Tinkering With The Nash Equilibrium, Pt. II- Beyond Unexploitable Shoving

In the last post, we took a look at quite a few hands that were profitable to shove when heads up in the small blind.  I had also shown the hands with which it were profitable to defend against this play.  This time around, however, we will take a different tack and assume that we know that the big blind will be defending with the proper range against the unexploitable shove range.  Once again, we will use my favorite hypothetical example of a $2/4 game with 20BB stacks and a 5% rake and a defending hand range of 44+, A7o+, A3s+, KJo+, KTs+, QJs.  The simulation was run Monte Carlo style 10000k times.

Now here is what we can push:

The rabbit hole keeps getting deeper....  Notice that even after running the simulation 10 million times, there is still a tiny sampling error with 93s and assumedly the 53s as well, as neither J3s nor T3s are profitable and the 53s shows a minuscule $.01 profit, respectively.  Our unexploitable range has now grown from 38.4% of hands to an incredible 54.7%.

But why stop here?  Most players I play against simply refuse to make calls with hands like KTs, A3s, and QJs...even guys who I play against every day.  Let's run the simulation one more time with a more "typical" calling range of 55+, A8o+, A7s+, KJo+, KJs+.

86.4% of all hands are now playable.  In other words, all but the biggest of turds.  Oh?  What is that you say?  86.4% is not enough?  Ok then, let's toss a dead small blind into the pot and run it again and see what happens.

Happy now?  Yes, it's true.  With a typical calling range aided by the compensation of a dead small blind, you can now shove every single hand.  Naturally, logic dictates that you shouldn't be doing this.  While it would work a few times, it would quickly backfire and cause otherwise nitty players to begin playing more correctly against you and would thwart future attempts with a tighter shove range.  Besides, it's hardly optimal.  Rather, this was just an intellectual primer for the third and final installment of this series, where we finally combine all this knowledge to make you the ultimate motherfuckin' shortstack Houdini. 

Tinkering With The Nash Equilibrium, Pt. I- Unexploitable Shoving

The situation:  everyone folds around to you in the small blind.  You have 20BBs.  While everyone is confident in their ability to play premium hands heads up out of position, certain hands like weak aces and suited connectors can pose a serious problem, particularly when you are lacking post-flop maneuverability due to your short stack and the inability to launch an elaborate three street bluff.  You can either raise small or limp, though each of them has their own weaknesses.  If you raise small, when you are 3-bet, you will have to lay down a majority of these hands, whether or not you believe that your opponent is bluffing.  Limping will cause a serious imbalance in your range and makes you vulnerable to an in-position opponent whose range is completely undefined.

Two other options remain, and those are folding and going all in.  Since the aggressive move is usually superior, I would opt to go all in.  But which hands are profitable to do so?  A few years back, I was in awe of the Sklansky-Chubukov numbers as outlined in No Limit Hold'Em Theory and Practice.  For those who have not heard, the SC numbers represent the upper limit of your stack size in a $1/2 game where you can move all in from the small blind and have that play be preferable to folding- if you were to flip your hand over first and allow your opponent to play perfectly against you.  

At first I thought this was magic and now I look back at it as being hilariously nitty.  I have since been taught how to use the Nash Equilibrium via StoxEV to shove the highest percentage of hands for the maximum profit.  Though I have no idea how this was solved, I don't need to know how to build a car to drive it, either.

Here are the hands that we can shove for 20BB in a $2/4 game with the rake factored in (which the SC numbers fail to account for).

Not bad, huh?  Now suppose that an astute opponent knows what you are doing and what your precise range is.  How should he defend?

Clearly, there is very little he can do...not to mention that many players are not even comfortable calling with the bottom of this range.  In fact, players can only react to this in one of two ways.  They will either start calling lighter, which is a mistake, or they can call tighter and try and wait you out, making your shoves more profitable.

Although this lesson was fairly remedial, in the next, we will move on to some more advanced related concepts and you with then really begin to see just how deep the rabbit hole goes....

Using Your Holdem Manager for Ultimate Domination

I have felt it and I know you have too.  There's that one guy who you know, you just KNOW has been 3-betting you light and stealing your blinds more often than your HUD would lead you to believe.  This of course brings us to the inherent flaw of using one: it can only give us average statistics, and quite often says little, if anything, about how a foe is playing against you in particular.  But what if we could just take a little extra time to dig a little bit deeper into our database to find out the exact answers to these otherwise simple little questions?

