Then there's the squeeze play all in for 5 times the pot and less. This is probably around 40 big blinds and less.
Today we are focusing specifically on the 2x pot shove. So if you have 15 big blinds and opponent in hijack makes it 2.5 and cutoff calls plus blinds and antes put 7.5 in the pot, you shove from the button for 15 big blinds.
We need to analyze this in a lot of depth. First, we need to know opponent's range of opening and calling range. Secondly we need to identify given your shove range how strong must opponent be to call. Then we must adjust both your shove range and opponent's call range until neither side can improve the EV by much.
To simplify, if one person calls the other's hand is dead and instantly mucks and it goes to a 1-on-1 all in showdown.
So let's start with the 10% raise and 10% caller.
10% of hands we will represent by
66+,AJ,A9s,+KTs+,QTs+,JTs
We will start by assuming one opponent calls with 50% of this range. That is 99+,AQ. Since there are two opponents, the chance that both opponents fold is 25%. .5*.5.
When you get folds, you pick up 1x the pot.
When you get called, you get 3x the pot when you win.
When you get called, you lose 2x the pot when you lose.
25% of the time you get 1x. This translates to .25 in value.
You must win 1/3rd of the time vs this range to shove.
Your shoving range vs this calling range are those hands which have 33.33% equity or better which translates into TT+,AQ+,AJs+,KTs+.
On average our equity of this range vs opponents range is 49.86% when called which translates to 0.6197 times the pot per shove. Since we shove with this range, we will only pick up .6197 pots 5.8823% of the time. This is important because a wider range that picks up a smaller amount more often may actually be better. so .6197*.058823=.036453x the pot per hand dealt If there are 7.5 big blinds in the pot that's 0.2734 big blinds per hand dealt.
What if opponent calls less? What if opponent calls more? What we are looking for now is a condition in which opponent can improve expected value vs this pushing range, and then we would in turn adjust our pushing range. If we are unable to reach a condition as profitable we're moving in the right direction. We'd then optimize pushing range vs that calling range, then adjust the calling range vs that pushing range and repeat until we can't really improve much.
We also want to find the point by which pushing with 27o and 23o are profitable so we can identify how overly tight opponents have to be until we can shove with any two. Hopefully, by identifying this spot and seeing a spot or two in between as well as finding the optimal shoving range, we can get a feel for how rapidly we can widen pushing range as opponents are less optimal.
What if opponent calls less? Calling range 99+,AK. Both fold 37.4471% of the time. We only need to be 28.03% to win so we can widen our range. This range is a bit strange since there is no AQ so Q8s is better than K9s. Also, Ax suited is good because it has a single overcard to a pair often enough to be profitable and since AQ is not in the mix it isn't as likely to be dominated by a premium ace.
Our shoving range is 22+,AT+,KJ+,QT+,A2s+,KTs+,Q8s+,J8s+
That translates into .212459x pots per shove but because we shove on 19.76% of hands in this spot, we actually gain .042 per hand dealt given this set up which is more than..0365 from looser calling ranges.
As a rule of thumb, usually when you can widen your profitable shove range, your opponent did something wrong. Usually either that means opponent makes shoving more hands profitable, because he folds too much, or more hands have value over opponent's calling range. A too tight opponent is the only situation where you can shove any two as the too loose one you still have to have equity over a random hand after pot odds.
So if 2 opponents who raise and call with 66+,AJ,A9s,+KTs+,QTs+,JTs only call a 2x pot shove with TT+,AKs, that means they are playing 34/134 combinations of hands or 25.4%. 2 opponents folding 74.62% means 55.7% chance both fold. With this information, we can see we only need to win 14.86% of the time.
If opponent tightens calling range up to TT+,AKs we can shove with any two and although 27o and 38 doesn't quite profit, it is within less than 1% of being profitable and 23o does and 28o does and 26o does so it's close enough for me.
So we found the tightest boundary. Now the question is, would our opponent loosening up their calling range from 99+,AQ force us to make less profits? If so, we are not quite at equilibrium.
Let's say opponent calls 88+,AQ+,AJs+,KQs. Both opponents fold only 15.06% of the time. This means we will have very little value in pushing with a poor hand. We need to be 36.46% to win to shove. I can already tell it's going to be close because before we couldn't push with 99, but now we can, but we can no longer push with KTs. The exact range is 99+,AQ+,AJs+,KJs+ which is pretty close to the same as the original.
We pick up .6505 pots when we shove on average. But we only shove on 6.03% of hands. The total of 0.039243917x pots per shove or about .294 big blinds per hand dealt per situation that comes up is more than our original esimation of 50% of hands.
Therefore we can conclude a shove range with 2x pot vs 10% raiser and 10% caller of TT+,AQ+,AJs+,KTs+ is approximately optimal with opponent's approximately optimal calling range of 99+AQ. The calling range should actually be slightly tighter for the initial raiser unless his sole goal is making us lose since he still has to worry about the opponent left to act. This means our shoving range may be slightly looser, but likely not by much if at all since there is also the possibility that both opponents call which wasn't calculated.
If opponent tightens up only slightly to 99+,AK our shoving range can widen to 22+,AT+,KJ+,QT+,A2s+,KTs+,Q8s+,J8s+
Shoving with any two becomes profitable when opponents in this spot only call your shove with TT+,AKs.
This should give us a better feel of how we can widen our shoving range as opponents tighten up their calling range
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notes:
However, always keep in mind that if opponents don't call optimally, shoving optimally is still more profitable than if opponents did not call optimally. You just have the opportunitiy for even greater gains if you can accurately speculate on what range opponents will call with. Typically people are going to be surprised at how opponents play and are not going to know how strong they will call. Plus, you already are making an assumption about your opponent's calling range which can also be incorrect. However, if you choose somewhere between "optimal" and exploitative" you have given yourself a margin of error if your assumptions are wrong. For example, if I thought opponent would call 99+,AK and he actually calls with AQ, I would make less that shoving the optimal range. But if I'm right, I'll make more shoving the exploitative range. By doing somewhere between, I can make a little more when I'm right and lose less, or have less missed opportunity.
So I might aim for something like 77+,AQ+,KQ,QJ,A9s+,KJs+,QTs+,JTs. That allows me more profits than just shoving the optimal amount if I'm right, and I lose less if I'm wrong than shoving the exploitable amount and because I'm probably right more often than not, but not to a large enough degree where it would be dangerous to shove with too wide of range, overall I should approximately optimiize my profits. Another alternative is having an "advertisment play. If you think opponent is playing tooo close to optimal, you can try to show either a crazy bluff or a KK,AA type hand so they are more likely to make a mistake later and adjust their range as a reaction to you.
Now we have to basically repeat this exercise for 3x,4x and 5x pot and also for hand ranges of initial raiser and caller of 20%,30%,40%,50%, 50% and 100% and any two for both. This means we have to do 15 times the work we just did, which will be exhausting, particularly as the range widens and there are more hands individually to run through to determine if they are okay to shove.
Nevertheless, doing work like this gives you so much better of a feel for poker than actually playing even 10,000 hands. So it actually happens to be a MAJOR shortcut to poker excellence.
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