What do you mean by points? Simply adding up all the individual scores?
If so, consider a match where the score is 4-4 - both players will double every turn until the match is decided since they can improve their tiebreaking power with very little downside.
I'd argue that strength of schedule is, in fact, the better indicator, although I think a bit of thought could result in a reasonable algorithm that combines both together.
If so, consider a match where the score is 4-4 - both players will double every turn until the match is decided since they can improve their tiebreaking power with very little downside.
Why do you people keep thinking there is ever a good idea to double like crazy?! If you are not winning the game, why would you want to help your opponent? It's not like poker where you can raise when you have a worthless hand of cards and fool your opponent into thinking you have a good hand. Everyone can see both player's hands right there on the table. If you see the other player is ahead, why in the world would you raise the stakes and give them free points?
It's still a lot like poker in that throughout almost all of the game, both players have a good chance of winning. Yes, you wouldn't double once your chance became very small, but up until then your incentives are huge.
Why? It's simple game theory. You have a lot more to gain by getting tie-breaking points than you have to lose by your opponent getting tie-breaking points. Why? Because you getting those points helps you against everyone else in the Grand Prix. Your opponent getting them only hurts you vs them, but not vs everyone else.
Consequently, by doubling a lot while the game is still relatively close (10% chance of winning is probably enough), both players gain expected utility at the expense of everyone else. Yes, the interactions are zero-sum when looked at over the tournament as a whole, but between those two players, they are not.
Also, even though I don't really need a further argument, situations where there is absolutely nothing to lose are in fact rather common.
For example - it's the sixth and last round of the tournament, and you and your opponent both have the exact same number of wins. As such, it's guaranteed that at the end of the tournament, you and your opponent will have different numbers of wins, which means that you cannot possibly be tie-breaking against one another. Consequently, there is no chance giving your opponent lots of points will hurt you in tie-breaking at all.
As a bare minimum, you can use the score delta rather than the absolute score to mitigate the problem, but it doesn't fully fix it, due to the payout structure of the tournament - the gaps get higher as you go up the ladder. Consequently, you have more to gain by getting a huge positive tie-breaking score than you have to lose by getting a huge negative one.
In order to solve that issue, you have to do something more, such as capping the score delta at some value (e.g. 5 points).
That said, I still think opponent strength is a more important indicator in this game than the score, especially when the primary goal is supposed to be winning the match, not maximising score.
Usually strength of schedule is the second tiebreaker after points. I chose to do it this way because that's the way Netrunner tournaments work.
Also MTG tournaments. As a first metric of tie breaking, it's the one that most "rewards" previous opponents for people not tanking it later.
If so, consider a match where the score is 4-4 - both players will double every turn until the match is decided since they can improve their tiebreaking power with very little downside.
If it's 4-4 Crawford is in effect and you can't double.
The most applicable example is a 4-3 match after the Crawford game. The moment the 4 point player doubles (which they never should unless they are 99% sure they should win), then the 3 point player accepts, doubles back and then the die sits with the other player for the rest of the game. That's the worst situation I can imagine and even that isn't that terrible.
If it's 4-4 Crawford is in effect and you can't double.
Nope. There is only one Crawford game per match. Imagine this situation.
The score is 2-3. Player 2 wins making the score 2-4. Now you play a Crawford game. Player 1 wins. Score is now 3-4. Player 1 wins the next game, the score is 4-4. You do not play a Crawford game. You already played one. Final score could be BIG NUMBER-4.
If it's 4-4 Crawford is in effect and you can't double.
No, it isn't. Crawford is in effect for only the first game where one player has 4 points, which is called the "Crawford game" - after that it no longer applies. If the scores are 4-4, it cannot be the first game where a player has 4 points.
Ah. Then Pogo where Apsup and I played was doing it wrong. Whatevers. The infinite double thing is still redonkey. You know what metagames that out the window?
Ok, amazingly everyone played. As soon as the last report is in I will put the pairings for the next round in the doc, which is here if you lost the URL.
Unless I'm misreading the chart, it looks like Snickety was awarded the round 2 bye? In a Swiss tournament, that's usually awarded to a person with a losing record, or rather lowest possible score. If he won his first match, I think that bye should go to someone who lost their first one.
