Reflections on the croco-puzzle ladder?

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kiwijam
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Re: Reflections on the croco-puzzle ladder?

Post by kiwijam » Tue 12 Jul, 2011 4:09 am

I've been thinking on this also. There is definitely elements of equilibrium and parity repetitive matches that have both been mentioned above. Most players just bobble up and down around a few matches. May I throw another option into the ring? My opinion is that a little more movement is desirable within the ladder, although the basic structure is similar.

8 players, in 4 matches of 2, as we currently have.

(Championship) Match #1 - Current Champion (winner #1) vs Challenger (winner #2)
(Challenger) Match #2 - Knockout match winners (winner #3) vs (winner #4)
(Second chance) Match #3 - (loser #1) vs (loser #2)
(New-comers) Match #4 - top 2 from waiting list

Basically every week we have four players (those in matches #3 and #4) that will play two knockout rounds. Whoever gets two wins becomes the Challenger. These four players consist of the two losers from the previous week's 'upper' matches and two from the waiting list.

Key points:
The road back to the championship match is now one duel longer for the loser, so there'll be more of a rotation around the top.
And consequently the lower players can rise faster if they have a good spell.
Each week two players are knocked off, and two rejoin the ladder. This reduces time spent in the waiting list.
And parity is gone - you could play almost anyone each week!

dickoon
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Re: Reflections on the croco-puzzle ladder?

Post by dickoon » Sun 17 Jul, 2011 9:49 pm

OK gang, please find attached a second head-to-head-to-head of croco-puzzle ladder match generation systems using the data for weeks 4 to 13. As before we're comparing the current system to the left and one implementation of the three-way system on the right. In the middle, this time, is one implementation of James' proposed system above. There are several other ways to implement the system, particularly with generating the original week 4 matches and with dealing with plucking two players from atop the waiting list when the waiting list only has one person on it.

I have some thoughts of my own but I'd be curious to hear yours first, from both players and non-players alike.
Attachments
croco scoring systems v2.txt
croco-puzzle ladder match generation system, version 2
(15.35 KiB) Downloaded 497 times

ColinMacLeod
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Re: Reflections on the croco-puzzle ladder?

Post by ColinMacLeod » Mon 18 Jul, 2011 8:53 pm

Re kiwijam's suggestion:

I like the "out of the box" thinking to try to increase entropy in the system, but I find the Second Chance match has lopsided results.

SC results by week:
4-6
4-6
7-1
8-2
1-8
9-1
4-2
6-4
9-1
8-2
9-1

7 of the 11 results have a 6+ margin, 2 of the close results occurred before the ladder "stabilized".

The main negative: unbalanced matchups, primarily in the Challenger and Second Chance matches. The Challenger match has a Second Chance victor (probably a former Champion/Contender) against a Relegation victor. The Second Chance match has a former Champion/Contender against the Challenger loser (probably a Relagation minnow). A player who wins a Relegation match gets rewarded with two painful losses.

Proposed statistic to measure fun: margin of victory, measured personally, in aggregate, and by match (championship, challenger, second chance, etc.). Anything decided aet should be a draw. I'm not sure how to measure/normalize for the 3-way matches; perhaps divide by 4 and take the 3 differences?

Another point: I don't think this format will scale to more people. I want to echo nickdeller's preference of keeping the wait list as short as possible (the difference between 1 and 5). I think it's better to have more matches to the top once the competitor pool is deep enough than have a 2-3 week wait on the Wait List. I have an idea of how kiwijam's format will scale, but I don't have the time or words for it right now.

Trayton
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dickoon
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Re: Reflections on the croco-puzzle ladder?

