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Ultimate tie break for three way tie http://lifein19x19.com/viewtopic.php?f=45&t=11530 
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Author:  Matti [ Fri Mar 06, 2015 2:02 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Mef wrote: Matti wrote: Mef wrote: I say we break the tie by awarding the win to the one with the fewest total ko captures at the end of the tournament. That way every time you think about fighting a ko, you not only have to count your threats, but think about how much you might hurt your chances in the metagame. Do you count only single stone captures or also if there are repeated captures of multiple stones? Single or multistone captures would both count, but we are counting the moves not the number of captures. For the sake of making it easy, a ko capture can be any move that both captures at least 1 stone and creates a board position where there is at least one point the opponent may not immediately play due to a ko restriction. Let's call the number of ko captures NKC tie breaker. In this three way tie scenario I could use the NKC, if the players are equal by the score totals. However usage of NKC requires the games to be recorded. 
Author:  Matti [ Tue Aug 13, 2019 2:36 am ] 
Post subject:  Penultimate tie break for three way tie 
I changed the subject to Penultimate tie break. if we want to break a three way tie by playing we need at least two games for it. The question is how to do the paring. Assuming the players are equal streth the player who gets dirctly into the final has 50% chance of winning while the other two have 25% chances. Lets list some choices. The penultimate tie break:
b. Rating c. Prior order d. An extra round robin in between, if tied revert to a, b or c e. An extra round robin with point scoring tie break In d. the chances of players winning are 6/16, 5/16 and 5/16. Do you find them equal enough? In my opinion tie breaker e., when time allows is better than any of a.,b.,c.. It is more related to the playing skill. One coud compare it to extra time and penalty shoot out in football. 
Author:  ez4u [ Tue Aug 13, 2019 6:24 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
The world has changed a bit since this thread began. I think that the interesting approach today would be to use an engine like Katago to determine a handicap/komi combination that gives Black a 66.7% chance of winning (let's guess it is something like a 2stone game with a 17 point komi). So then... 1. Draw lots to give one player a bye (player C) 2. Players A and B play an even game (each has a 50% chance of winning). 3. The winner of this game (assume it is player A) takes Black against player C with the above mentioned handicap/komi kombo. This would result in both Players A (50% * 66.7%) and C a 33.3% chance of winning if I did my math right. What do you think?! Maybe someone here could get Katago to spit out a sample configuration for the final game. 
Author:  Matti [ Tue Aug 13, 2019 12:48 pm ] 
Post subject:  Re: Ultimate tie break for three way tie 
ez4u wrote: The world has changed a bit since this thread began. I think that the interesting approach today would be to use an engine like Katago to determine a handicap/komi combination that gives Black a 66.7% chance of winning (let's guess it is something like a 2stone game with a 17 point komi). So then... 1. Draw lots to give one player a bye (player C) 2. Players A and B play an even game (each has a 50% chance of winning). 3. The winner of this game (assume it is player A) takes Black against player C with the above mentioned handicap/komi kombo. This would result in both Players A (50% * 66.7%) and C a 33.3% chance of winning if I did my math right. What do you think?! Maybe someone here could get Katago to spit out a sample configuration for the final game. Interesting. 
Author:  Waylon [ Tue Aug 13, 2019 11:12 pm ] 
Post subject:  Re: Ultimate tie break for three way tie 
ez4u wrote: The world has changed a bit since this thread began. I think that the interesting approach today would be to use an engine like Katago to determine a handicap/komi combination that gives Black a 66.7% chance of winning (let's guess it is something like a 2stone game with a 17 point komi). So then... 1. Draw lots to give one player a bye (player C) 2. Players A and B play an even game (each has a 50% chance of winning). 3. The winner of this game (assume it is player A) takes Black against player C with the above mentioned handicap/komi kombo. This would result in both Players A (50% * 66.7%) and C a 33.3% chance of winning if I did my math right. What do you think?! Maybe someone here could get Katago to spit out a sample configuration for the final game. Interesting idea. Alternatively, you can make a kind of auction. The person who is willing to give the highest handicap in the final game, (stones or komi or whatever), goes directly to the final. This way no luck is involved and they do not depend on the accuracy of a bot evaluation. The players themselves decide, what kind of risk they are willing to take. 
Author:  Matti [ Wed Aug 14, 2019 12:54 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Waylon wrote: Interesting idea. Alternatively, you can make a kind of auction. The person who is willing to give the highest handicap in the final game, (stones or komi or whatever), goes directly to the final. This way no luck is involved and they do not depend on the accuracy of a bot evaluation. The players themselves decide, what kind of risk they are willing to take. How do you compare handicap and komi, for example 2 stones handicap vs. 20 points komi? 
