Handicapping Poker Tournaments

The variables that must be considered

by Matt Matros | Published: Mar 07, 2006

Poker has become so mainstream that it's actually possible to place wagers through online betting establishments on who will win most major poker tournaments. I wonder if the day will come when we'll walk into Vegas sportsbooks and see "World Series of Poker Odds" staring back at us in those big red lights. Since this is supposed to be a poker math column, I thought I'd take a look at how to interpret the published odds for poker tournaments, and how to handicap tournaments ourselves.

What are the chances that a given player will win a poker tournament? Well, for an average player, his chances of winning a tournament are 1/N, where N is the number of players in the event. So, in a 10-player tournament, the average person would have a 1-in-10, or 10 percent, chance of winning. But wait, what is an average player? Let's say in our 10-player tournament that there is one exceptionally good player who is twice as good as the average player in the tournament. That means he has a 20 percent chance of winning. Let's say furthermore that the other nine players are all about equal. That means each of those nine players has an (80/9) percent = 8.9 percent chance of winning the tournament. So, only one player in the entire field is an above-average player! In practice, this means that only the very good player should expect to make money in this 10-player tournament. The other nine players all have a negative EV (expected value).

What if we vary it a little bit and say that in addition to the one very strong player in the tournament, there is also one truly terrible player. The truly terrible player has half the chance of winning as an average player; he's only a 1-in-20 shot (5 percent) to win the tournament. That still means that each of the other eight players, who are all about equal, has only a 9.4 percent chance of winning. It would take two truly terrible players in the field (with 5 percent chances of winning each) to offset the effect of the very good player. With one very good player, two terrible players, and seven equally skilled players, the seven middling players would once again have a 1-in-10 chance to win the tournament, making them average players, and zero EV (assuming no rake – ha!).

The point of all of this is that, for the average player, it usually takes several terrible players to make up for just one excellent player in a given tournament. We all know that terrible players find their way into poker tournaments all the time, but are there really enough of them to overcome the excellent players?

Let's try to make some estimates to answer this question. If there are 6,000 players in the 2006 WSOP championship event, and you could perfectly rank them in skill level from 1 to 6,000, what player would you have to get down to before your group of players had a 20 percent chance of winning the tournament? 300? 600? 1,200? If the answer is 300, that means the average player among the top 300 would win the WSOP four times as often as he would if the results were based entirely on luck; 600 means the talent isn't quite so top-heavy, and that the top 600 players win only twice as often as they'd win by chance; 1,200 means the tournament is all luck, and the top 20 percent of the field is no different from the bottom 20 percent of the field. So, how much skill is there in the WSOP main event, and how good are the very best players? No one has a definitive answer to this question. My personal opinion is that we'd need to pick the top 500 players before we would have, collectively, a 20 percent chance to win the tournament. In other words, I think most very good players win the tournament only about two and a half times as often as the average player does. Bear that in mind when making your wagers.

Next question: Starting from the bottom of the ranking list, how many players would we need to pick before we'd have a 10 percent chance to win the tournament? This question is perhaps even trickier than the first one. There are some people who play so badly (perhaps they're playing the WSOP for fun, having never played poker before) that they essentially have zero chance of winning the tournament. And there are some players who have a clue about hand values, but have such large flaws in their games that they are at an enormous disadvantage. And then there are those who, while clearly below average, play a style that at least gives them a chance to win if they get run over by the deck. My personal estimate is that the bottom 1,500 players would collectively have a 10 percent chance to win the event.

These estimates leave 4,000 players in the middle, and to keep things simple, let's say they're all relatively equal in skill level. That group of players collectively has a 70 percent chance of winning the tournament. Individually, a member of that group can expect to win the tournament once every 5,714 tries. That's better than average! So, in my opinion, there are enough bad players in the WSOP main event to offset the effect of the very good players, making it a profitable investment for the merely good players. (I hope this is encouraging to a lot of readers.)

Now, how does this affect gambling on poker? Well, let's say we find a sportsbook that offers lines on 500 players for this year's WSOP (I don't think this is such a bad assumption, by the way). According to my above estimates, the average player on that list should have a line of about 2,500-1, if (and this is an enormous if) the sportsbook has accurately listed the 500 players most likely to win the tournament. In real life, there is no way anyone could know who the best 500 players in the WSOP are. Bearing this in mind, I find it hard to imagine that there should be more than 50 players deserving of a 2,500-1 line. I don't think more than a handful of players should be listed at 1,500-1. And there isn't a player in the world whom I'd consider a good bet at less than 1,500-1 (well, maybe Phil Ivey).

Betting the "field," or betting that one of the unnamed players will win the tournament, is an interesting proposition. Assuming that the 500 named players are more likely than 500 random players to win the tournament, but less likely than the top 500 players would be, I'd guess that the 500 named players would collectively have about a 15 percent chance of winning the event. That leaves the other 85 percent for the field – making the appropriate odds for betting on the field 1-5.7. I'd be surprised if any sportsbook offers better than 1-9 (meaning you'd risk $900 to win $100) on the field in the 2006 WSOP. But if you do find a field wager in the neighborhood of 1-3, in my opinion you should scoop it up, assuming the sportsbook has set lines on fewer than 10 percent of the players in the field.

In summary, when considering betting on a poker tournament – and, indeed, when considering whether to enter a poker tournament – be sure to think of (1) the percentage of truly great players in the field, (2) the percentage of clueless players in the field, (3) the number of entrants in the event, (4) the "skill factor" of the event (events with more play generally enable better players to increase their edge over the field), and most obviously (5) the relative skill of the actual players you might wager on. Notice that I spent no time giving you my opinions of the relative strengths of today's name poker players. Don't expect that pattern to change in these pages anytime soon.