Post by dickoon » Wed 20 Jul, 2011 9:52 pm

To perform a counterpart analysis to the previous ones, we get the following results:

KIWIJAM SCHEME:

drsteve: detuned x3, rodders x2, afcwarren x2, dickoon x2, oenomel x1
detuned: drsteve x3, rodders x1, afcwarren x1, PuzzleScot x1, ronaldx x3, puzzlemad x1
rodders: drsteve x2, detuned x1, PuzzleScot x2, ronaldx x1, puzzlemad x2, dickoon x1, kiwijam x1
afcwarren: drsteve x2, detuned x1, PuzzleScot x1, ronaldx x1, dickoon x2
PuzzleScot: detuned x1, rodders x2, afcwarren x1, ronaldx x1, puzzlemad x2, kiwijam x1
ronaldx: detuned x3, rodders x1, afcwarren x1, PuzzleScot x1, puzzlemad x1, dickoon x2, oenomel x1
puzzlemad: detuned x1, rodders x2, PuzzleScot x2, ronaldx x1, dickoon x1, oenomel x2
dickoon: drsteve x2, rodders x1, afcwarren x2, ronaldx x2, puzzlemad x1, oenomel x1
oenomel: drsteve x1, ronaldx x1, puzzlemad x2, dickoon x1
kiwijam: rodders x1, PuzzleScot x1

This has generated 27 out of a theoretical 45 and practically possible 34 pairings (remembering oenomel played at most five matches and kiwijam at most two), rather higher than the 19 and 20 we got from the two other schemes. In this regard, this is clearly the most successful scheme. However, I don't believe it should be the only metric, and I rather like Trayton's "margin of victory" scheme. Then again, perhaps people would prefer to face a wide variety of opponents and not mind lop-sided matches so much rather than facing a relatively small variety of opponents with tight matches; I wouldn't have thought so, but this is a personal preference and one that anecdotally I do not think is necessarily shared. I don't know what the degree of preference is between tight matches and fresh match-ups; if it's sufficiently far towards the latter, perhaps we would be better off going with some sort of seasonal round-robin competition.

There are other ways to implement schemes like kiwijam's. For instance, perhaps the losers of the championship and challenger matches might not face each other, but they might face the newcomers instead. The big issue is how we know which newcomer faces which of the previous week's defeated competitors, because one match would be likely to be rather easier than the other. An obvious solution would be to draw randomly between the two newcomers and the two defeated competitors. This could work, but the additional randomness would be another factor in the league. It's also true that one newcomer would face an extremely difficult opening match and the scheme would tend to entrench the established competitors in the league, though this is always going to be true to some extent with any scheme.

I suppose a key question is how tied to the nature of a ladder competition we necessarily are; kiwijam's scheme did tend to move some distance away from the concept of a ladder, and more towards a series of elimination competitions (semi-finals -> challenger final -> challenge match). Not necessarily a bad thing, but somewhat different from a ladder. However, if some non-ladder competition would suit the players better, then perhaps we should be having a non-ladder competition instead.

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Re: Reflections on the croco-puzzle ladder?

Post by PuzzleScot » Fri 19 Aug, 2011 12:35 am

With the absence of major changes, how about a minor one?
Can the ladder be extended to include everyone who is registered? ie, with the 10 people we have, why not have 5 matches? Loser of bottom game stays down, in the same way as winner of top game stays up.

The way things are, if you wait 3 weeks for a match, and lose it, you have to wait another 3 weeks to participate again (like just happened to me).

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Re: Reflections on the croco-puzzle ladder?

Post by puzzlemad » Fri 19 Aug, 2011 8:26 pm

PuzzleScot wrote:With the absence of major changes, how about a minor one?
Can the ladder be extended to include everyone who is registered? ie, with the 10 people we have, why not have 5 matches? Loser of bottom game stays down, in the same way as winner of top game stays up.
I wondered about that too! Simple to implement.

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Re: Reflections on the croco-puzzle ladder?

Post by dickoon » Sat 20 Aug, 2011 8:48 pm

I'm really gratified by that, Alan and Liane; thank you!

In general, I regard the presence of a meaningful waiting list as a feature, not a bug, speaking as someone who has spent a large but fair share of time on there. (I like the general principle of "Leave 'em wanting more!") With only ten players on the ladder, one of whom has expressed an intention to drop out when he floats down the ladder and through the bottom by himself (trouble is, he can't stop himself from winning matches!) then I don't think extension is appropriate. With eleven players, none of whom are intending to drop out, I think I'd seriously consider stretching the ladder from eight to ten; at the moment, I don't really see the need. That said, if you both agreed, I could run a one-off match between the two of you to see who advances from the waiting list to the ladder next week...