Thus began my quest to find such answers.  Don't get me wrong.  Although I have railed against using a HUD in the past, I have since jumped this hurdle as I began to realize that using one is not something you do, but rather, something that you learn.  Helpful as they are, I was still craving these answers and knew that I could never be EXCELLENT as a shortstacker until I found it out.  Many people are reading this and surely believing that you can just tweak the filters and voila, there you have it.  Nope.  The "Vs Player" filter will only give you basic information such as total winnings and show you hands where said player is sitting at the same table as you.  Even if you try to get clever and filter it further for only hands where the action was unopened and you raised on the button and the big blind 3-bet you, the first thing that you will likely see when you replay a hand is that the villain you were looking to get a read on had already exited the hand.

I tried posting on forums, collaborating with confidants, and even writing to the actual programmers to find out how to do this.  Perhaps I was not explicit enough in that I was looking for actual percentages, but I got the same information over and over. It was simply not functional and led me to the same dead end.

Then the news broke on Pokertableratings about the 40putts/Kinetica/Littlezen shortstacker softplaying scandal.  A member of the esteemed DeucesCracked training site playing under the name NoahSD had taken extensive time to write a long and detailed report using statistical analysis to break down the 3-bet ranges of these players when playing against each other.  Aha!  So there is somebody out there who actually knows how to do this!

I thought for a while on how best to get this information from him, but then just decided to simply ask.  Lo and behold, in less than an hour's time, here is what he replied:

Hi Lorin,
Unfortunately HM isn't really designed to do this. I've been told that they plan to eventually add the stat "Player A's 3-bet % vs. Player B", but I think it's likely to be far in the future.

I used custom software to get my own answers, and frankly I have no idea how it works.  The only way I know how to do this without hiring a programmer to do it for you is with this tedious method:

To get Player A's 3-bet % vs. Player B:

1) Select player B in HM.
2) In the filter menu, go to more filters and add "PFR = True".
3) Run the report.
4) In the bottom half of HM, select the "All" radio button next to "last 500". Right click and select "export all hands to hard drive" and choose a spot to export those hands.
5) Options -> Database Management. Create a new database.
6) Import the hands that you exported into that database. This is a database of all hands where player B raised preflop.
7) Select Player A and run a report with no filter. The 3-bet % that the report shows is Player A's 3-bet % when Player B raised.

If you make a database with all the hands where you raised preflop, you should be able to quickly look at the 3-bet %s that various players have against you.

Hope that helps,
Noah


This was just awesome to me.  Though he might consider this tedious (and technically it is), I am no stranger to tedious work as I have spent countless hours running simulations using Stox EV that could often top 5 minutes for just a single, detailed run.  So what is one to do with such information?

Use it to completely dominate and control your opposition.

That statement being rather vague, I will give an example using a player whom we will term "KaySmash" to show you just how we can put this into practice.  On the HUD, it says that KaySmash opens the button 44% of the time.  I filtered out all hands where I was on the big blind.  Then I created a new database per the instructions and when I loaded it up, I set my filters to "Unopened" and "Button" and set it to run the report against KaySmash.  True to form, he actually was raising that frequency.  All that victimization was just a figment of my imagination!  More importantly, I can now see that he is folding to my 3-bet 44% of the time.  Since I am now armed with the information that he is not attempting to exploit my folding tendencies and just playing by a script, I can hereby assume that he will be treating me no differently when I am in the small blind as well.

While this information is excellent, it allows to me play a perfect shove or fold game against him, but doesn't really allow for much room for true exploitation since he is calling rather frequently.  So digging a little deeper, I then follow NoahSD's plan to find out how often KaySmash is 3-betting me by filtering out the hands where I raise the button and then running the report with KaySmash in the big blind and the small blind has declined to enter the pot.  Here is where it gets really interesting.

KaySmash is 3-betting me approximately 18% of the time, and never, ever just flat calling.  Though I was quite sure of this, since I am dealing with a rotating base of players on any single day, it is often easy to confuse them.  The fact that he is unwilling to get tricky makes him extraordinarily easy to beat.

I will give you guys a chance to digest this information for a few days and then in the next post I will show you precisely how we can use this information for an optimal strategy against this particular opponent.

Peace!