Author:  Waylon [ Wed Aug 14, 2019 2:09 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Matti wrote: How do you compare handicap and komi, for example 2 stones handicap vs. 20 points komi? Results from pro games and bot games suggest that the advantage for the first move is close to 7 points. 2 handicap stones should be approximately equal to 21 points of komi. The sorted list of possible handicaps for the auction is probably not the gametheoretic truth. I don't see this as a major problem, as long as the list is created by reasonably competent players and made public in the tournament conditions, to which all participants agree. 
Author:  Matti [ Wed Aug 14, 2019 2:28 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Next one needs to decide how to carry out the auction:
from high to low first bid simultaneous bids in envelopes Each way has its own ramifications. 
Author:  Bantari [ Wed Aug 14, 2019 2:29 pm ] 
Post subject:  Re: Ultimate tie break for three way tie 
Not to appear too flippant, but I like Mike's tongueincheek suggestion  why not just draw straws? With respect to the tiebreak being in any way connected to the strength, skill, or performance of the players  drawing straws is about as meaningful or as meaningless as what the OP proposes. The bonus of drawing straws is that it does not influence the strategy and/and tactics of preceding games. If we really want to have a *meaningful* tiebreaker  I see no other way than to make them play games until a winner emerges. This might be inconvenient for the organizers, but such is the nature of this game. Everything else is uncivilized. 
Author:  Bantari [ Wed Aug 14, 2019 2:36 pm ] 
Post subject:  Re: Ultimate tie break for three way tie 
Oh... I forgot. And if we want something like penalty kicks in soccer to be a tiebreaker  we can get them to solve go problems and see who does it faster. This might be a good alternative, corresponding to penalty kicks. Just sayin.... 
Author:  Matti [ Sat Aug 17, 2019 12:44 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Bantari wrote: Not to appear too flippant, but I like Mike's tongueincheek suggestion  why not just draw straws? With respect to the tiebreak being in any way connected to the strength, skill, or performance of the players  drawing straws is about as meaningful or as meaningless as what the OP proposes. The bonus of drawing straws is that it does not influence the strategy and/and tactics of preceding games. If we really want to have a *meaningful* tiebreaker  I see no other way than to make them play games until a winner emerges. This might be inconvenient for the organizers, but such is the nature of this game. Everything else is uncivilized. Let's assume that some games will be played to break the tie and for pairng purposes we order prior the tie break games detrmined the way you prefer: A > B > C. Also we assume a 50% chance for either player in a game. We set the maximum limit for the numbers to be played. If there is at least three game remaining a round robn is played. If tied continue. If there is two games left play B vs. C and the winner plays A. If one game is left play A vs. B and the winner is the winner. If there is no game left the prior order stands. In the table are propabilities for each player to win with maximum numbers of rounds. Code: Winning propability Rounds A B C 0 1 0 0 1 1/2 1/2 0 2 1/2 1/4 1/4 3 1/2 1/4 1/4 4 3/8 3/8 1/4 5 6/16 5/16 5/16 6 6/16 5/16 5/16 7 11/32 11/32 10/32 8 22/64 21/64 21/64 etc. How many rounds do you find good enough? 
Author:  Bantari [ Sat Aug 17, 2019 2:05 pm ] 
Post subject:  Re: Ultimate tie break for three way tie 
Matti wrote: How many rounds do you find good enough? I don't really care, to be honest  we can certainly agree on some number. Will probably be based on the resources we have (time, location, etc) and the input from organizers. So lets say  up to 3 rounds then we draw straws. Or solve tsumego puzzles. The former is as meaningful as what you propose and the latter is more so. Both have the advantage of not affecting the prior games. Your argument seems to evolve around the fact that a situation is possible when a lot of rounds might still not produce clear winner. I grant that this is possible. But the system you propose has exactly the same weakness. Lets say each player has exactly the same number of "points" at the end. What then? (A beats B by 3.5, B beats C by 3.5, and C beats A by 3.5  its possible. You can include more players, and it is still possible that the final points fall in a way which will not produce a proper winner.) You'll be down to drawing straws as well. So why not try something actually meaningful first? Lets give it a try (say 3 rounds) and if it fails, we do random pick. 
Author:  Matti [ Mon Aug 19, 2019 3:10 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Bantari wrote: Your argument seems to evolve around the fact that a situation is possible when a lot of rounds might still not produce clear winner. I grant that this is possible. But the system you propose has exactly the same weakness. Lets say each player has exactly the same number of "points" at the end. What then? (A beats B by 3.5, B beats C by 3.5, and C beats A by 3.5  its possible. You can include more players, and it is still possible that the final points fall in a way which will not produce a proper winner.) You'll be down to drawing straws as well. I had thought about this problem. If players tie on the number of points the player who has played his games earlier is considered having done better, because the others already know to what result to aim at. if we assume the rder of games above then the system would continue with A playing c and B playing the winner. 