The croco-puzzle ladder format has loads of potential, though I don't think I'm capable of exploiting it at the moment. There's definitely scope for non-UK ladders and there could be a really, really interesting team competition on a ladder (or tournament, etc.) basis. However, I don't want to start anything and turn out to make a lousy job of it; if anyone wants to jump ahead and start their own competition then please don't feel the need to wait for my blessing to do so. Feel free to use my rules if you like, or to use different ones that might suit your competition better. Your competition, your rules.

In part, I don't really feel I've reached a conclusion about how best to run the competition; I think I'd prefer to be a bit surer in my own mind before branching off afresh. Specifically, I do recognise the issues with repetitive matches, but I'm not convinced that any of the two-person alternatives that we have yet considered are actively better. (In truth, I think the real way to cut down on repetition is to have more people invovled, though my preference for competitive matches over varied ones may not be to everybody's taste.) I was surprised by how interesting the results of the three-person competition simulation were; perhaps that might work better in practice, though there are several unanswered questions about it as a possibility. Part of me doesn't want to go on and on about it all the time; I can't help feeling that the ladder takes up too much of the forum as it is...

rodders
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Re: Reflections on the croco-puzzle ladder?

Post by rodders » Wed 24 Aug, 2011 9:40 am

Going back to the question of tie-breaks which has been discussed previously, last week reminded me that more weight is given to harder puzzles when it comes to a tie-break, as the difference in times is likely to be larger, the harder the puzzle. I'm in two minds as to whether this is fair or not, as part of me feels that the player who completes the harder puzzles the quicker is the desrving winner of the tie-break. However, when someone doesn't complete a puzzle, they currently automatically become the loser of a tie-break (assuming their opponent completes all puzzles that week). This also applies if for any reason someone hasn't been able to attempt a puzzle without previously requesting a bye.

Again, some might regard this as fair as it is. Certainly last week, when I didn't complete the slalom, I am perfectly happy to accept a loss to someone who did. I wonder though whether there is any merit in a solution which uses finishing positions rather than time as the tie-break decider. My proposal would be to rank all ladder players from 1 to x for each puzzle (with 1 being the best time and x being the worst), and use the sum of these finishing positions over the week as the tie-break decider. Anyone who didn't complete a puzzle would automatically be given x+1 meaning they are punished for not completing the puzzle, but they can also claw their way back with some exceptional performances. We would need to consider whether a bye day(s) would be given an average finishing position or excluded for that day(s).

Interested to hear whether anyone thinks this might work and/or whether it might have changed any previous tie-breaks. Apologies if anything similar has been discussed previously - I sometimes lose track of these threads!

ColinMacLeod
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Re: Reflections on the croco-puzzle ladder?

Post by ColinMacLeod » Wed 07 Sep, 2011 6:46 am

rodders wrote:My proposal would be to rank all ladder players from 1 to x for each puzzle (with 1 being the best time and x being the worst), and use the sum of these finishing positions over the week as the tie-break decider. Anyone who didn't complete a puzzle would automatically be given x+1.
My instinct is that external influences on the match is a negative, especially with a small population (<5% of croco's already small population). Any kind of strict ranking system doesn't allow for degrees of separation. For example, Player A has a time of 5:00 and Player B has a time of 8:00. In one case, the rest of the ladder has a time grouped around 5:15. In the second case, the ladder has a time around 8:15. In both cases, player A gets a rank of 1. In the former, player B gets a rank of N which is "fair" given the relative scores. In the latter he gets a rank of 2 which doesn't describe the 3 minute disparity in times.

I think it's been mentioned before, but aggregate/average puzzle rating for the week may be the best tiebreaker, assuming a population of 300+ is a sufficient sampling size. If only that was easily accessible.

Trayton

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Re: Reflections on the croco-puzzle ladder?

