Friday, August 27, 2010

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....

Sunday, August 22, 2010

Determining the Correct 3-Bet Calling Frequency

Compared to the previous examples, finding your correct 3-bet calling frequency against a specific opponent is easy, though it takes a large sample.  Unlike 3-bet shoving, however, the penalty for making the wrong decision here is quite severe, being that you are now limiting to only winning one way- showdown.  Other than your opponent's range, you have two other considerations: the rake and the effective stack size.  For this example, I will summon our old friend "KaySmash" with a 20BB effective stack size and a $2/4 setting.  The stakes are very important here and that is due to the impact of the rake, which you will soon see.  In case you don't recall, KaySmash has a 3-bet range of 18%.  For this exercise, we will treat all 3-bets as an all-in shove, particularly since the 4-bet re-shove gets called somewhere in excess of 90%, despite the size of the 3-bet.

Using NoahSD's method as discussed previously, we combine the 18% 3-bet frequency with a quick hand history review off all such hands that were shown down.  For this particular player, we have a range of approximately 22+, A7o+, A2s+, KJo+, and KTs+ (actually 18.5%).  This is a fairly strong and not uncommon re-steal range.

For the simulation, I open min-raised every hand and then called with every single hand against the 18.5% range.  Here is what we get:

Probably a little tighter that you would expect?  The good thing is that this information is not privy to all players and they frequently make mistakes in this category...even when they [think they] understand what a shortstacker is doing.  While a call with with KQs is just a marginal no-no, a call with KQo or KJs is just disastrous!  Take a look at similar calls that often seem correct to players, like 22, A7o, and KJo.  And they say that being suited is overrated?

Even when we reduce the effective stack size to 16BB, the calling range changes only slightly, with the addition that you can now also call with A9o, A8s, and KQs.

A much more dramatic thing happens when we begin begin tinkering with the stakes.  Let's now run the simulation with 20BB's in a $.50/1.00 game.  Here is what we get:

Looks like 44 is now a clear fold with the stronger impact of the rake.  The effects become much more dramatic as we increase the re-steal range, but the evidence is clear- the rake matters.  What's more is that it penalizes the calling player more, since the winning player is the one who pays it, and when you call you only have the option of winning at showdown.

Friday, August 13, 2010

Using Your Holdem Manager for Ultimate Domination, Cont.

In a previous post, I had outlined a plan on how you can sift through your HEM database to gain crushing information on your opponents.  I had offered some specific numbers on Kaysmash, and now I will show you how we can use this information against him with StoxEV.  Here is what we do:

If we assume that he is raising 2.5x 44% of the time, his range is approximately 22+, A2o+, A2s+, K9o+, K2s+, Q9o+, Q8s+, J9o+, J8s+, 76o+, 54s+, 86o+, 64s+.  This does not need to be exact, as he will be folding out the weakest part of this range virtually* every time.  The important thing is getting his raising frequency correct, which we have already determined.

Now we must figure out his calling frequency of 56% (since he is folding 44%).  This not quite exact either, but still easy to figure out, particularly when reviewing my hand histories to find specific examples of hands he has called with.  In so doing, we get a calling range of 22+, A5o+,  A2s+, KTo+, K9s+, QJo+, QTs+, JTs.  This is an admittedly broad calling range, but in so doing, he prevents getting heavily exploited by shortstackers.

By factoring in the stakes of $2/4, rake and dead money from the blinds and then running the simulation 5000k times with a 20BB stack, here is what we end up with:

Voila!  The highlighted hands are the profitable reshoving range and the number below is the exact amount in $ that we can expect to profit per trial, on average.  Depending on the stack size, we can begin to shove more or less hands, but now his calling frequency will also be affected as well.  However, if we were to deduct just 3BB from the effective stack (this will not likely change his default calling range), the grid now appears as thus:

Amazing!  Now the next time you hear someone complain about a shortstacker having a mathematical advantage you will have a true understanding of what they are talking about.

For those of you who are interested in this incredible piece of software, please contact me and I can get you a $35 discount. 

*Even good players sometimes get frustrated and go on tilt and will call with a ridiculous hand like 97s.  For players who do this consistently, you now must fold your "non-showdown" hands such as low off-suit broadways and middle suited connectors.

Saturday, August 7, 2010

Finding Hidden Value in Pokerworld "Gold Chip Double Up to Cash" SNG's

At Pokerworld, there is currently a promotion offering two separate gold chip sit and goes.  The details are as follows:

12 entrants, top 6 earn cash!

Though the payouts are small at $5 and $15 respectively, the gambler in me is always looking for that freeroll hustle!  As it were, though these are a fairly easy score, they do not fill up often.  Just the other night, I had signed up for the $15 payout one, only to find that hours later, it did not even fill up.  I guess this would be understandable, as there are many gold chip satellite events that offer the potential of a significantly higher payout...if you have a few hours to spare.

However, if you plan on putting in large volume of hands and get started early in the day, you can score some extra EV, often just by sitting down!  How?  Since these take so long to fill up, it is very easy for someone to either have forgotten that they had entered (perhaps even the night before) or have gotten up to do something else and neglected them altogether.  The one I played in had just such a player.  He was "sitting" to left and we all had a field day stealing his blinds.   Having just one such player missing brings your average EV from $7.50 to $8.18.  That's an automatic increase of 9%.  Doesn't sound like much, but that ask any SNG pro if that matters, and they will all tell you that they would kill for such an extra edge!

Just remember to unregister before you leave your computer!

Tuesday, August 3, 2010

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,

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.