The next night, invigorated with my success, I scoured the PartyBets site for more profitable bets. I soon saw another match, this time between Japan and the Ivory Coast, that struck me as very similar to the Australia v Ghana game. As was the case for the Socceroos, Japan’s odds of 2.6 to 1 seemed quite high. Not only were they playing at home but the Ivory Coast, like Ghana, was missing many of its stars (Chelsea’s Drogba, in particular) due to injury or the Champions League final. Accordingly, I decided to bet another $100 on Japan and soon found myself another $160 richer when Japan notched up a slim 1-0 victory.
At this point, I considered myself quite the sports betting fiend and decided to keep looking for more profitable bets. Soon, I came across PartyBets.com’s WSOP Main Event final table betting. This intrigued me for obvious reasons but the odds offered seemed gravely lacking. To check this, I decided to do some rough calculations which I now present here. I was hoping that I could find someone to bet on since it would make following the main event that much more exciting. At the same time, I didn’t want to be making some massively –EV bet which I would come to regret.
The Maths
The first number that I had to estimate was the number of entrants into this year’s main event. Last year, there were 6,358 entrants, in 2006 there were 8,773 and in 2005 there were 5,619. With the exception of last year (due to the passage of UIEGA), the number of WSOP entrants has grown each year, so I expect that this year’s figure will be higher than last year’s. How much so is however a difficult question. On the one hand, sites and players have learnt to better understand and deal with the effects of UIGEA and so some of the players lost to UIGEA last year should make a return this year. On the other hand, the poker boom has come to an end and poker television has declined in popularity. As a result, your average Joe is a lot less likely to fork out ten grand and try his hand at stardom. Overall, I thought that there would be a modest increase in the number of players to about 7000.
This means that, disregarding skill, each player has a 1 in 777 (7000 divided by 9) chance of making the final table. What we then have to ask is how the presence of skill changes those odds. Does a pro, due to his skill, have twice the chance of making the final table? Three times the chance? Four?
The answer to this is, of course, impossible to calculate precisely, but there are ways of getting an approximation. One way is to observe the pro to amateur ratio at the start of the main event and to compare it to the pro to amateur ratio at the final table. If, for example, we find that the ratio of pros to amateurs at the final table is twice that at the start of the event, we can infer that pros are roughly twice as likely to make the final table as amateurs. Doing this for the last three or four years (when the fields were of comparable sizes), we should be able to get a pretty decent rough estimate.
Unfortunately, accurately observing the pro to amateur ratio at the start of the main event would require scanning through thousands of names and categorising each player as a pro or an amateur. Not only would this be ridiculously time-consuming, it would also probably be fruitless since in many cases I wouldn’t be able to discern pro from amateur anyway. Thus, I decided that it would be better, although less accurate, to simply compare the fields of the WPT Championship and the WSOP Main Event. In theory, since most pros will attend both the WPT and the WSOP, while amateurs will only attend the WSOP, the ratio of WPT entrants to WSOP entrants should give a rough indication of the pro to amateur ratio.
Here’s some data for the last few years.
Thus, pros, on average, make up about 9.6% of the starting field at the main event.
The next question then is what percentage of the final table they comprise. First, here’s a table outlining the names and number of pros at each of the final tables from 2004 to 2007.
Thus, we can see that, on average, 2.75 pros make the final table. This means that pros make up (2.75/9)*100 = 31% of the final table. This number is significantly greater than the 9.6% starting composition of pros and suggests that your average pro is 31/9.6 = 3.2 times more likely than an amateur to reach the final table. Thus, rather than having a 1 in 700 shot, each pro has a 1 in 700/3.2 = 1 in 220 shot of making the final table due to their superior skill.
Turning now to the odds offered by PartyBets.com, we can see that no pro offers odds of 220 to 1 or better (indeed, only two people offer odds better than 220 to 1 – Ben Affleck and Boris Becker – and they are both clearly amateurs). This suggests that no one on PartyBets.com is worth betting on. It should however be remembered that 220 to 1 are the odds you should be getting on your average pro. Some pros will obviously be better than others and thus should offer lower odds. If, for example, I felt that Phil Ivey was twice as good as your average pro, I should be willing to accept 110 to 1 odds on him. However, twice as good in this sense does not mean twice as skilful but rather twice as likely to final table. In a field of this size, even with far superior skill edges, it is doubtful whether any elite pro can truly be said to be twice as likely as an average pro to make the final table since there is so much luck involved. Thus, I don’t think it’d be wise to accept odds of less than 200 to 1 on any given pro.
Time to Bet! Or Not?
I was pretty happy to come to this conclusion, but unhappy that I wasn’t able to apply it anywhere. Or rather, my applying it was simply abstaining from betting! This was not what I had hoped for. So I looked around to see if any other sites offered betting on the final table. Fortunately, not only did I come across one, but the odds it was offering were in a different galaxy to PartyBets.com. Maybe a profitable bet was to be found after all! The site I had found was PaddyPower.com. Here are the bets it offered.
Looking at these, we can see several pros with odds of 200 to 1 or better. If my calculations are correct, betting on any pro with odds of 250 to 1 should be profitable in itself while betting on an above average pro with odds of 200 to 1 should be fine too. Of course, my calculations are not correct; they are only rough estimates. Thus, I had no intention of following them blindly and some intuition would still be required. However, at least I knew now not to bet on anyone with odds worse than 200 to 1.
Anyway, here’s the list of players I eventually settled on (I put $10 on each). Tell me what you guys think!
Edit: I've since added David Singer to the list (200 to 1).
