Arimaa Forum - Print Page


    
      
        Arimaa Forum
        (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi)
      

        Arimaa >> General Discussion >> Level Tournament a.k.a. Human Ladder
        
(Message started by: Fritzlein on Jan 26^th, 2008, 10:38am)

Title: Level Tournament a.k.a. Human Ladder
Post by Fritzlein on Jan 26^th, 2008, 10:38am

Unlike in past years where an upset or two always spiced up the early rounds, this year's World Championship has seen the higher-seeded player win 24 of 24 times over the board. David and Goliath pairings are fun in some respects, and indeed inevitable if we are trying to accurately determine who is best in a short span of time. On the other hand level games are usually better for learning, and give everyone a chance to win now and then.

Recently, in separate conversations with me, Omar and froody each proposed setting up a human challenge ladder, which I think is a great idea. We need more human vs. human games, and a mechanism to encourage them is all to the good.

On the other hand the mechanics of ladders vary a great deal, and their success depends on the mechanic not being so dumb as to drive people away. Typical ladders disproportionately reward playing lots of games and reward cleverly avoiding certain opponents. Often you can leapfrog a strong opponent by challenging a weaker opponent who happens to be ahead of him, and if you win the stronger opponent drops a spot from inactivity. This discourages stronger players from taking the ladder seriously. If you look at the Yahoo game room ladders, for example, many of the best players avoid the ladder entirely and just play for rating points, because the rating system (however lame) is better than an even lamer ladder.

So let me propose what I think would be a good ladder system, one that is fair, generates lots of even games, sorts players in a reasonable way, and is fun for everyone.

First, everyone plays one game per week, as if they were in a regular tournament. Game times would be decided by the regular scheduling tool. Since everyone plays an equal number of ladder games, there is no "activity penalty", unless you can't play for a week, which will cost you a spot or two in the ladder.

Second, the pairings each week are automatic. There is no reward for making favorable challenges and avoiding unfavorable ones. The pairings are entirely determined by ladder position, and always aim for level games: 1 vs. 2, 3 vs. 4, 5 vs. 6, etc. If there are an odd number of players in the ladder, the lowest player in the ladder gets a bye (i.e. automatic win).

After the games, the positions are adjusted as follows: first, for each game where the underdog won, swap their position with the favorite they beat. Second, for each game where the favorite won, swap them with the loser from the next-higher group. Thus every winner ends one position higher, and losers end lower by zero, one, or two places.

Here's an example of how ladder positions would be adjusted based on results:

2 beats 1
3 beats 4
5 beats 6
8 beats 7
10 beats 9
11 beats 12
13 beats 14
15 bye

Old New
--- ---
1 3
2 1
3 2
4 5
5 4
6 6
7 8
8 7
9 11
10 9
11 10
12 13
13 12
14 15
15 14

One potential issue froody pointed out is that you could end up playing the same people over and over. It is true that there is nearly 1/4 chance you will play the same opponent twice in a row. However, the community is so small at the moment that playing repeat opponents is always an issue. If I end up playing chessandgo every other week, that's not a bug, that's a feature. A primary objective is for everyone to get a good game every week. Meanwhile, if the ladder gets up to any size, there will be a fair bit of mixing in the middle.

I know that this isn't a typical ladder, so people may intuitively prefer different systems, but if you have a different ladder idea, please explain the mechanics in detail, keeping in mind how to address the "activity penalty" and the "opponent avoidance reward". If we can get any kind of well-functioning ladder for live human games, I would be delighted.

Title: Re: Level Tournament a.k.a. Human Ladder
Post by mistre on Jan 26^th, 2008, 1:14pm

I really like the idea. If we have enough participation, how about having the winner gain 2 spots and the loser drop up to 3 spots? Would that work? The idea is to mix things up a bit more and widen the potential opponents for each player.

Would this system replace the Player of the Month or just supplement it? Maybe we should split up the prize money for each one.

I would wait to start this until after the World Championship is over to prevent scheduling conflicts.

Lastly, the scheduling tool could be looked at for potential improvements.

Title: Re: Level Tournament a.k.a. Human Ladder
Post by Janzert on Jan 26^th, 2008, 2:21pm

Maybe mix the opponents up a bit more. Perhaps something like this:

If there are an odd number of players randomly select one for a bye.

Select the top unpaired player.

Randomly select one player from the next n unpaired players as his opponent. Where n is probably from 3-8 or possibly a percentage of the total ladder size.

Repeat until all players have been paired.

Janzert

Title: Re: Level Tournament a.k.a. Human Ladder
Post by chessandgo on Jan 26^th, 2008, 3:34pm

Nice idea Karl !

Your system is commonly used for sportive trainings with few players and over a short period of time, with several fields within a gymnasium, like at badminton or volley-ball. Winner of field n goes to field n-1, and loser of field n goes to field n+1. It works extremely well under these conditions.

