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BGonline.org Forums
The real reason to have a win-once final in double elim
Posted By: Rich Munitz In Response To: A fair spot for the undefeated player (Sam Pottle)
Date: Friday, 19 June 2009, at 3:52 a.m.
Sam, this is pretty much exactly what David Rockwell inferred using logic in an email exchange. But ultimately it makes sense. The question was where was the error in the math. Thanks for clearing it up.
I've always felt it to be as steep or steeper a hill to climb to win a progressive consolation than to win the main event. (Perhaps that is why Stick has been so successful there - maybe he is the best). But we all seem to accept the consolation winner not getting the same prize as the main tournament winner.
So why does a win-once final in a double elim make sense? I think I have the answer. The answer is that the win-twice format violates an axiom of elimination tournaments. It makes the single semi-final match worth more than the potentially two match final.
Hopefully I got the math right this time.
Here are the details:
Lets look at the prize pool equities in a double elimination undefeated finals. Keep in mind that % of prize pool could be interchanged with % of ABT points. I assume a 2:1 payout ratio at each level advanced.
Two players reach the undefeated finals. The winner is in the tournament finals. The loser drops down to the once-defeated and must now win two more matches to reach the tournament finals.
Shares paid in LA 64 player draw (22 shares total) are:
8: 1st Main 4: 2nd Main 2: 3rd Main 4: 1st Cons 2: 2nd Cons 1/1: 3/4 Cons
The undefeated main final loser's outcomes are:
25% - reaches the tournament finals (some split of 12 shares) 25% - cashes 3rd place Main (2 shares) 50% - enters Consolation bracket in round of 8; splits Consolation prize pool (8 shares) = 1 share
If the once-defeated finalist must win once to win the tournament, his equity is 50% of the finals shares or 6 shares. The undefeated finalist's equity is also 6 shares. In this scenario, the loser of the finals of the undefeated bracket has an overall equity of (6*25% + 2*25% + 1*50%) / 100% = 2.5 shares. The net gain from winning the finals of the undefeated bracket is 6 - 2.5 = 3.5 shares.
If the once-defeated finalist must win twice to win the tournament, at this point, he is guaranteed 1/3 of the prize pool for second place (4 shares), his opponent is also guaranteed 1/3 (4 shares), and they are playing for the remaining 4 shares in which he has a 25% equity stake, giving the once-defeated finalist a total equity of 4+1 = 5 shares. The undefeated finalist's equity upon winning the undefeated bracket is 7 shares. In this scenario, the loser of the finals of the undefeated bracket has an overall equity of (5*25% + 2*25% + 1*50%) / 100% = 2.25 shares. The net gain from winning the finals of the undefeated bracket is 7 - 2.25 = 4.75 shares.
Forget for now the issues of difficulty and which bracket might produce the stronger player. The best reason to have a one match final is schedule. Less time, easier to plan. The second best reason is what was layed out above. Matches should have increasing equity gains the further one advances, and there should not be monstrous equity swings in a single match. There are 4 winner-take-all shares at stake in the finals (whether "finals means" 1 or 2 matches). It is simply crazy that in the win-twice format, the match the undefeated players play before the finals should be worth 4.75 shares to the winner - more than 4.0 that the potential 2 match finals is worth to the winner. That's 13.8 ABT points for winning a semifinal match of a 64 player tournament! Making the finals 1 match makes the prior round worth 3.5 shares - still close in absolute value to the finals, still a very substantial equity payout to the winner that they can only be happy to receive, but less in value to the finals, as it should be.
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