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[Watno]

I thought about the scoring system with the potential 6th game a bit and I don't like it.
I think it advantages the second player of the first game. Assume that all games except one are won by their first player. If it was the first player who lost one of "his games", he loses the match. If the second player lost one of "his" games, the match is a tie. So basically the second player is allowed on slip, while the first isn't.
I think a better solution would be to always play an even number of games (6).

Also, I think it would be better to alternate starting player regardless of who won the previous game. That what increase the value of taking a game your opponent started, by not allowing him to start the next gameif you do.

(Obviously I think the rules for the current season shouldn't be changed, this is meant for future tournaments I'm hoping for.

[Rabid]

If the second player lost one of "his" games, the match is a tie.

White I agree the score system has room for improvement.
This quote above is incorrect.
If 2nd Player "loses serve" once then P1 wins 4-2
P1: WLWWLW
P2: LWLLWL

[Watno]

Oh yeah, must have gotten confused there. Sorry.

[Kirian]

Let me briefly describe my reasoning for the current setup.  I think we can all agree that winning from the first seat is easier, on average.  So we can use the "break" idea from tennis, where winning games off of the other person's serve is necessary to win a set or a match.

So there are a number of different permutations that can happen.  I'll use players A and B, with A always leading after the fifth game.  Here are the various possibilities:

  12211     12121     12112     12112     11212     11122
A WWLLW   A WLWLW   A WLLWW   A LWWLW   A LWLWW   A LLWWW
B LLWWL   B LWLWL   B LWWLL   B WLLWL   B WLWLL   B WWLLL
  21122     21212     21221     21221     22121     22211

  22211     22121     22112     21221     21212     21122
A WWLLW   A WLWLW   A WLLWW   A LWWLW   A LWLWW   A LLWWW
B LLWWL   B LWLWL   B LWWLL   B WLLWL   B WLWLL   B WWLLL
  11122     11212     11221     12112     12121     12211

In the top row are all the possibilities where Player A went first in the first game, and player A is leading 3-2.  In all of these groups, the number of games won from seat 2 is equal for both players; each has "broken service" the same number of times.

In the bottom row are all the possibilities where Player A went second in the first game, and player A is leading 3-2.  In all of these groups, Player A has one more win from seat 2 than player B does.

In the top row, in other words, there is evidence that both players are of equal strength from the second seat; in the bottom row, there is evidence that Player A is stronger from that seat than Player B.  But the only difference in the two rows is whether Player A went first or second in the first game.  Therefore:

In the bottom row, the leading player went second in the first game, and has won the match.  In the top row, the leading player went first in the first game, but hasn't won the match due to not showing that he can break more often than Player B.

[soulnet]

I think the only advantage for the player going second in the first game is that in the last match, he knows he cannot tie, while 1st player is in doubt if given the opportunity to tie in the 5th game with 2-2 partial score.
Also, in case he wins 3-2, he had one more opportunity to break, so he still has some advantage.

It would be more fair that, if there is a tie after 4 games, 2 more games are played despite of the result of the 5th match. That way, if player that started in 2nd seat is 3-2, he still needs to tie or win from first seat once more. This player still has some additional advantage because of additional knowledge, but I don't see a way around it (although, maybe starting ABBABA or something non-alternating -like NBA playoffs do- is better, to balance the excess of knowledge)

[Stealth Tomato]

Let me briefly describe my reasoning for the current setup.  I think we can all agree that winning from the first seat is easier, on average.  So we can use the "break" idea from tennis, where winning games off of the other person's serve is necessary to win a set or a match.

So there are a number of different permutations that can happen.  I'll use players A and B, with A always leading after the fifth game.  Here are the various possibilities:

  12211     12121     12112     12112     11212     11122
A WWLLW   A WLWLW   A WLLWW   A LWWLW   A LWLWW   A LLWWW
B LLWWL   B LWLWL   B LWWLL   B WLLWL   B WLWLL   B WWLLL
  21122     21212     21221     21221     22121     22211

  22211     22121     22112     21221     21212     21122
A WWLLW   A WLWLW   A WLLWW   A LWWLW   A LWLWW   A LLWWW
B LLWWL   B LWLWL   B LWWLL   B WLLWL   B WLWLL   B WWLLL
  11122     11212     11221     12112     12121     12211

In the top row are all the possibilities where Player A went first in the first game, and player A is leading 3-2.  In all of these groups, the number of games won from seat 2 is equal for both players; each has "broken service" the same number of times.

In the bottom row are all the possibilities where Player A went second in the first game, and player A is leading 3-2.  In all of these groups, Player A has one more win from seat 2 than player B does.

In the top row, in other words, there is evidence that both players are of equal strength from the second seat; in the bottom row, there is evidence that Player A is stronger from that seat than Player B.  But the only difference in the two rows is whether Player A went first or second in the first game.  Therefore:

In the bottom row, the leading player went second in the first game, and has won the match.  In the top row, the leading player went first in the first game, but hasn't won the match due to not showing that he can break more often than Player B.