Post by dickoon » Wed 07 Sep, 2011 7:11 am

On the "overall time" tie-breaker front, one thing I've been considering is changing from an arithmetic sum of times to a geometric mean of times - i.e., multiply them all together and take the tenth (or however many) root. Effectively, it's no longer the absolute difference between times that is relevant, but the relative difference; if you take twice as long as your opponent on one puzzle but half as long on another puzzle then the two cancel each other out. I have a suspicion that this will change the emphasis from being heavily on the long puzzles, where an absolute difference of many minutes is relatively easy, to being heavily on the short puzzles, where a relative difference of a factor of two is relatively easy. (If need be, I'll produce some worked examples to illustrate this.) Nevertheless, at the moment I would say that I am 52:48 in favour (in theory, though not in practice) to a move to taking a geometric mean and would welcome people's comments on the proposal.

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Re: Reflections on the croco-puzzle ladder?

Post by PuzzleScot » Wed 07 Sep, 2011 8:23 am

dickoon wrote:multiply them all together and take the tenth (or however many) root.
That's an improvement for sure!

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Re: Reflections on the croco-puzzle ladder?

Post by sknight » Wed 07 Sep, 2011 3:17 pm

I like the idea of using the Geometric mean. It definitely seems to me that if on one puzzle, Player A takes 2 min while Player B takes 5, and then on a second puzzle player A takes 26 min and player B takes 22, it seems off that (using arithmetic sums/means) Player B wins on total time. The geometric mean would correctly recognize that the performance gap is greater on the first puzzle.

There's a roughly comparable system in place already on Croco-Puzzle for counting Fehlversuch penalties. While the list displays them as 5 minute penalties (per FV), they are later adjusted based on the length of the puzzle, so that they will count less than 5 minutes each on a puzzle that only takes a minute to solve for most people (and more than 5 minutes on the longer puzzles).

The geometric mean option would tend to count unsolved short puzzles as being worse than unsolved long puzzles, but that's also true of the arithmetic mean.

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furudo.erika
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Re: Reflections on the croco-puzzle ladder?

Post by furudo.erika » Sun 11 Sep, 2011 3:14 pm

Another vote for geometric mean here. It certainly feels fairer to me,

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Re: Reflections on the croco-puzzle ladder?

Post by drsteve » Thu 22 Sep, 2011 5:55 am

Given one of today's puzzles, the Gebeitsummen, I wonder is the penalty for not taking part is too harsh

Given that some of the very best puzzlers in the world are taking 30 minutes plus on it, I simply do not have the time in the day to start a puzzle that I know will take that length of time even if it goes well and may well take significantly longer. I'm not dodging the puzzle, but I have a job and other responsibilities.

Obviously if someone of the pair completes it, they should win, but if it were to come to a tie-break, the problem is that I'd be basically losing due to not having enough time in the day.

It's not going to affect this week (sorry, Nick) but I'd hate for this to be the deciding factor.

You'll note that I'm not offering any solutions here...

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Re: Reflections on the croco-puzzle ladder?

Post by berni » Thu 22 Sep, 2011 9:52 am

A note: In the german forum people complained about the league-system which decided to types of puzzle of the next month. Therefore from october on, the puzzletypes will be chosen randomingly among all available types and the Ü2 is supposed to be a little bit harder than it's up to now (I guess it will most of the time not be as hard as todays Ü2, but still...). Maybe you might to include this knowledge in your discussion about how to score Fehlversuche.

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Re: Reflections on the croco-puzzle ladder?

Post by nickdeller » Thu 22 Sep, 2011 10:07 am

I'm rather with Steve on this one, and this even after spending two hours of late-night hell on the Gebietsummen. :lol: Would it be too far off the mark to cap the differential between a pair of solvers on a single puzzle?

Pulling some totally arbitrary numbers out of the air, a non-solve - or a prodigiously slow solve - could be scored at (opponent's time plus ten minutes) for arithmetic mean or (opponent's time multiplied by four) for geometric mean. The penalty then would be painful but entirely retrievable over the other 11 puzzles in a week where total time becomes an issue.

Thoughts?

