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Joe, your brilliant !! I will analyse using the new rolled out MET
Posted By: neilkaz In Response To: Playoff with three finalists (Joe Russell)
Date: Saturday, 9 January 2010, at 3:29 p.m.
First of all if the 2nd match could be played from a score that gives the leader 2/3 chances to win, each of the 3 players would have exactly 1/3 chance to win either 1st, 2nd, or 3rd place.
The new GNU Supremo MET (RO's for 14 pts wb done in a few hours, and 15 pts by next weekend) says that a 3-0 lead to 9 is worth .667856 chances. This is really very close to 2/3 or.666667 !
Now I'll recalculate. The bye player wins the 2nd match 66.7856% of the time and then wins the 3rd and final match half the time, thereby winning the T (I'll round) 33.39% of the time (very close to 1/3). He also finishes 2nd (having lost the final) 33.39% of the time. He loses the 2nd match and finishes in 3rd place 33.22% of the time (very close to 1/3). So this is really fair for the bye player, giving only a very small fractional equity gain above 1/3 (we can safely ignore that, IMHO).
The loser of the first match loses the 2nd match 66.78% of the time and finishes 3rd. Since each of the non-bye players is 50/50 to win match 1, both are 33.39% to finish 3rd.
33.22% of the time the bye player loses match 2 and then the winner of match 1 wins the T. Since he is 50/50 to win match 1, this quick road to victory occurs 16.61% of the time for each of the two non byes.
66.78% of the time the bye player wins match 2 and then plays the winner of match 1 for the title. The winner of match 1 being 50/50 in each of the two matches will win the T by the slower route 1/4 x 66.78% = 16.695%
The total chance to win the T for each of the non byes is 16.61%+16.695% = 33.305% which again is very close to 1/3.
To summarize, Joe's method is extremely fair since it gives each of the 3 remaining players almost exactly 1/3 chance to win the T. Using GNU Supremo MET the bye is a teeny tiny advantage and using mec26 a tiny disadvantage. We can safely igonore any of those small fractions.
Since Joe's method is fair, there's no need for compensation of prizes or ABT points and they can be awarded as normal. Of course there has to be something for 3rd place to use this method, but that is fine in a decent sized field.
The only drawback of this method is that 2/3 of the time a 3rd round is needed to complete the event, whereas my proposed compensation method always ends the event in 2 rounds.
I do think that there's time in Madison to use Joe's method, noting that all matches including the finals are 9 pts. Of course the final few matches must be clocked, and the way to clock the match where one player has a 3 pt lead is to make reserve time 15 minutes rather than 18 since that match is 15/18 shorter in terms of combined points to win.
I like Joe's method for ABT main events, but for side jackpots (master's, doubles etc) I still prefer the quicker compensation for bye method unless there's lots of extra time.
I'll also point out, once again, that my work with the Swiss-elim spread sheet shows that having 3 equal players as the only 3 remaining from a draw of about 50 is quite rare. Perhaps someone with a more sophicasted spread sheet shows differently?
Also, if one of the 3 players had an earlier bye, he can't get one now. Therefore he has to have 25% to win the T using Joe's method, so we need a way to make the other 2 bye eligible players each be 37.5% to win.
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