# Handicap of poker tournaments

Poker is so fashionable it is currently possible to bet on Internet sites, on the player who we think will win such or such big poker event. I wonder if someday we can walk in Vegas and see in sports guides, ratings for the World Series of Poker.

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The variables that must be considered

Poker is so fashionable it is currently possible to bet on Internet sites, on the player who we think will win such or such big poker event. I wonder if someday we can walk in Vegas and see in sports guides, ratings for the World Series of Poker. Because it is a column on the mathematics of poker, I think that I will watch and try to interpret the release of ratings for poker tournaments and try to explain how to calculate a handicap.

What are the chances for a player given to win a poker tournament? And well, for an average player, his chances of winning are 1/N, where N is the number of players to the event. If so 10 players in the tournament, the average player will have 1 chance in 10 or 10% of the odds of winning the tournament. But wait a moment, that is an average player? Suppose that among the 10 players in the tournament, there is an exceptional player who is two times better than the average player of the tournament. Which means that it has 20% chance to win. Suppose also that the other 9 remaining players are all equal. Which means that these players have (80/9 =) 8.9% the chances of winning the tournament. So, here there is only a player who is more likely than the average to win the tournament. In practice, this means that it is the only one who can be expected to make money in this tournament with 10 players. The other players all have a negative EV.

What happens if one varies a little by adding 1 player very strong in the tournament, as well as a terribly bad player? The worst player has half the average players chances to win the tournament; his chances of winning are 1 against 20 (5%). Which means that the chances of the other 8 players are equal to 9.4%. Should be 2 very bad players in the tournament (each with 5% of chances of winning) to cancel the effect of the very good player. So if there was 1 very good player and 2 very bad, the other 7 remaining players would each have 1 chance in 10 to win the tournament, making them average players with an EV of 0 (without the rakes).

In summary, for the average player, it takes him 2 players bad to counter the effect of a very good player and thus raise its chances of winning. We know that all tournaments have a lot of very bad players, but is it enough to counter the effect of the very good players?

Try a few estimates to answer this question. There are 6,000 players at the WSOP and you could evaluate them on a scale of 1 to 6,000, how many players should remain until your group of players has 20% of chances of winning? 300? 600? 1,200? If the answer is 300, this means that the average player will win the WSOP 4 times more often than if the game was based on luck. At 600, talent is not there is more important and good players do earn only 2 times more often than the average player. To 1,200, the tournament is lucky and the best 20% earn no more often than the worst 20%. Therefore, how much talent there at the WSOP and how good are the best players? No one has definitive answer to this question. My personal opinion is that we should select the top 500 players until everyone has, collectively, 20% chance of winning the tournament. In other words, I think that the majority of very good players have about 2 times or twice and a half more than chances to win a big tournament as an average player. Keep this in mind when you make your bets.

Next question: starting from the bottom of the list, how many players you need to select before you have a 10% chance of winning the tournament? This question is perhaps a bit more complex than the first. There are players who play so badly (maybe they are at the WSOP for fun and they have never played poker before) that they have about 0% chance of winning the tournament. And there are other players who have a minimum of knowledge about poker, but who have so many flaws in their game, they have a huge disadvantage. And it is these players who will be significantly below the average of other players, that can barely win even if the cards play for them. My personal estimate is that the latter 1,5000 players have collectively 10% chance to win the tournament.

This estimate leaves 4,000 players in the middle and to keep things simple, let's say that they are all equal in skill. This group of players collectively is 70% chance to win the tournament. A player of this category can estimate win the WSOP once by 5714 entries. It's better than average! In my opinion, there is enough bad players to the WSOP to cancel the effect of the very good players, making this profitable investment for the average player. (I hope this is encouraging for the readers).

Now, how does this affect the paris Poker? And well, let's say we find a sports book in which one side 500 players to the WSOP of this year (I don't think that this is a bad assumption). According to my latest estimates, the average of these players has a rating of 2,500 - 1, if (and thats a big if) the sports guide correctly listed 500 favourites to win this tournament. In real life, no one can say are the top 500 players in the WSOP. Keep in mind that I find it hard to imagine that there are 50 players who deserve to be rated 2, 5000-1. I do not think that more than a handshake of players should be listed at 1, 500-1. And there's not a player in the world which I consider to be a good bet less than 1, 500-1 (maybe Phil Ivey...).

Bet on No. name player who has the most chance of winning the tournament is interesting. Suppose that there are 500 randomly selected names and that it is not the top 500, I guess that these players will collectively have 15% chance to win the tournament. Leaving 85 per cent for the other categories - which gives ratings of 1 - 3.5 for this field. I'd be surprised that the sporting sides offer more than 1-9 (meaning that you can \$ 900 to win \$ 100) in this specific field. But if you find a scoop with ratings of 1-3, you should not hesitate to take it, assuming that the book of the sides has taken a sample of 10% of the players only.

In summary, when you consider leverage a poker tournament - and obviously, when you consider entering a tournament of poker - make sure to think of (1) the % of very good players in the tournament, (2) % of bad players in the tournament, (3) the number of entries in the tournament, (4) factor 'suitability' for the tournament (when there are many players in a tournament(, the good players have a lower edge ), and, the most obvious (5) the relative skills of players on which you want to bet. Note that I don't lose no time to give you my opinion on the relative strength of the players of today. Do expect this to change in the upcoming pages.