A Slave to Variance

Site down.

January 22nd, 2007

I’m sure that most of you know this, but the pokerstove.com site has been down for the better part of two weeks. I hope to have this resolved by the end of the month, in the time being, the latest version of the software can be found at:

http://208.109.202.54

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Minor PokerStove update

December 30th, 2006

I’ve uploaded a very minor update to PokerStove. You can see the changes in the changelog. Several of the changes were to the Monte Carlo evaluation, which was sufficiently neglected so as to have a fair amount of bugs. Also, I’ve begun development on version 2.0 of the software. Hopefully, it will be done sooner than later.

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The Mathematics of Poker

November 6th, 2006

A very good book has just gone to press:

The Mathematics of Poker, by Bill Chen and Jerrod Ankenman.

I received a review copy of it and found it to be an informative and challenging read. Short review: This is one of the most important books about poker ever published. For a longer review you can read Terrence Chan’s great early review of the book.

Few books on gambling take a truly analytical approach. In fact, the only other book in my library which comes close is The Theory of Gambling and Statistical Logic, Revised Edition, by Richard Epstein. Unfortunatly, that book has very little poker poker content. Chen and Ankenment do the world a service by with their thorough analysis of poker. Their methodology is clear, the problems and solutions are interesting, and their insights into the game are remarkable. They’ve also done an excellent job of keeping most of the mathematics accessible to anyone who has a solid grasp of algebra.

Here is an example of the kinds of insights you can get from reading and understanding this book. Below is a topological representation of the solution to the one street heads-up finite pot game with a maximum of two bets.

The strongest hands are at the top of the chart, and the weakest hands are at the bottom. The action maps as: f=fold, k=check, c=call, b=bet, r=raise. Each column reprsents the optimal strategy for the game. The strategy for the first player is in the X column, and the strategy for the second player is in the Y columns. If X bets, then the Y(b) column is used, if X checks, then the Y(k) column is used. It’s important to note that the actual location of the boundaries are not illustrated here, only their relative ordering.

Some basic insights from the solution: You need a stronger hand to check-raise with than you bet-call with. You should fold some of your value bets. Your bluff raises should be done with hands which are stronger (not weaker) than your bluffs.

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An interesting post about stud/8

October 1st, 2006

There’s a good post about playing high pairs in stud/8 at the 2+2 magazine. It illustrates a few common scenarios that you might face when you are heads up with a big pair versus someone going low. The basic conclusion is a bit muddied in the article, but can be summarized as follows:

Big pairs get crushed when a single low opponent - with no high draws - catches well on fourth (and fifth).

While a big pair still has an equity edge on 4th street if the low catches, that edge is tiny unless the big pair has not caught a second pair. The big problem is that if the low draw doesn’t brick on 5th the big pair is now caught in a reverse implied odds situation where while they have equity to show the hand down they will be giving up $ on every street from 5th-7th. And this is about as good as it gets for big pairs. If the low draw has as much as a gutshot, ace high, or two backdoor draws for high, the big pair has less than 50% equity.

On that note, this week I will begin working on a version of PokerStove which can handle stud and stud/8 so as to better estimate equity evaluation in those games.

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