Unless I'm misreading the chart, it looks like Snickety was awarded the round 2 bye? In a Swiss tournament, that's usually awarded to a person with a losing record, or rather lowest possible score. If he won his first match, I think that bye should go to someone who lost their first one.
I am aware, but I'm not a fan. I chose instead to hand out the bye completely randomly.
I think Dromaro is right. Since not everyone gets a bye, it would be better to give it to low-scoring players to minimize the overall distortion. The differences in Grand Prix points are, after all, rather top-heavy.
It is true that it may create more distortion if a bye gives someone an extra few grand prix points by moving them one position up. However, always giving it to the bottom creates a general fairness issue. The players who are just above the bye threshhold will likely end up in last place undeservedly. Theortetically you could have a player score four real points by winning four games end up below a whole bunch of players who got 5 for free and never won anything. That's a lot of positions for one person. If you're giving out a free win, may as well distribute them with complete randomness. If a really good player gets a bye, that can even be considered less intrusive since they probably would have gotten 5 points anyway. It may even hurt them if they were going to score more than 5.
Well, as I've already stated, your proposed tie-breaking system isn't very good.
Regardless, you can fix the issue you mentioned pretty easily - simply don't give people who get byes 5 backgammon points. Give them a smaller number, or zero.
Comments
If so, consider a match where the score is 4-4 - both players will double every turn until the match is decided since they can improve their tiebreaking power with very little downside.
I'd argue that strength of schedule is, in fact, the better indicator, although I think a bit of thought could result in a reasonable algorithm that combines both together.
Also, let's wait until we actually have a tie.
Why? It's simple game theory. You have a lot more to gain by getting tie-breaking points than you have to lose by your opponent getting tie-breaking points. Why? Because you getting those points helps you against everyone else in the Grand Prix. Your opponent getting them only hurts you vs them, but not vs everyone else.
Consequently, by doubling a lot while the game is still relatively close (10% chance of winning is probably enough), both players gain expected utility at the expense of everyone else. Yes, the interactions are zero-sum when looked at over the tournament as a whole, but between those two players, they are not.
For example - it's the sixth and last round of the tournament, and you and your opponent both have the exact same number of wins. As such, it's guaranteed that at the end of the tournament, you and your opponent will have different numbers of wins, which means that you cannot possibly be tie-breaking against one another. Consequently, there is no chance giving your opponent lots of points will hurt you in tie-breaking at all.
In order to solve that issue, you have to do something more, such as capping the score delta at some value (e.g. 5 points).
That said, I still think opponent strength is a more important indicator in this game than the score, especially when the primary goal is supposed to be winning the match, not maximising score.
If it's 4-4 Crawford is in effect and you can't double.
The most applicable example is a 4-3 match after the Crawford game. The moment the 4 point player doubles (which they never should unless they are 99% sure they should win), then the 3 point player accepts, doubles back and then the die sits with the other player for the rest of the game. That's the worst situation I can imagine and even that isn't that terrible.
The score is 2-3. Player 2 wins making the score 2-4. Now you play a Crawford game. Player 1 wins. Score is now 3-4. Player 1 wins the next game, the score is 4-4. You do not play a Crawford game. You already played one. Final score could be BIG NUMBER-4.
Winning all your matches.
Thats my pro-tip of the day.
I can't believe I got this lucky when usually it's so bad I'm tempted to throw the computer out of the window. lackofcheese can testify to that.
https://docs.google.com/spreadsheet/ccc?key=0Amh4XYkHbJgfdGNoSTZRZVlXVF9fR0dETF8zcFhUWWc&usp=sharing
Me (5) vs No fun girl (4)
April 6th, 17:00 UTC
I hope there is no ambiguity in the deadline anymore.
Unless I'm misreading the chart, it looks like Snickety was awarded the round 2 bye? In a Swiss tournament, that's usually awarded to a person with a losing record, or rather lowest possible score. If he won his first match, I think that bye should go to someone who lost their first one.
I'll, umm... just talk to Scott in a bit about... like random stuff, you know...
Regardless, you can fix the issue you mentioned pretty easily - simply don't give people who get byes 5 backgammon points. Give them a smaller number, or zero.