Poker Articles

In The Long Run
By Lou Krieger

Everyone who takes poker seriously, and spends time thinking about the game knows this to be true: "In the short run, luck can determine your results; In the long run, skill is what counts." But how do you know when you are in the long run?

Recently a player seated near me in a $20-$40 hold'em game mentioned that he sat down at the table and had not won a hand until he dropped $1,200. I didn't think he was a particularly good player, but he wasn't all that bad either. Anyway, losing $1,200 for a player of his ability seemed indeed to be a rather bad run of luck. But was he in the short run or in the long run? And how do you know when you get into the long run. Is losing $1,200 before you win a hand being in the long run? Does it take a week of play to get there, or does it take longer?

Is hitting the long run something like StarTrek, when they jump into hyperspace at warp speed? Do lights go off? Do bells ring? How do you know when you are in the long run? It's an important question, because once you're in the long run, luck has been totally filtered out, and all your achievements or failures can no longer be attributed to it. When you're in the long run, your results as a poker player are entirely a product of your own skill and discipline.

I decided to use a computer to simulate play and help me determine just how long it takes to get into the long run. Computers offer a way of playing thousands of hands in a very short time. I set up some scenarios. In the first, I used a Rock player program. In the second, a Fish, and in the third I used a Solid player. In the final scenario, I used each of these three player profiles to fill in 9 seats at my computerized table.

With the Rock player-profile occupying all 9 seats, I asked the computer to play 60,000 hands of $10-$20 Texas hold'em. That's about one year of play, if you figure that a dealer will put out 30 hands per hour and you play 2,000 hours (that's 8 hours per day, five days a week, for fifty weeks) annually. I didn't rake the pot, or toke the computerized dealers. Since the same player program was loaded into each seat at the table, the mathematical expectation would be zero in the long run. Since the playing profiles are identical, the players in each seat should neither win nor lose. Each figured to break even - eventually.

That, however, was not the case. The Rock in seat 9 lost $6,368, while seat 6 won $3,985. All of the other players had results that were somewhere between these limits. Overall, there were 4 losers and 5 winners. Seat 9 lost at the rate of $3.18 per hour while seat 6 won at the rate of $1.99. That's a difference of more than $5 per hour - and its clear that the rocks never got into the long run, even after a year of simulated play.

When I sat 9 Fish at the table, I expected more overall action, since a table full of bad players figured to be in more hands, and frequently chase to the river with little chance of winning. That's exactly what happened, even though the expectation for each individual player was still zero. The big winner took in $9,918. There were two big losers: Seat 4 lost $5,300 and Seat 5 lost $5,268. That's a difference of $7.61 per hour. Once again, even after an entire year of simulated play, the Fish never got into the long run, even after 60,000 hands.

With a table full of Solid players, there was one big winner: Seat 5 won $5,630 while the two biggest losers lost $4,968 and $4,226. This is a difference of $5.30 between the biggest winner and biggest loser. Once again, with a zero expectation, a table full of players who played fairly well never got into the long run.

Just for the fun of it, I ran one last scenario. I put 3 Rocks, 3 Solid Players, and since the Fish had absolutely no chance - I added 3 Average players to the table. The latter played more solidly than the Fish, but not nearly as well as the Solid Player. They were seated in a rotation: Rock, Average, Solid to fill 9 seats. Guess what? Only the Solid Players booked wins. They won: $32,582; $30,715 and $10,721 while the rocks and average low limit players lost at about the same rate.

The long run was not reached in this scenario either, since the big winner averaged $16.29 per hour in winnings (which is quite realistic for a $10-$20 hold'em game) and the small winner won at the rate of only $5.36 per hour. Remember, since their playing characteristics were identical, even though they did not play as real players would, they had an identical statistical expectation. Because of the difference in player characteristics at the table, that expectation is greater than zero, but it cannot be calculated with any precision. However, with a difference of $10.93 between the big and the small winners, each of whom had an identical predictive expectation, the table of players with mixed abilities never reached the long run either.

What's the lesson here? Well it is clear that the player who complained to me that he lost $1,200 before he won a pot was not born under a bad sign. His short losing streak was not unexpected, given the results of my simulations. In fact, an entire year of play is not enough time to reach that elusive plateau where short-term luck is filtered out, and long-term results can be solely ascribed to skill.

I'm still not sure when you reach the long run. It apparently takes more than one year. Maybe more than two, maybe more than five years. I intend to do more research on this in the future. Until then, I've got a new appreciation for the expected fluctuations in a poker game. And if I'm right - if these fluctuations can be expected to persist for a long time before aggregate results can be attributed solely to skill - then it is clear to me that the majority of players are playing in games with stakes too big for their bankroll.

That's not critical if you are a recreational player and supplement your playing bankroll with money earned elsewhere, but the working professional poker player ought to take heed. You have to play in a game where your bankroll can withstand the expected fluctuations, or you can expect to be on the rail sometime in the future.