While you're right, the math doesn't work out.
At 12:8 first player edge, P2 will win 46% of matches (.46144) and 20% will draw (.19872).
At 11:9, it gets worse, with P2 winning 48% (.48112) and 18% drawing (.17607).
If we assume no first-player edge, P2 wins half of matches... but only loses 34% (drawing 16%, or .15625).

In an evenly matched game, I want to be second player. That's unfair. The easiest way to enforce this is to play best-of-seven where each player plays 3 home games, seventh game being up to random draw, which makes the probabilities much less skewed.

To reduce the "6-game match is fair" to the absurd, let's make it a 2-game match:
4 scenarios for me as 2nd player.
W2, W2
W2, L2
L2, W1
L2, L1
I win the first two scenarios (one on games and one on turn order), draw the third, and lose the fourth.

[Watno]

Why don't you think 6 games would be a good idea? There'ss no reason to avoid match ties.

[Kirian]

To reduce the "6-game match is fair" to the absurd, let's make it a 2-game match:
4 scenarios for me as 2nd player.
W2, W2
W2, L2
L2, W1
L2, L1
I win the first two scenarios (one on games and one on turn order), draw the third, and lose the fourth.

I'll have to look at the rest of your math, but this RIA doesn't work; you're assuming two scenarios (W/W, W/L) where two scenarios don't exist.

That said, assuming your numbers are correct, they present a compelling argument for playing game 6 regardless, not an argument for playing 7 games--which just reintroduces the problem of playing five games.

[Stealth Tomato]

I'll have to look at the rest of your math, but this RIA doesn't work; you're assuming two scenarios (W/W, W/L) where two scenarios don't exist.

You're right, but that doesn't change that "P2 wins" is a 50/50 proposition (40% if FTA is 60:40) and "P1 wins" is 25% (24% if FTA is 60:40). Whether you play the irrelevant second game is, well, irrelevant.

That said, assuming your numbers are correct, they present a compelling argument for playing game 6 regardless, not an argument for playing 7 games--which just reintroduces the problem of playing five games.

Which is fair, although playing 7 is still more equitable than the current scenario; about 30% of matches would go to 7 games, giving the Game 7 first player about a 6% match edge at 60:40 FTA, rather than today's 12% edge for game 1 P2. The question is whether we're okay with nearly 1/3 of matches ending in a draw.

Why don't you think 6 games would be a good idea? There'ss no reason to avoid match ties.

Which is not an unreasonable sentiment, but there's also no reason to encourage match ties.

[Polk5440]

It would be more fair that, if there is a tie after 4 games, 2 more games are played despite of the result of the 5th match. That way, if player that started in 2nd seat is 3-2, he still needs to tie or win from first seat once more. This player still has some additional advantage because of additional knowledge, but I don't see a way around it (although, maybe starting ABBABA or something non-alternating -like NBA playoffs do- is better, to balance the excess of knowledge)

Alternatively, you could just call it after 4 games. Each player starts first twice. At the end of 4 games, it's either tied (2-2-0, 1-1-2, 0-0-4) or one player has more wins and wins the match.

Or for a longer match, play 6 games for sure, each player starts first 3 times.

Of course, more games would yield more accurate results, but 7 games is too many to play at once -- for me anyway. 6 games today in a row was really pushing it.

Re: first player advantage. Wasn't the Council Room data showing a 55-45 advantage on Iso? It was significant.

@Stealth Tomato. For the calculations, if you assume ties in a game happen with more than 0% probability, does the bias go down?

[Stealth Tomato]

It would be more fair that, if there is a tie after 4 games, 2 more games are played despite of the result of the 5th match. That way, if player that started in 2nd seat is 3-2, he still needs to tie or win from first seat once more. This player still has some additional advantage because of additional knowledge, but I don't see a way around it (although, maybe starting ABBABA or something non-alternating -like NBA playoffs do- is better, to balance the excess of knowledge)

@Stealth Tomato. For the calculations, if you assume ties in a game happen with more than 0% probability, does the bias go down?

Currently working on that, but of note, there's no clarity on what happens when the match is 3-2 after 6 games. Particularly if the players tie the first game (or any game where the seat order is the same as Game 1), which causes all sorts of unhandled exceptions. For example (I'm P2 to start, each match denoted by result and seat number of me):
T2   W1   L2   W1   L2   W1
Do I win or is it a draw? I've won more games (3-2) but every win was from first seat. Neither player has won more games going second.

e: it gets even worse if you tie a game where the seat order is opposite Game 1.
L2   T1   W2   W2   L2   L1
My opponent is 3-2 but has actually lost twice from first seat (games 3-4) and only won once from second (game 6).

