Thursday, November 25, 2010

Tinkering With The Nash Equilibrium, Pt. III- The Short Stack Houdini

In the last post about this subject, I ended with a note of how just adding a dead small blind can seriously impact what you can get away with in terms of open shoving a 20BB stack.  This is a direct benefit of short stacking and does not have much of an effect for larger stacks, as the potential gain becomes a much smaller percentage of the total stack size while severely increasing the risk.  This week's post takes the concept of pushing complete trash to the extreme and examines what happens when you have a player who posts on the cutoff and the action passes to you in the blinds. 

Before I get into it, let's take a look at what I normally do in this situation:

Now, time for a quick quiz:

Q. What the fuck just happened there?

A) Short stack donk on tilt.
B) Idiot who thinks Q8 "double suited" is the nuts because it can make two different straight flushes.
C) Astute short stacker looking to gain a quick and easy profit against two very weak hand ranges.

Answer: C

Think about what happens after someone posts and then checks.  His range is now weaker than the big blind's.  It's simple: he had the option to make a cheap raise in a steal position and declined to do so.  Of course, he could be trapping, but this becomes very unlikely, for these reasons:

1) The button still has to act, meaning that this player is potentially acting out of position against three players whose ranges are completely undefined.  Furthermore, if he was hoping to limp-reraise against the button, even the fish know that this would be a parlay of highly unlikely events that includes having the button raising and calling the back raise, yet NOT having enough of a hand to call a single open raise.

2) Few hands can stand any real pressure against two completely random hands and expect to both win the hand WHILE ALSO generating a medium to large pot without the fear of overcards.  This includes 99-KK, and good broadway hands.  Therefore, it generally makes more sense to just raise with these hands, especially when you factor in what I pointed out in Part 1.

The bottom line is that most players will play their hand's straight up when posting in, meaning that they will raise when they have a good hand and check when they don't.  Since there are very hands that are not good enough to raise yet believe they are good enough to call a shove.....we do the shoving!

At this point in time, this should be making sense.  Of course, since I have the tools to prove my hypothesis, I will do so.  The simulation that I will run builds upon the knowledge from the other TWTNE posts, so if you have not read them already, I would go back and do so now so that your understanding of this part is complete.

Step 1- Assigning a Range to the Poster

This can never be an exact science since everyone is a little bit different, so we must figure out what a "reasonably reasonable" player would do.  Here is what I came up with:

Yes, I expect that most players will be open raising with at least 55-88 as well as many other hands in this range, but I prefer to leave them in to compensate for when the player does something completely unexpected, like check with AA or AQ.

Step 2- Assign a Calling Range for the Big Blind

Although once again this is not perfect, this is a little easier to do since I have a lot of experience with the calling ranges of heads up shoves.  Even though I expect the actual calling range to be tighter than this, I will use the optimal call of the Nash Equilibrium shove.  That range is 44+, A7o+, A3s+, KJo+. KTs+, QJs.

Step 3- Assign a Calling Range for the Poster

While I could certainly figure out a CALL, CALL range, over the hundreds of times that I have done this, I have never seen both players call.  I therefore assume that if the big blind calls, the poster will fold, especially because several of the calling hands I assign to him do not match up well in large 3-way pots.  

Instead, I give him a call range of 44-88, A5o-A9o, and A2s-A8s.  Of course, most of this is purely theoretical and assumedly tighter than what I present here, yet I still feel that this a good approximation of a worst case scenario.  

Now it's time to run the simulation.  I use a $3/6 game with 20BB effective stacks.  

It is pretty difficult to tell whether or not the 73s is a sampling size error, so during play, I prefer to err on the side of aggression in situations where the cost of being wrong is usually tiny in the long run, yet the upside is likely high, especially when you factor in metagame benefits.  

Once again, let's see what happens when the poster puts up both the big blind and a dead small blind and things get even more interesting.....

That's right, bitches!

Remember...this is the worst case scenario.  I normally shove all hands (ok, maybe not the best hands) with or without the dead small blind present.  After all, the only guys who might be keen on the fact that I am shoving everything here are the regs and they will often be too involved in their other games to know whether or not the poster had just posted or if he had limped.  Even still, they might consider the proposition too risky overall to call light since they don't understand as well as I do how often the poster is actually making the call.

This play has nothing but upsides:  

A) They fold and you pick up some easy money.  This happens about 85% of the time.
B) They call and you suck out and win.  No explanation needed here!
C) They call and you showdown a turd and lose.  Now you look like a complete spewtard and you will have no trouble getting action from that point on.

Final note: you can do this play over and over again because it is a very infrequent scenario that would allow you to do this to the same person several times.  While this could happen in full ring games, there still is nothing much that people can do about it, particularly because so few of these hands are ever getting shown down and it is consistent with how I play many high quality hands as well.  In 6-max games, the situation becomes even better as those players who are not patient enough to wait 3 hands until the big blind hits them will likely not last long enough to become a victim of this play a second time.

In conclusion, I hoped that you all have enjoyed this series and it has opened your eyes to things that you never thought possible.