Short- and Long-Term Expectation (Answers)

Writer's note: This column is written in tandem with fellow columnist Nolan Dalla. See Nolan's column, "Tales From the Felt," in which he raises issues and questions answered here.

In my recent book Poker for Dummies, I talked about how much money players can expect to win (or lose) over given periods of time. Poker players call this "expectation," and it's really nothing more complicated than an estimate based on betting limits, the number of hours played, the house rake, and the relationship between a player's skill level and that of his opponents.

The information used to support my assertions about how much a player can expect to win were based on computer simulations conducted while writing my first book, Hold'em Excellence: From Beginner to Winner. These simulations showed that expectation is based more on the relative difference in skill between opponents than on any attained level of ability.

In other words, the weaker your opponents, the more money you figure to win. A "good" player figures to win more money against weak opposition than a really top-notch player is likely to win against opponents who are almost – but not quite – up to his level of proficiency.

In his companion column, Nolan Dalla said, "… look for games with plenty of contributors. The question is, how many contributors do you need?" And rather than idling away his time musing rhetorically, Nolan raised some specific questions for me to answer.

Question (Nolan Dalla): If the very best player in a $20-$40 game with two bad players in it could earn only $12 per hour, does that mean it's (essentially) purposeless to play in any poker game in which the number of good players outnumbers bad players 4-1?

Answer (Lou Krieger): Not at all. But to really support this assertion, it's important to understand how I conducted these computer simulations. I used Wilson Software's Turbo Texas Hold'em, and assigned player profiles to each of nine seats. Seven of the profiles were identical: a profile programmed to play a good, solid game – and the seven clones did just that for a simulated 30 hands per hour, 40 hours per week, 50 weeks per year, for 50 years. That's much more than a lifetime for most poker players. I also added one very loose player and one who was very tight to this simulated lifetime of poker.

In real life, you'd never find seven identical clones at a table. A few players might be very good and one or two might be terrible, while the others would probably be found at various points within this continuum.

Talking about "good" and "bad" players tends to give these terms an aura of absolute stature and measurement. That's misleading; it's not at all like that in real life. The very best player in today's game might be the worst tomorrow, depending on the skill level of his opponents. Or, he might be somewhere in between – better than some but not as good as others. Our hero might be a winning player against today's lineup and a losing player the very next day.

But if you're one of the best players in the game every day, you can figure to win more than $12 per hour in a $20-$40 game against typical lineups. People do this every day, and real-world experience is a lot better at predicting the future than any simulation.

Question (Nolan Dalla): Does four bad players in a $10-$20 game equal two bad players in a $20-$40 game (in terms of expected earnings)?

Answer (Lou Krieger): I could have speculated all day about this, but I decided to do some more research. Once again, I simulated 50 years of hold'em using Turbo Texas Hold'em. One game was $20-$40 hold'em, and a strong player profile was inserted into seven seats. The remaining two seats housed veritable calling stations.

I also simulated a $10-$20 game with the same strong profile in five of the seats, and calling stations in the other four. To negate any skewed data that might have accrued from the random distribution of cards, I used Wilson Software's "repeatable deal" feature. In other words, for a simulated 50 years, the same hands were dealt to each table. The only differences were the stakes and the player mix at each table.

In the $20-$40 game with seven strong players and two weak ones, the strong profiles each won between $1.2 million and $1.3 million. The calling stations each lost about $4 million. In the $10-$20 game, the strong profiles each won between $1.2 million and $1.4 million, and the weak players each lost between $1.4 million and $1.7 million. The strong players did equally well, although less money was at risk in the smaller game than the larger one. The message is crystal clear. Don't necessarily look for the biggest game; choose a game with an optimal mix of betting limit and weak players.

The biggest winners in these games were seated to the immediate left of the weak players, which ought to settle any remaining debate about whether it is advantageous to act before or after weak opponents. If your opponents are weak primarily because they call when they ought to fold, these simulations show that it is very advantageous to act after them.

Another interesting point is that the smaller game was also better for the poor players. While the strong profiles did just as well in that game even though the stakes were smaller, the poor players each lost less money.

Question (Nolan Dalla): What would the result be if you had four bad players in a $10-$20 game vs. two bad players in a $100-$200 game?

Answer (Lou Krieger): The simulation discussed above provides ample evidence. Simply by extrapolating the results from the $20-$40 game, you can see that when you multiply the results by five, the strong players in a $100-$200 game each would have won between $6 million and $7 million over that time span.

While many of the same players meander back and forth among middle-limit games, in the real world (sigh), you just won't find players of the same caliber in a $100-$200 game.

Question (Nolan Dalla): Which is better, six bad players in an $8-$16 game or two bad players in a $20-$40 game?

Answer (Lou Krieger): Six bad players in an $8-$16 game is a better situation for a skilled player than two bad players and seven experts in a $20-$40 game. In the $20-$40 game, we simulated with seven strong players and two weak ones, and the strong profiles each won between $1.2 million and $1.3 million. We used the same player profiles in an $8-$16 game, along with the same repeatable deal code; all we changed was the mix.

After three million hands, the three winners were ahead about $1.5 million each. The losers were stuck an average of $750,000 each. Winners in the smaller $8-$16 game did just as well as those in the $20-$40 game, while putting substantially less money at risk. Anytime you can win the same amount of money while subjecting far less of your bankroll to the vicissitudes of poker's insanely high variance, you're in a better game.

Question (Nolan Dalla): What is the result of one bad player at the $300-$600 level playing – let's say – sixhanded?

Answer (Lou Krieger): After running this scenario with the same player profiles, our lone weak player contributed more than $70 million to the five strong profiles – each of whom won an average of $140 per hour from the weak player.

Question (Nolan Dalla): If the number of bad players increases in a game, and since they will trade off money between themselves, does that mean over the course of a year that a bad player can actually be a winner (let's assume that he puts in full-time hours)?

Answer (Lou Krieger): A bad player can easily be a winner for life, as long as he can find games with players who, on average, do not play as well as he does.

In poker, as in so much of life, things are relative. When you were a kid, the guy who was the best basketball player on the playground was probably not as good as the best player on the high school team. And that prep star might not have been the league's best player. And the league's MVP might not have been the best player on his team in collage. And that college star might not have made it to the pros, and if he did, he might have been the guy at the end of the bench. So, the question of whether the best ballplayer in your neighborhood was "good" or not is sort of meaningless, unless it's considered against the level of opposition.

After all, there aren't many like Michael Jordan or Tiger Woods, who live at the polar extreme of whatever scale you choose to use in assessing talent. The same is true in poker. "Good" and "bad" are relative. And in poker, unlike professional sports, one need not be one of the best in the world to make money at the game. You just have to outplay your opponents.

Technical notes: For those who use Wilson's Turbo Texas Hold'em, these simulations were run using repeatable deal code 25,000, under the "raise often" feature. "Bret Maverick" was the strong profile; the calling station was "Welcome Waldo." Three million hands were dealt in each simulation, and neither rakes nor tokes were accounted for.

Visit my website at www.loukrieger.com. My newest book, Poker for Dummies, is available at major bookstores everywhere.