Friday, May 26, 2006

No, I am not a Calculator

Raveen made a comment on my last real post on squeezing EV out of a loss, so I looked him up and saw a question for a basic mathematical analysis of a particular poker decision. My kind of puzzle, I put out a comment calculating the EV of the options fairly precisely.

Mookie in a comment to my last post pimping Bloggerstars asked how much math I actual use in big hands at the table. My response here is to that question:

Nothing close to that kind of calculation on the fly. His hand was actually pretty easy because he was so clear on his read (that his opponent was drawing to the nut flush) and because the chips were mostly all in already--no question of calculating implied odds there. In a real game, I wouldn't have done anything like the whole analysis but like most people know that a flush draw is basically 2:1 behind at the flop and that my opponent was not going to be able to fold. The choices were either call with half my chips behind and wait to see a turn (folding if the board 3 flushed) or push on the flop and let the cards fall.

The exact EV I calculated in the comment I would not be able to determine, but I would know that I would be losing EV if I checked and my opponent was capable of folding the turn and gaining it if he was not (aside: there is a variation of this situation however if less chips are in the pot versus the stack sizes where it is better to bet less than all in to give your opponent the opportunity to make two mistakes, one on the flop and one on the turn--FTrain has pointed this out to me and he is quite right that it goes against my natural inclination to get it all in sooner--this is a hole in my game--I believe Raveen's situation was different however).

The math I use in post-hand analysis is not that complex, but still not something I am capable of doing in real time. My actual math technique at the table when it's close enough to need computation is to first quickly as I can determine the pot odds I am getting, then I will guess the hands my opponent likely has and the outs I have against them (or vice versa), discounting outs that might be "bad".

For example, let's say on the flop if I have a flush draw with middle pair and a gut shot, and put my opponent on two pair or a set, or maybe just maybe top pair top kicker. Against the worst of his hands I have 18 outs, against two pair I have 12 outs against 4 redraws, and against the set I have either 9 or 11 outs (depending on whether it's bottom or top set) versus 9 redraws. This much I probably can spot at the time or close enough (if he is all in, I can take my time, otherwise I can still think but at the cost of giving away some information--much more likely to do this live BTW)--I would at some quick point take a rough guess that I have about 10-11 "effective" outs against the range (I have heavily discounted TPTK) and redraws. With two cards to come, using the rule of 4, I have about 40-45% chance to win--again this I can and do on the fly. The math is not perfect, but enough to guide me and any error is less than that attributable to the reads.

After I make this calculation, unless the action is all-in or fold, I'll also need to figure how I think my opponent will react to my actions. The actual decision paths will vary depending on the strength of the opponent and the size of stacks behind, if any--here there is math moving through my head in the background, but it's not something I will consciously calculate (see my post on the Math-Feel Balance a few posts ago).

I want to say doing all this does is not sufficient to make good decisions--though I think all good players do some form of this either consciously or intuitively (for some people, they have seen so many hands that the right analysis just comes, and for still others I've heard just get it from the get go).

I recognize that I am no such savant, and made the commitment to myself a way back to force myself to run the numbers afterward on close hands to gain the maximum learning value and to check whether my thinking at the table was on the right track. Running through the full math after-the-fact makes it easier to react faster to those situations at the table in actual real time when similar situations occur. This is also one of the primary reasons that I blog.

It is worth noting however that for this kind of math to result in better decisions, your reads have to be right--if you assign incorrect values to your effective outs because you fail to see a likely holding or give too much weight a less likely holding, all math will do is lead you to a bad decision. More simply put: garbage in, garbage out.

Again, some people get this through massive experience at pattern recognition, others I suppose through physical reads (I for one on rarely benefit from the latter).

Personally, I think I’ve got the math largely down, and I’m getting better at the reads, though I still have a lot of room for improvement. The last primary component I think is the discipline to follow through the results of the first two. You can get your reads down, you can calculate the optimal move that results from those reads and your own holding, but if you fail to execute—which in any given context can mean failing to fold, call or raise—you will lose. Anything that causes one to lose this discipline can make the perfect reader with the perfect calculation skills a perfect loser.

Unfortunately, I sometimes resemble this remark, without the first two perfects.


At Sat May 27, 11:17:00 AM 2006, Blogger Garthmeister J. said...

Math is hard.

At Sun May 28, 05:05:00 PM 2006, Anonymous mookie99 said...

Great post. Thanks for taking the time to answer my question and in so much detail.


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