This is similar to Sklansky's basketball question.

You take a player who is competent and currently winning enough to support himself through online mid stakes SNG/Cash games.
- He is prepared to make his life goal winning a WSOP bracelet.
- He is perhaps 20 now and expects to live to 70.
- We can assume he will spend the duration of each WSOP in Las Vegas entering as many events as possible

Rate the chance that he will win a bracelet throughout his lifetime and give any assumptions you make which I have left out.

This would depend on how well he knows how to play non-holdem games.

If he is a purely NLHE player, 50%.
If he is a good player all-around in other games, 95%.

Also, I think a player who is 20 years old and "currently winning enough to support himself through online mid stakes SNG/Cash games" is much better than the "average player" at the WSOP.

I think a player who is 20 years old and currently winning enough to support himself is playing illegally.

Not where I come from. Perhaps if I made him aged 21 you could offer your thoughts.

if the guy was competent why would he make his life goal winning a WSOP bracelet?

Competence in a particular field does not imply sanity.

100% if you get lucky.

And 95% if you don't.

Granted, I know it's hard to win a bracelet. But I think 90% of it is having the money to win one. I mean, the law of averages say you have to win a tourniment sooner or later. But if someone has $500,000 to blow every year for 50 years on WSOP Tourniments, odds are he will win one. I suck at poker, but I know if I had Phi Ivey's money, I could win a WSOP Tourniment sooner or later. Yes, it may take 50 years, but it would happen.

assume that there are 50 tournaments a year, each with 2000 entrants. he will play 2,500 tournaments in his life.

if he is a perfectly average player, then he has a 1/2000 chance of winning each one, and has a 71% chance of winning a bracelet.

if he is just twice as likely as the field to win, then he has a 92% chance of winning a bracelet.

Hold it right there, because if he makes a living online, he is not exactly an average player.

For this exercise, it may be better to say he is average and has plenty of time and money to spend on the WSOP.

But see, when you assume that, the probability goes higher to like 96%.

So basically this question can be rewritten as:
"What are the chances Jamie Gold wins another event?"

There are not 2,000 entrants in every WSOP event. In fact, MOST events don't have 2000 players. Note that when assessing the chance that he will win ONE bracelet, events that have like 200 players are far more important that ones with 2000 players. Also, you can't *really* play 50 events a year, because sometimes you make it to day 2 or you haven't busted from the morning tournament.

Still, I think someone sufficiently motivated by just winning bracelets could probably have at least a 5% chance per year, perhaps as high as 10% depending on how good he is at secondary games with smaller fields.