One of the problems is the "parity" effects : around the middle of the ladder, you'll end up on a field with the same parity as your starting field on each odd round, and different on each even round. That is to say there's half of the players within your strength zone that you'll never play with, because they started on a field with the different parity as yours. Only the top and bottom fields yield a "side effect" that may alter the parity. For instance, in your example, player 8 will never play against players 9 or 10 in the future, unless one of them goes all the way up and wins once on field 1, or all the way down to field "bye".

I like the idea of Janzert, with n around 2, 3 or 4 for instance, because it would prevent the parity effect in addition to giving a greater variety of opponents.

In any event, I hope your idea or some variation of it will be tried, having more human games would hugely benefit to the community.

Title: Re: Level Tournament a.k.a. Human Ladder
Post by Janzert on Jan 26^th, 2008, 4:53pm

One thing I neglected to mention in my first post about the alternate selection method is that it (purposely) introduces a bias in opponent selection based on position in the ladder. Although for small n this bias won't be very large.

The bias is that the top positions are more likely to play a very close opponent than the bottom positions. For example if n is 3; the first position will play one of 2-4. If he plays 4 then 2 will play one of 3, 5, 6. If 2 happens to play 6 then 3 will play one of 5, 7, 8. This should cause slightly more pressure on the top few positions and a little faster rise at first for players just entering the ladder but belonging higher up.

If this bias was not desired it should be possible to eliminate it by simply choosing a player at random and then choosing his opponent from the unpaired players above and below him. But this will cause a larger variance in opponents position on the ladder and an unlimited maximum spread.

Janzert

Title: Re: Level Tournament a.k.a. Human Ladder
Post by Fritzlein on Jan 26^th, 2008, 10:47pm

Mistre, I wasn't envisioning any prize money, just glory for having a high spot. If everyone starts playing in the human ladder, then having a high spot could engender more respect than a high rating does at present. And we all see what lengths people go to at present for nothing other than a high rating. ;-)

Chessandgo, there is no parity problem with my original proposal. The winners always go up one place, but the losers may go down 0, 1, or 2 places, which breaks the parity.

I like the idea of inducing greater mixing with Janzert's idea for pairing, with n=2 or 3. It preserves the equal activity for all players and prevent players from self-selecting opponents. It could still be entirely automated. But how would the players' positions change after each game? For example, suppose 1 loses to 4 and 2 beats 3. Both 2 and 4 have a claim to move up to the top spot. Who gets it? But if you could work that out satisfactorily, I might like the aspect of introducing some randomness into the pairing.

Title: Re: Level Tournament a.k.a. Human Ladder
Post by Janzert on Jan 27^th, 2008, 5:49am

I thought the standard practice for a ladder and the method I had envisioned was that the the winner of a game got the high slot that the two players initially occupied and the loser was placed into the low slot.

Janzert

Title: Re: Level Tournament a.k.a. Human Ladder
Post by chessandgo on Jan 27^th, 2008, 10:40am

My bad, I haden't understood the rules properly, thought the winner always ended up ahead of the next group loser. So for instance if every underdog wins, then the next round pairings are the same ?

on 01/26/08 at 22:47:31, Fritzlein wrote:

Chessandgo, there is no parity problem with my original proposal. The winners always go up one place, but the losers may go down 0, 1, or 2 places, which breaks the parity.

Title: Re: Level Tournament a.k.a. Human Ladder
Post by Fritzlein on Jan 27^th, 2008, 4:27pm

on 01/27/08 at 10:40:34, chessandgo wrote:

So for instance if every underdog wins, then the next round pairings are the same ?

Yes, I guess the pairings would all be the same if all the underdogs win. Maybe this is too boring...

on 01/27/08 at 05:49:23, Janzert wrote:

So if the favorite wins, neither player changes ladder position in your scheme? This isn't necessarily bad; I'm just clarifying. My first thought was that if all the favorites win we have the same no-variety problem as in my original proposal when all the underdogs win. But I guess that even if nobody changes position, the semi-random pairings would keep it mixed up. I'm starting to like it...

I think, however, that n=3 is a maximum, and n=2 deserves consideration. If I'm the number two player, I only get a shot at playing the top player with probability 1/n. It's no comfort to me that players ranked #3 and lower have a chance to jump up to the top with an upset victory, because then I have only a 1/n shot of getting to play whoever got up there! It would be frustrating to only defend challenges with no reward for winning other than standing still. (Unless, of course, I was at the top of the ladder, in which case standing still would be an appropriate reward for winning. :))

One mathematical tidbit: for n=2 every player in the ladder (except first and last) has an even chance of playing up or playing down. For n=3 all the even-numbered ladder spots have a 5/9 chance of playing up, whereas the odd-numbered ladder spots have a 4/9 chance of playing up. (Except the extremes: #1 has 0/9 chance of playing up and #2 has 3/9 chance of playing up.)

It may seem that n=2 doesn't provide enough variety, but actually it gives everyone in the middle of the ladder four equally likely opponents. #4 and #5 will each play (#2, #3, #6, #7) with equal probability. #6 and #7 will each play (#4, #5, #8, #9) with equal probability, etc. That's a reasonable amount of mixing even without changing ladder spots, and as people move up and down there will be further mixing.

