Short- and Long-Term Expectation (Questions)

In his book Poker for Dummies, Lou Krieger brought up several interesting points about short- and long-term expectation in poker. Expectation is defined as what a player can expect to win (or lose) over a given period of time. Expectation is based on several key factors. These factors include (but are not limited to) the betting limits, number of hours played, the house rake, and one's skill level in relation to opponents.

Without knowing it at the time, Krieger may have touched upon every poker player's "Holy Grail." His findings, if defined in theory and applied in practice, may constitute a blueprint for maximizing earning potential at the poker table – for all players, in all games, and at all limits. At the very least, he shows that some games are totally pointless to play in, while others can be immensely profitable for the better players.

Krieger used a computer simulation and ran several tests. He set up a number of $20-$40 hold'em games with different player characteristics. Each game had a full table of nine players. He ran every game eight hours a day, 40 hours a week, for 50 straight weeks – which provided a simulation of expected results over a one-year period. Since the computer simulations generated data rapidly and were far more reliable than polling a random group of $20-$40 players (and the results would, in fact, be verifiable), the data provided a clear portrait of how much variance a player can expect, both in the short and long term. In addition to measuring game variance, the real goal was to see what earnings different types of games would generate for the more skillful players, based upon varied game conditions. Since 2,000 hours represented what a working pro could realistically expect to play in a year's time, it in effect represented the annual earning potential for a full-time poker player (playing in live-action games).

The results proved to be fascinating. The first thing Krieger discovered was that things do not necessarily even out at the poker table, even in the long run. To the contrary, some players win more or less than others, although they may be of equal skill. In most games, players of roughly equal ability would be expected to win or lose approximately the same amount of money. But, this was proven not to be the case. For instance, in one test, Krieger used identical player profiles for all nine seats. Then, he ran the game for 60,000 hands – about the number of hands that a full-time pro is dealt in one full year. Even after 60,000 hands, player earnings in a $20-$40 game differed by as much as $5 an hour! The data shows us that solid players can be small losers or may achieve only marginal earnings when they are repeatedly confronted with games full of players of roughly equal skill levels to themselves (in other words, when they choose to repeatedly play in tougher games).

So, if the results can vary by as much as $5 per player per hour in one year, how many years does it take to achieve equal distribution? Brace yourselves for the answer. Krieger discovered that the results never quite even out. Even after 50 years – in other words, what a full-time player could expect to play over his entire lifetime – the earnings remained relatively inconsistent. Given that the players in the simulation were of identical skill and playing at the same table for 50 years, one would probably expect the difference in earnings to be marginal – perhaps only a few cents from player to player. But, surprisingly, the biggest-winning player in the simulation still won 95 cents an hour more than the biggest-losing player (remember, all of the players had identical skill!). So, as you can see, there is no guarantee that things will "balance out" in the long run. In fact, it would take three or four lifetimes to reduce the distribution to the smallest fraction.

As has been pointed out many times before in the tenets of poker's most respected writings, the key to winning in poker is not necessarily how good a player you are. Rather, it's your skill in relation to that of your opponents. Illustrated by the use of computer simulations, one can now see how critical game selection is in making a living (or earning money) playing poker. It is much more important to pick games with weak opponents than it is to try to outfox players who are in your same class. It may even be pointless to do so. Krieger proved this point when he introduced below-average players into the game simulation. With just a few bad players included at the table, the results changed dramatically. It became a game of "positive expectation" for all of the good players. They all won – different amounts, to be sure, but they all won money.

To simulate the effects of below-average players on a poker game, Krieger first introduced two players – one very tight player and one very loose player – into the simulation. The other seven players remained solid. The tight player lost about $3 million over the course of his lifetime. The loose player lost about $4 million. All of the other players at the table won money, ranging from $800,000 (low) to $1.2 million (high). This means that two bad players and seven very good players at the $20-$40 level translates into earnings of only about $8-$12 per hour for the good players – before the rake and tip (which means that virtually no one is a winning player under these conditions). This fact should be alarming to so-called "good players" who are sitting in tough games yet are probably not earning much money because they consistently choose to play in them. The hourly win rate of $12 for the top player in the group is a far cry from the goal of most low- and middle-limit players, which is between one and one and a half big bets per hour. Krieger's simulations suggest that even with two bad players in the game, one big bet per hour is simply not possible.

For all serious players, then, the key question becomes how many bad or marginal players in a game are necessary to create a respectable earning wage? Indeed, that's the million dollar question. It is not easy to answer. First, it should be pointed out that players do not play the same way on a consistent basis. No player plays like a robot, as in the simulation. Even good players may go on tilt occasionally, or will change their characteristics depending on the game. A winning $15-$30 player may be a losing $40-$80 player. Furthermore, bad players often improve or can even play well on occasions when they are surrounded by even weaker competition. That is why some relatively poor players may actually win at very low limits. They usually aren't very good, but their opponents are so bad that even the subpar player may be a winner. Nevertheless, the computer results show that there needs to be several bad players in the game to achieve the standard expectation of one big bet per hour. Even though you may not face the same lineup of tough opponents every night for 50 straight years, if you continuously place yourself in that situation, you might as well forget about making anywhere close to one big bet per hour. You might as well play the game for recreation. Otherwise, it's pointless.

How many "bad players" are needed to generate the benchmark of one big bet per hour? While one big bet per hour in a $10-$20 game would constitute a modest income, the same level of achievement at the $20-$40 level would be a very nice living for most people (about $80,000 annually). Of course, in games at very high limits, such as $100-$200 and higher, one big bet per hour is not a realistic expectation, except in the most ideal conditions, which rarely occur. This is because there are not many $100-$200 (and higher) players who play horribly. The key is to look for games with plenty of contributors, which happens more frequently at the middle and low limits.

This leads to other issues, as well. What happens if the bad players outnumber the good players? What if, instead of just two bad players, there are six or seven bad players at the table? Would all of the bad players lose money to the good players? Or, could a bad player actually be a winner over a long period of time? Do bad players cancel each other out, and in effect trade off their money? And, what variance might a good player expect when there are wild games full of bad players?

Since Krieger introduced the concept of short- and long-term expectation in his previous writings, I submitted several questions to him that may allow us to better understand what constitutes an "ideal" poker game. This joint effort is designed to give readers a better understanding of short- and long-term expectation and what we can expect from playing in different kinds of games.

This is important because I think every serious poker player wants to know what he can expect to earn – either hourly, yearly, or perhaps even over the course of his lifetime – playing poker. The computer simulations may very well give players a road map to achieve their desired results – by focusing on games in which the right conditions exist to win the maximum amount of money. I will leave it up to Krieger to identify and comment upon these conditions in his column, which immediately follows this column.

Nolan Dalla can be reached at

[email protected].