Ultimate tie break for three way tie

[Matti]

Not to appear too flippant, but I like Mike's tongue-in-cheek 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: Select all

        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?

[Bantari]

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 tsume-go 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.

[Matti]

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.

[Matti]

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.

Lt's assume that there is (at least) one day for the tie break.

So lets say - up to 3 rounds then we draw straws. Or solve tsume-go 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.

[Bill Spight]

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.

[Matti]

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.

[Bill Spight]

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?

[Matti]

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?

[Bantari]

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 tie-breaker 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.

[Bill Spight]

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?

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.

[Matti]

If the players are tied by wins after the round robin, two more games will be played. The pairing will be made by ordering the players and the two last play a game ad the winner plays against the first. The ordering will be made by points added from player's games. If points are tied, the tied players are ordered by the time of their free round, a later free round being better.

[ez4u]

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 game-theoretic 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.

I think that Waylon's auction idea is the most interesting. After a little fooling around with katago, it seems that the range of alternatives can be quite short. Simply declare that the player with the bye in game one will take black in game two. The auction is for how much komi black will give. Under Chinese rules black should be willing to give 9.5 but reluctant to give 11.5 points (37% winrate versus 28%). Under Japanese rules the choices would be a little more nuanced with 10.5 also in the mix.

However, the idea of drawing straws is also an attractive way to cut to the chase. If we have a three way tie, split the prize money evenly but draw straws to choose which two players will complete in a single game for the trophy and the title of "Champion". The chances are the same for everyone at each stage and will not influence earlier play.

[Bill Spight]

If the players are tied by wins after the round robin, two more games will be played. The pairing will be made by ordering the players and the two last play a game ad the winner plays against the first. The ordering will be made by points added from player's games. If points are tied, the tied players are ordered by the time of their free round, a later free round being better.

Well, as I said, I have not been following this discussion. I thought that if the tie-break games did not produce a clear winner, the point total of those three games would be used to break that tie. A three way tie is still possible that way, but unlikely.

[Matti]

If the players are tied by wins after the round robin, two more games will be played. The pairing will be made by ordering the players and the two last play a game ad the winner plays against the first. The ordering will be made by points added from player's games. If points are tied, the tied players are ordered by the time of their free round, a later free round being better.

Well, as I said, I have not been following this discussion. I thought that if the tie-break games did not produce a clear winner, the point total of those three games would be used to break that tie. A three way tie is still possible that way, but unlikely.

Not exactly. If the players are tied by wins after the three games they are ranked by sum of points and if that tied then by having the bye round later. Tww lowest ranked play a game and the winer play against the highest to decide the winner.

[Matti]

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 game-theoretic 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.

I think that Waylon's auction idea is the most interesting. After a little fooling around with katago, it seems that the range of alternatives can be quite short. Simply declare that the player with the bye in game one will take black in game two. The auction is for how much komi black will give. Under Chinese rules black should be willing to give 9.5 but reluctant to give 11.5 points (37% winrate versus 28%). Under Japanese rules the choices would be a little more nuanced with 10.5 also in the mix.

So one would draw lots for the order to make a bid.

There might be some ramifications like A would bid over B's 9.5 bid, but not C's 9.5 bid.