Title: Re: Level Tournament a.k.a. Human Ladder
Post by Janzert on Jan 27^th, 2008, 9:53pm

on 01/27/08 at 16:27:27, Fritzlein wrote:

So if the favorite wins, neither player changes ladder position in your scheme?

Correct.

Quote:

I think, however, that n=3 is a maximum, and n=2 deserves consideration.

(Snip interesting thoughts on why n should be very small and probably 2)

While I think it's fairly obvious that the goal of an individual player is to go as high on the ladder as possible and ultimately reach the top, I think the overall of goal of the ladder should be to provide as many 'interesting' or 'fun' games as possible.

In achieving that global goal there are at least two somewhat contradictory indicators for what may lead to an interesting game. The first is that the two players should be close to the same ability. This is the reason for pairing players near each other in the ladder. The second is providing a variety of opponents. This is why the pairings should allow more variability.

So ideally I think n should depend on the spread of ability between different ranks in the ladder, so that n would include all the players that are competitive against each other. But I don't know any good way of determining this and may in fact be generally unsolvable.

Janzert

Title: Re: Level Tournament a.k.a. Human Ladder
Post by 99of9 on Jan 28^th, 2008, 6:55am

I think you need to think in more detail about what happens when people can't/don't play. You say that other ladders penalise inactivity too much, but it sounds like yours will too (if someone doesn't play one week, they automatically drop down). Maybe it'll turn out to be what you want, but make sure you have considered:

*Only about 20 people have committed to the WC, which requires a similar commitment but only for 6 weeks. Some of them have failed to play/complete games.

*In the last few POTM, the number of people who've played >= 4 human games has been around 8-11 each month. Even those 8 aren't exactly the same each month. Amongst them the "ranking" is reasonably clear anyway.

*Are you likely to have the entire arimaa roster on the ladder? 20 people? 8 people?

*What if one player doesn't show?

*What if neither player shows?

*If someone needs to be away from arimaa for an extended time, will they start again at the bottom?

*Will requiring people to play weekly be more of a net encouragement than it is a net burden? (for most likely ladder participants)

*Is there a way to make an asynchronous ladder work? (e.g. Once challenged, your next ladder game must be against the challenger. Thereafter you are free to make a challenge. You can challenge up to X spots higher.)

Title: Re: Level Tournament a.k.a. Human Ladder
Post by camelback on Jan 28^th, 2008, 11:07pm

I was thinking that the schedule for the ladder to be aggressive. 99of9 posted the questions very clearly and in great detail. :)

Thinking more about the asynchronous ladder, we can have games with the possible opponents to be queued and have that to be completed in a specific time, say 3 games in 6 weeks. you may be penalized only if you can't complete the games in specific time.

If you complete sooner you can have more games assigned with whoever is available closer to your rating. Specific details of the scheme is open for discussion.

Flexible schedule will enable more players to participate.

Title: Re: Level Tournament a.k.a. Human Ladder
Post by Fritzlein on Jan 29^th, 2008, 1:50am

It makes sense that if ladder games are less frequent, more people will be able to participate. I had forgotten that one game per week was enough to keep some people out of the World Championship. If we had a ladder, I would want to shoot for at least twenty people participating.

Would one game every two weeks be a reasonable compromise? Of course the longer the time period, the more people can participate, but at some point the gain in participants is canceled by the wait between games. We would want to find the sweet spot that maximizes the interest and number of games played. (And if the sweet spot for a ladder is too small, it would seem prudent to shelve the whole idea until the community is bigger. In the mean time we can happily continue with people inviting each other to games as at present.)

There is a big difference between a system where everyone plays the same number of ladder games, at whatever the common pace is set to be, and playing asynchronously. I am eager to hear more details from either 99of9 or camelback how asynchronous ladder games would work. Some questions:

If I challenge you, how is the game scheduled? Do you have to play within a certain time, or can you say that you are too busy for the next two months? What if the cutoff is two weeks, and you say that you are available to play in the next two weeks, but only in time slots that are three in the morning for me? Does one of us have to forfeit? If so, which one of us? If not, isn't that the same as being able to refuse a challenge?

What if three players challenge me all at the same time? Do I have to accept all the challenges, or a specific one of the challenges, or can I choose which one suits me best? If there is a queue of challenges, do the players later in the queue get to make other challenges while they are waiting, or do they have to earn the right to get in each queue?

My hunch was that if you enforce some kind of rule that when you are challenged you must play within X time period or else forfeit, we might as well just set X to the period of one round where everyone plays one game. And if we have a method of determining whose fault it was the game wasn't played within X time, we might as well use the existing scheduling tool to set the game time. And if we have a system for sorting out which of multiple challenges must be accepted and which can be deferred, we might as well have the pairings be automatic.

I am, however, open to persuasion about why self-selection of opponents and an asynchronous schedule would work better.

One possible idea would be to have a synchronous ladder, with automatically paired and formally scheduled games every two weeks, but also allow any two players who can agree on a time to play an extra ladder game to do so. These extra ladder games would be purely voluntary and up to the players involved.