## A Mathematical Example of Why “Small Ball” Tournament Play Works

Mathematics, Tournaments
May 5, 2008

For those not familiar with the terms, “small ball” tournament play is a style of play in NL tournaments (usually holdem) where you avoid large confrontations unless you believe you have a huge edge – a small positive expectation in tournament chips isn’t enough to justify going all in against someone.

For some reason, small ball is a concept that a lot of people have a hard time grasping, or believing is correct. Read the rest of this entry »

## Game Theory Part 4: Personal Opinions, Or Why I’m Not a Big Fan of Game Theory

Mathematics, Poker Concepts, Strategy
May 4, 2008

It’s time to talk personal playing philosophy. Over the last month or so, I’ve written a ton about strategy rhos and game theory. I’ve talked about several different rhos:

If you read these articles carefully, you’ll notice that I’ve adopted three different and indeed incompatible approaches to poker strategy in the three series Read the rest of this entry »

## Aces & Set farming Part 1

Mathematics, No Limit Texas Holdem
April 26, 2008

It’s time for one of the most important things I’ve got to say about no limit Texas holdem. We’ve talked previously about the topic of set farming when discussing the 5/10 rule. Specifically,

Set farming is calling a bet preflop with a small to medium pocket pair (which is unlikely to be best by the river if it doesn’t improve) hoping to hit a set (3 of a kind made with one on board plus your pair). It’s a longshot play where you rarely hit, but when you do you have a hand that’s almost certainly best, and you can comfortably get your stack in.

Set farming is a very central part of correct NL play. In fact, against certain opponents, it is the single most profitable tactic in your arsenal. To understand why, consider this hypothetical hand: Read the rest of this entry »

## Game Theory Part 3: Observations

Mathematics, Strategy
April 13, 2008

In the last game theory column, I presented a real-world poker problem, and started through the process of figuring out the equilibrium solution. As you probably noticed, I simply told you what the solution was without explaining how I got that solution. Now I owe it to you to explain how I did it. Read the rest of this entry »

## Game Theory Part 2: Applications To Poker

Mathematics, Poker Concepts, Strategy
April 11, 2008

Last time, I explained what game theory is using examples from roshambo. That’s all well and good, but this isn’t a roshambo strategy site. So let’s look at the poker implications. As we stated, any time there is a strategy rho, you can minimize the worst result you can get by choosing randomly between the options in the head of the rho at some frequency. Thus far, for poker, we’ve only discussed one rho: the big rho of tight play, aggressive play, and calling down. This is certainly an interesting example of a strategy rho, but it’s lousy for a discussion of game theory. The reason is that it’s somewhat of an abstract concept – we haven’t defined what exactly each strategy entails, and therefore it’s impossible to figure out the exact expectation when two strategies meet. This makes solving the associated game theory problem of how frequently you should do each to get a game theoretic optimal result impossible. To that end I want to introduce a new rho: the bluffing and calling on the end rho. Read the rest of this entry »

## Game Theory Part 1: What Is It?

Mathematics, Poker Concepts, Strategy
April 9, 2008

Game theory is somewhat of a hot topic right now. The application of said theory to poker has always been a topic of discussion amongst certain mathematicians and players. Then The Mathematics of Poker was published, and it temporarily put game theory front and center in the poker discussion. However, I would happily wager that 90%+ of winning players at any level could not give a correct and comprehensive explanation of what game theory is.

So for all you folks who don’t really know what game theory is, or what it has to do with poker, never fear. CardSharp is here to help Read the rest of this entry »

## Making Poker Math Easier

Mathematics, Strategy
October 15, 2007

A while back we did a big example of odds math and discounting outs.  These examples were somewhat complicated because I wanted to give a comprehensive picture of what can be involved in an odds problem.  Indeed, these problems were so complicated that the math really pushed the edge of what a player could be expected to do at the table.  In other words, those articles fell slightly short of my own standards of what constitutes good poker math.  I want to rectify that here and also present the process I use to do so as a template for simplifying other poker math problems. Read the rest of this entry »

## Chinese Peasants, Logic, and Poker

Mathematics, Strategy
September 28, 2007

There is a classic logical fallacy, the Emperor’s nose fallacy, that all poker players need to be aware of because it appears so often in poker reasoning (especially in poker books and forums) and has become increasingly common of late. Read the rest of this entry »

## Doing Arithmetic With Odds

Mathematics, Strategy
September 6, 2007

Previously, I’ve tried to convince you that doing your poker math in odds notation is far easier, once you get used to it, than using percentages. Now, I want to show you how to do some of the arithmetic usually associated with percentages faster and easier using odds. But first we need to lay some groundwork. Read the rest of this entry »

## Poker Mathematics & Arithmetic

Mathematics, Strategy
September 4, 2007

I’d like to say a little bit about my philosophy on mathematics in poker. Generally speaking, there seem to be two vocal camps on this topic. One camp is full of math-phobic players and writers (often forum posters) who will try to convince you that poker is a game of psychology, not numbers. The other group is the ever-growing number of mathematician players and writers who seem to talk about equilibrium solutions and similar high math incessantly. Read the rest of this entry »