[soulnet]

T2   W1   L2   W1   L2   W1
Do I win or is it a draw? I've won more games (3-2) but every win was from first seat. Neither player has won more games going second.

You should clearly win, as you did equally or better than your opponent in every seat arrangement, and strictly better in one of them.

e: it gets even worse if you tie a game where the seat order is opposite Game 1.
L2   T1   W2   W2   L2   L1
My opponent is 3-2 but has actually lost twice from first seat (games 3-4) and only won once from second (game 6).

Hence, we should always play the same number of times from seat 1 than from seat 2 (sometimes we may finish early because there is no way one of the players will win or tie the match).

[andwilk]

I suggest for future tournaments, each player should have an equal number of starts in first seat (ideally just alternate starting player every game).  Match end criteria would be 4 wins or play a maximum of 6 games.  This seems pretty fair.  Thoughts?

[Kirian]

Hence, we should always play the same number of times from seat 1 than from seat 2 (sometimes we may finish early because there is no way one of the players will win or tie the match).

Given this discussion, I am starting to lean strongly toward this as the basis of the format for next season.  The format would likely be:

Each game is worth 1 match point for a win, 0.5 for a draw.
Each match is first to 3 points, with a maximum of six games.
The first player for the first game is determined randomly; call this player A.  In order, the first player for the games will be: A-B-B-A-A-B
If one player has won 3 match points after 3 or 4 games, that player wins the match.
If one player has won 3.5 match points after 5 games, that player wins the match.
If neither of those conditions is satisfied, the sixth game must be played.  After six games, the player with the larger number of match points wins the match; if both players have equal match points, the match is a draw.

[Polk5440]

I suggest for future tournaments, each player should have an equal number of starts in first seat (ideally just alternate starting player every game).  Match end criteria would be 4 wins or play a maximum of 6 games.  This seems pretty fair.  Thoughts?

As I stated (not very clearly) above, I think I would prefer first to 3.5 points (ties count as half points), rather than 4 points.

[Polk5440]

Hence, we should always play the same number of times from seat 1 than from seat 2 (sometimes we may finish early because there is no way one of the players will win or tie the match).

Given this discussion, I am starting to lean strongly toward this as the basis of the format for next season.  The format would likely be:

Each game is worth 1 match point for a win, 0.5 for a draw.
Each match is first to 3 points, with a maximum of six games.
The first player for the first game is determined randomly; call this player A.  In order, the first player for the games will be: A-B-B-A-A-B
If one player has won 3 match points after 3 or 4 games, that player wins the match.
If one player has won 3.5 match points after 5 games, that player wins the match.
If neither of those conditions is satisfied, the sixth game must be played.  After six games, the player with the larger number of match points wins the match; if both players have equal match points, the match is a draw.

I guess I am with andwilk and soulnet in that if 6 games isn't too long, there isn't really a need to specify a very particular win condition for 5 games. (And if six games is too long, I would vote for just doing 4 games.)

Not having the win condition after 5 games makes the statement of scoring easy: Match winner is the first to 3.5 points. Six games max. If no one get 3.5 points after 6 games, match is a draw. (Augmented with whatever agreeable seating rule so that each player is scheduled to go first 3 times)

[Stealth Tomato]

It would be more fair that, if there is a tie after 4 games, 2 more games are played despite of the result of the 5th match. That way, if player that started in 2nd seat is 3-2, he still needs to tie or win from first seat once more. This player still has some additional advantage because of additional knowledge, but I don't see a way around it (although, maybe starting ABBABA or something non-alternating -like NBA playoffs do- is better, to balance the excess of knowledge)

Re: first player advantage. Wasn't the Council Room data showing a 55-45 advantage on Iso? It was significant.

@Stealth Tomato. For the calculations, if you assume ties in a game happen with more than 0% probability, does the bias go down?

I ran it with 55-45 first player advantage and 5% chance of a draw.
P2 wins 47.7% of matches and draws 13.4%, giving him 54.4% win equity, slightly more fair than the 56.9% win equity if we assume no ties. Still not quite fair. For comparison, a simple best-of-seven (each player goes first 3x, random draw for game 7) gives about 51.5% win equity to P1.

[Polk5440]

Thanks for rerunning the calculations. (Things don't add up to 105%, though, right?)

For comparison, a simple best-of-seven (each player goes first 3x, random draw for game 7) gives about 51.5% win equity to P1.

Why isn't this last case with random start game 7 resulting in 50-50 win equity? I ask, because the "random draw" element gets away from the first player advantage problem, I think. If you play one game with random starting player and each player is of equal skill, it should be 50-50 no matter the first player advantage because each player has an equal likelihood of going first. So the random draw for the seventh game shouldn't matter, right? So is there something in the first 6 games that's still causing a bias to player 1?

