 25% of the time and I maintain that this is a decent assumption.
What if we assumed differently? Say we expected to get called 20%, 30%, 40%, or even 50% of the time? Well let’s have a look. Using the same method of above, here are the results:
20% (67.85% to beat 3-2s) – shoving has EV $148.83 vs EV of folding = $148.28.
30% (66.34% vs 3-2s) – shoving has EV $148.19 vs EV of folding $148.28.
40% (65.97% vs 3-2s) – shoving has EV $147.56 vs EV of folding = $148.28
50% (65.67% vs 3-2s) – shoving has EV $146.94 vs EV of folding = $148.28
As you can see from these results, you are actually marginally better of shoving 3-2s unless you are getting called 30% or more of the time.
Although shoving 3-2s looks pretty awful on the face of it, it leads to elimination a lot less than you’d think. If you get called 25% of the time, you get eliminated less than 17% of the time because you still win one in three of those times you do get called.
In this case I think the guy shoving 3-2s was actually unlucky to run into a player who was prepared to call with J-8o. Calling with J-8o is the riskier play in my opinion. So is there a moral to this story?
Well if there is, it’s that perhaps we ought to be sticking our stack in a bit more readily than we do! So go forth and start spewing (I mean shoving) those chips around !
*Appendix: ICM Explained (source unknown):
ICM stands for Independent Chip Model…don’t worry about the name, it’s not worth it. It’s one of many attempts to try to equate tournament chips to cash. Like the rest of them, it’s not perfect…there’s way too many factors involved to get an exact answer to what your stack is worth – player skill, style matchup, desperation by very short stacks, tilt…stuff like that is just too arbitrary and complicated to put into a model. So…assuming equal skill, enough skill that straight style isn’t much of an effect, no-one’s very short stacked (like 3xBB) or tilting, ICM does pretty well at equating tourney stacks to cash.
The idea behind the model is that every chip is a ticket to a lottery. To figure out who gets first place, you pick a ticket at random and that person wins. Take their tickets out and draw again for 2nd, and repeat that for 3rd, etc ’til you’re out of the money. Now, we all know that’s now how poker works, but remember, this is a model…a guess. Let’s look at an example.
3 players, stack sizes: 5k 4k 1k
Each person’s chance of winning 1st is their stack/10k, their chance of getting picked in the first lottery. To figure out who’d come in second given who comes in 1st, their chance is stack/(sum of remaining stacks). We end up with our estimated equities.
1/2 – chance of 5k winning
2/5 – chance of 4k winning
1/10 – chance of 1k winning
If 5k wins:
4/5 – chance of 4k in 2nd
1/5 – chance of 1k in 2nd
If 4k wins:
5/6 – chance of 5k in 2nd
1/6 – chance of 1k in 2nd
If 1k wins:
5/9 – chance of 5k in 2nd
4/9 – chance of 4k in 2nd
Let’s go with a $100 pot, to make things easy on me, with standard payout of 50/30/20
Equity of the 5k stack:
(Chance of 1st) + (Equity if 4k wins) + (Equity if 1k wins)
(1/2 * 50) + 2/5 * (5/6 * 30 + 1/6 * 20) + 1/10 * (5/9 * 30 + 4/9 * 20)
(1/2 * 50) + 2/5 * (25 + 10/3) + 1/10 * (50/3 + 80/9)
25 + 2/5 * 28 1/3 + 1/10 * 25 5/9
25 + 11 1/3 + 2 5/9
Equity of the 4k stack:
(Chance of 1st) + (Equity if 5k wins) + (Equity if 1k wins)
(2/5 * 50) + .5 * (4/5 * 30 + 1/5 * 20) + 1/10 * (4/9 * 30 + 5/9 * 20)
(2/5 * 50) + .5 * (24 + 4) + 1/10 * (13 1/3 + 11 1/9)
20 + .5 * 28 + 1/10 * 24 4/9
20 + 14 + 2 4/9
Equity of the 1k stack:
(Chance of 1st) + (Equity if 5k wins) + (Equity if 4k wins)
(1/10 * 50) + 1/2 * (1/5 * 30 + 4/5 * 20) + 2/5 * (1/6 * 30 + 5/6 * 20)
(1/10 * 50) + 1/2 * (6 + 16) + 2/5 * (5 + 16 2/3)
5 + 1/2 * 22 + 2/5 * 21 2/3
5 + 11 + 8 2/3
So what we got is:
Which makes some sense – everyone’s got at least $20 equity because they’re in the money now, and the 5k is slightly better off than the 4k, and both are way better off than 1k.