Author:  Matti [ Mon Aug 19, 2019 3:21 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Bantari wrote: Matti wrote: How many rounds do you find good enough? I don't really care, to be honest  we can certainly agree on some number. Will probably be based on the resources we have (time, location, etc) and the input from organizers. Quote: So lets say  up to 3 rounds then we draw straws. Or solve tsumego puzzles. The former is as meaningful as what you propose and the latter is more so. Both have the advantage of not affecting the prior games. So why not try something actually meaningful first? Lets give it a try (say 3 rounds) and if it fails, we do random pick. I prefer fast games to tsume go. Anyway playng 3 rounds first and then if needed drawing straws for example to do pairing for two more games would be good enough. To win one might need to play 4 games. 
Author:  Bill Spight [ Mon Aug 19, 2019 4:33 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Matti wrote: I had thought about this problem. If players tie on the number of points the player who has played his games earlier is considered having done better, because the others already know to what result to aim at. Why? After each game let the players turn in the result to the TD, but it remains confidential until the end. Any player who reveals the score to anyone before the TD does at the end is disqualified. 
Author:  Matti [ Mon Aug 19, 2019 5:16 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Bill Spight wrote: Matti wrote: I had thought about this problem. If players tie on the number of points the player who has played his games earlier is considered having done better, because the others already know to what result to aim at. Why? After each game let the players turn in the result to the TD, but it remains confidential until the end. Any player who reveals the score to anyone before the TD does at the end is disqualified. Players know their results from their previous games anyway. Suppose A beats B by 3.5 and B decides that a win against C by 3.5 is good enough and manges to get it. Next C decides that 3.5 against A is good enough and manages it. Then we have the scenario presented before. 
Author:  Bill Spight [ Mon Aug 19, 2019 6:54 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Matti wrote: Bill Spight wrote: Matti wrote: I had thought about this problem. If players tie on the number of points the player who has played his games earlier is considered having done better, because the others already know to what result to aim at. Why? After each game let the players turn in the result to the TD, but it remains confidential until the end. Any player who reveals the score to anyone before the TD does at the end is disqualified. Players know their results from their previous games anyway. Suppose A beats B by 3.5 and B decides that a win against C by 3.5 is good enough and manges to get it. Next C decides that 3.5 against A is good enough and manages it. Then we have the scenario presented before. You want something foolproof? 
Author:  Matti [ Mon Aug 19, 2019 7:21 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Bill Spight wrote: Matti wrote: Bill Spight wrote: Why? After each game let the players turn in the result to the TD, but it remains confidential until the end. Any player who reveals the score to anyone before the TD does at the end is disqualified. Players know their results from their previous games anyway. Suppose A beats B by 3.5 and B decides that a win against C by 3.5 is good enough and manges to get it. Next C decides that 3.5 against A is good enough and manages it. Then we have the scenario presented before. You want something foolproof? Don't you think my suggestion is good enough: If players tie on the number of points, the player who has played his games earlier is considered having done better? 
Author:  Bantari [ Mon Aug 19, 2019 9:00 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
I feel at this point we are just arguing for the sake of arguing. So let me just restate my objections and then bow out of the thread. I think Matti's proposal is bad because: 1> The tiebreaker is not based on skill and/or performance, and 2> It might/will influence the gams too much. If we don't care about #1, then we might as well draw straws  at least this avoids #2. If we care about #1 (and #2)  lets find something else. 
Author:  Bill Spight [ Mon Aug 19, 2019 9:20 am ] 
Post subject:  Re: Ultimate tie break for three way tie 
Bill Spight wrote: Matti wrote: Bill Spight wrote: Why? After each game let the players turn in the result to the TD, but it remains confidential until the end. Any player who reveals the score to anyone before the TD does at the end is disqualified. Players know their results from their previous games anyway. Suppose A beats B by 3.5 and B decides that a win against C by 3.5 is good enough and manges to get it. Next C decides that 3.5 against A is good enough and manages it. Then we have the scenario presented before. You want something foolproof? Matti wrote: Don't you think my suggestion is good enough: If players tie on the number of points, the player who has played his games earlier is considered having done better? I haven't really been following the discussion. But if that is your criterion, shouldn't C play A on game 2? If A wins, that's that. C does not know how much he has to beat A by, but A knows that if he loses by more than 3.5 pts., he is in total negative territory and cannot with the tiebreak, so A has an advantage there. OTOH, if A loses by even 0.5 pts. he could lose the tiebreak, so he can't be satisfied with a loss. (And C has the advantage in the case of a tie that he will beat A, because A played first. Edit: I got that backwards. But if the player's results are not known to his opponent, maybe the later player, who lacks the knowledge of earlier results, should win a tie.) Edit: And if C beats A and then B and C play, neither player knows how much he has to win by to beat A's result. 
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