I think any solution to address first player advantage problem should not rely on random starts in any game to get an unbiased/fair outcome. That was the problem with the straight up best of 5 (or best of 7) format. Ex ante, it's fair because each player has an equal chance of going first the first game. But once that uncertainty is resolved, the win equity is biased due to "nature resolving" rather than any action by the players and there aren't enough rounds (esp in a knockout format) for people to feel like this bias averages out.

[WanderingWinder]

Thanks for rerunning the calculations. (Things don't add up to 105%, though, right?)

For comparison, a simple best-of-seven (each player goes first 3x, random draw for game 7) gives about 51.5% win equity to P1.

Why isn't this last case with random start game 7 resulting in 50-50 win equity? I ask, because the "random draw" element gets away from the first player advantage problem, I think. If you play one game with random starting player and each player is of equal skill, it should be 50-50 no matter the first player advantage because each player has an equal likelihood of going first. So the random draw for the seventh game shouldn't matter, right? So is there something in the first 6 games that's still causing a bias to player 1?

I think any solution to address first player advantage problem should not rely on random starts in any game to get an unbiased/fair outcome. That was the problem with the straight up best of 5 (or best of 7) format. Ex ante, it's fair because each player has an equal chance of going first the first game. But once that uncertainty is resolved, the win equity is biased due to "nature resolving" rather than any action by the players and there aren't enough rounds (esp in a knockout format) for people to feel like this bias averages out.

He means that whoever wins the coin flip of going first has 51.5% win equity, not that player A, from the point before said coinflip, wins the match more often than the other buy - obviously identically skilled player in the identical situation expect to win identically the same amount - no math needed.

[Stealth Tomato]

Thanks for rerunning the calculations. (Things don't add up to 105%, though, right?)

Correct, the 5% is taken equally out of each player's wins, giving them 55:45 win equity (52.5% P1, 42.5% P2, 5% Draw)

On a side note, the player order determination mechanism is a pain in the ass to deal with mathematically, and I didn't feel like scripting, so I've been enumerating game outcomes by hand. I disregarded outcomes with 3 or more draws (<.03% of cases, almost all of which are a match draw). This means that minor errors are possible but the numbers will be largely correct, and the 2-game example verifies the concept that P2 has an inherent advantage.

The interesting thing about this system is that P1 actually has a match edge at very high seat-1 advantage. He breaks even around 77.5% win equity, and approaches a 52% win equity at 90% seat-1 advantage (although at that point, the players are drawing nearly half their matches). Over 90%, there's very little win equity available because the players are drawing the match so often.

[Polk5440]

@WW, ST: ok, thanks.

[andwilk]

Hence, we should always play the same number of times from seat 1 than from seat 2 (sometimes we may finish early because there is no way one of the players will win or tie the match).

Given this discussion, I am starting to lean strongly toward this as the basis of the format for next season.  The format would likely be:

Each game is worth 1 match point for a win, 0.5 for a draw.
Each match is first to 3 points, with a maximum of six games.
The first player for the first game is determined randomly; call this player A.  In order, the first player for the games will be: A-B-B-A-A-B
If one player has won 3 match points after 3 or 4 games, that player wins the match.
If one player has won 3.5 match points after 5 games, that player wins the match.
If neither of those conditions is satisfied, the sixth game must be played.  After six games, the player with the larger number of match points wins the match; if both players have equal match points, the match is a draw.

I guess I am with andwilk and soulnet in that if 6 games isn't too long, there isn't really a need to specify a very particular win condition for 5 games. (And if six games is too long, I would vote for just doing 4 games.)

Not having the win condition after 5 games makes the statement of scoring easy: Match winner is the first to 3.5 points. Six games max. If no one get 3.5 points after 6 games, match is a draw. (Augmented with whatever agreeable seating rule so that each player is scheduled to go first 3 times)

The win condition for a 5-game set that Kirian listed is more of a default condition since if one player has 3.5 points after 5 games, there is no point in playing the sixth game since the match result cannot change.

This is different than the match conditions laid out for a 3 or 4 game match (one player must reach 3 points) since the trailing player can still catch up by the sixth game.

[Polk5440]

This is different than the match conditions laid out for a 3 or 4 game match (one player must reach 3 points) since the trailing player can still catch up by the sixth game.

Right. I am with you with 3-0 or 3-1 ending the match isn't that great because the other player could catch up if 6 games were played. I had this in mind when I suggested:

Match winner is the first to 3.5 points. Six games max. If no one get 3.5 points after 6 games, match is a draw. (Augmented with whatever agreeable seating rule so that each player is scheduled to go first 3 times)

I just didn't articulate it well.

[kn1tt3r]

I think the current rules are okay, but I really like the idea (at least for a swiss system) to play a defined (even) number games (like 4 or 6) no matter what, and just alternate the starting position. This is basically the only way to have absolutely fair results and the same conditions for every player.