Interesting math

  • 13 replies
    • carusel
      carusel
      Bronze
      Joined: 28.10.2007 Posts: 202
      very interesting:)

      Stu is about 99.79 percent to have won one or more events.
      thats not something i want to bet against ^^

      Raymer said that before he entered the main event he put his chances to win in 2004 at about 1/1000, 2,5 better than the average player.
      acording to this article, stu ungar was 300 times better than the average player, if i'm not wrong

      Ungar>all
      the first time he player no limit holdem was at the world series main event and he won it
    • ManniXXX
      ManniXXX
      Bronze
      Joined: 05.09.2007 Posts: 707
      I like it. Underlines the importance of variance imo. Also that Ungar was an alien with superhuman poker skills from the planet Myplos in the Jishni nebula.
    • carusel
      carusel
      Bronze
      Joined: 28.10.2007 Posts: 202
      my bad, ungar was 3000 times as likely as the average player to win ,not 300
      Interpretation: A player 30 times as likely to win as an average player in a 200-player field will win 10 out of 30 tournaments about 1 out of 100 times.

      he won 10/30
    • Mugge88
      Mugge88
      Bronze
      Joined: 29.10.2006 Posts: 510
      The article doesn't state how much better Stu Ungar was supposed to be, but he just calculates how likely he was to win 10/30 big tours if he was respectively an average player, 10 times better than the average player and 30 times better than the average player.

      You can't sa exactly how much better he is (because that's not possible to define in poker since there are so many variables), and you can't say that he was 3000 times better - both because i think it's impossible to be 3000 times better than the average player at the big tours but mostly because, you cannot really calculate it quite that easily (according to your calculations he should win 10/30 tours 100% of the time - which of course isn't possible for anyone to say - it will always be probabilities we are looking at in this kind of math). My guess on how much better than the average player he was is at good at yours, but one thing is certain: No one can claim that poker is all about luck when you find out that this outcome (winning 10/30 expensive tours with ~200 participants) would only happen 0.0000000000000026 percent of the time!

      Best regards,
      Mugge
    • DE4DLY
      DE4DLY
      Bronze
      Joined: 27.01.2007 Posts: 109
      Wow.
      ....

      That has changed my perspective on the big picture of the game.

      What an excellent article.
      Cheers for the linkage.

      *wanders off stroking his chin*
    • carusel
      carusel
      Bronze
      Joined: 28.10.2007 Posts: 202
      mugge i ment 3000 times more likely to win, not 3000 times better :P
    • chenny8888
      chenny8888
      Bronze
      Joined: 03.10.2007 Posts: 19,324
      Originally posted by carusel
      mugge i ment 3000 times more likely to win, not 3000 times better :P
      that's wrong. as soon as you become 200 times more likely, you win every single tournament as P becomes 1.
    • erob60
      erob60
      Gold
      Joined: 08.03.2007 Posts: 165
      Originally posted by chenny8888
      Originally posted by carusel
      mugge i ment 3000 times more likely to win, not 3000 times better :P
      that's wrong. as soon as you become 200 times more likely, you win every single tournament as P becomes 1.
      No

      In a player field of 200, he could have 200/399 probability of winning, whereas the other 199 players on average have a 1/399 chance of winning. Thus giving him 200 times the chance of winning, but still only wins half the time.
    • chenny8888
      chenny8888
      Bronze
      Joined: 03.10.2007 Posts: 19,324
      that's not how phil gordon did his calculations
    • erob60
      erob60
      Gold
      Joined: 08.03.2007 Posts: 165
      Well whatever calculations you're using you cocked something up:

      Suppose player A is 200 times more like to win than player B, that is, P(A wins) = 200 x P(B wins), but also P(A wins)=1, then since all probabilities add up to 1, P(B wins)=0.

      But then 0 = 0 x 200 = 200
    • carusel
      carusel
      Bronze
      Joined: 28.10.2007 Posts: 202
      Originally posted by chenny8888
      Originally posted by carusel
      mugge i ment 3000 times more likely to win, not 3000 times better :P
      that's wrong. as soon as you become 200 times more likely, you win every single tournament as P becomes 1.

      Gordon :
      Interpretation: A player 30 times as likely to win as an average player in a 200-player field will win 10 out of 30 tournaments about 1 out of 100 times.


      ungar finished 10 out of 30 tournaments 100 times out of 100
      doesnt that mean that he's 100 times better than a player 30 times as likely to win as an average player ? =3000 times better than average
    • erob60
      erob60
      Gold
      Joined: 08.03.2007 Posts: 165
      Nope.

      Something which has 1% probability happens now and then. The sample size is 1 (he lived only once), from which you can't draw any such conclusion. There's a minuscule chance that Joe Average could do the same if he got lucky enough.

      He did not "finish 10 out of 30 tournaments 100 times out of 100", he won 10 out of 30 tournaments 1 time out of 1.

      If he played the 30 tournaments 100 times each and his average wins for each run through was 10, (in other words winning 1000 out of 3000 tournaments) then you could perhaps say something way more outlandish like him being 3000 times better (however, the maths isn't quite that simple so the figure wouldn't be 3000).
    • chenny8888
      chenny8888
      Bronze
      Joined: 03.10.2007 Posts: 19,324
      Originally posted by erob60
      Well whatever calculations you're using you cocked something up:

      Suppose player A is 200 times more like to win than player B, that is, P(A wins) = 200 x P(B wins), but also P(A wins)=1, then since all probabilities add up to 1, P(B wins)=0.

      But then 0 = 0 x 200 = 200
      i didn't cock it up, phil gordon did :P , cf his article!

      Originally posted by erob60
      Nope.

      Something which has 1% probability happens now and then. The sample size is 1 (he lived only once), from which you can't draw any such conclusion. There's a minuscule chance that Joe Average could do the same if he got lucky enough.

      He did not "finish 10 out of 30 tournaments 100 times out of 100", he won 10 out of 30 tournaments 1 time out of 1.

      If he played the 30 tournaments 100 times each and his average wins for each run through was 10, (in other words winning 1000 out of 3000 tournaments) then you could perhaps say something way more outlandish like him being 3000 times better (however, the maths isn't quite that simple so the figure wouldn't be 3000).
      very valid point.