[Edited 17:43 Thursday to add] It would probably make sense to set the cap for "did not solve" slightly higher than that for "solved at a snail's pace" so there's always incentive to keep trying - maybe times 4.5 and times 4? It would of course be a challenging formula to program into Excel... that's a GOOD thing, right? ;)
Last edited by nickdeller on Thu 22 Sep, 2011 4:47 pm, edited 1 time in total.

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furudo.erika
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Re: Reflections on the croco-puzzle ladder?

Post by furudo.erika » Thu 22 Sep, 2011 11:42 am

I also am not going to be able to do puzzles like todays Gebeitsummen without being fired or locked in overnight at work.

I like Nick's idea of capping the difference for a single puzzle. Maybe you could use geometric mean and have the multiplier scale down based on median solver time. If you're concerned people will try to dodge certain types with the penalty reduced you could adjust for user rating against the puzzle type.

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Re: Reflections on the croco-puzzle ladder?

Post by dickoon » Thu 22 Sep, 2011 7:18 pm

I've skipped it too, for what it's worth. Croco-puzzle is something we do for fun; if it's not fun, or isn't fun on any particular day, stop doing it. Some people on the ladder have the happy knack of winning matches despite missing days and that's absolutely, completely OK.

However, when the league tests the ability to solve croco-puzzle U-ratsel puzzles, part of the skillset required is dedication. I'm happy if the league does reward someone with a win through sheer dedication from time to time. I'm also happy that it doesn't seem to happen too often. It's also true that the total / mean tie-breaker does not come into play too often - off the top of my head, perhaps five or ten times in close to a hundred matches? - so I'm reasonably relaxed about it.

Part of the joy of croco-puzzle is the wide variety of difficulties of puzzles offered. There's a part of me that suspects that I would happen to enjoy it more if the shortest puzzles were less short and if the longest puzzles were less long, but extremely short and extremely long puzzles are so rare (could we collate stats for median completion time, perhaps?) that the balance is probably about right already as it is. I liked the League system for determining puzzle representation in coming months, but I'm sure that I'll also like whatever comes to replace it as well.

On the basis of what I've learnt, I'm inclined towards making a tied match resolve in this order:
a) result of extra time
b) number of puzzles solved regardless of time taken (my gut feeling is that I'd be happy to privilege those with the time and dedication to spend on the longest puzzles here at a point where it only makes a difference in 2% of matches, though I'd think again if it turned out to make a difference in 8% of matches)
c) geometric mean of times, capping the difference per puzzle, though more to impact the effect of blow-outs in the shortest puzzles than to impact the effect of blow-outs in the longest puzzles - and I'm inclined to keep the cap at perhaps 6-10 rather than 4. I like the theory behind having different caps for non-solves and slow solves, but suspect it's confusing and unnecessary if there's a separate "how many puzzles were solved at all?" tie-breaker.

One worrying item in the back of my head is that I'm still not convinced that we shouldn't move to three-way matches - the results were surprisingly interesting! - and I'm not sure how to create analogues to the structures for two-way matches for three-way ones. 1 point for beating two opponents, 1/2 point for beating one opponent and losing to one opponent and 0 points for losing to both opponents (with quarter-points as necessary arising from tied times) is a good start, but I'm not quite sure where to go after there.

Thoughts are most welcome, as ever!

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Re: Reflections on the croco-puzzle ladder?

Post by kiwijam » Thu 22 Sep, 2011 11:35 pm

I've been thinking about the geometric mean tie-breaker, not a big fan I admit. It's more complicated, much harder for a player to work out if they're ahead or not, just shifts the bias from one type (slow) to another (fast), and will be the same as the current system 95% of the time.
But my main worry is for Fehlversuchs (and DNFs?). Previously if contestants did a Fehlversuch each in different puzzles they would cancel out. Now a Fehlversuch in a fast puzzle (which is when they are most likely) obliterates your tie-breaker. e.g. Yesterday Tom took 47 seconds with a Fehlversuch for the Tapa, becoming 347 seconds. This is 10 times slower than my time, which I think would be mighty unfair and completely unrecoverable.

Having said that, I don't like the current tie-break system either (yes I'm being a real whiner today sorry!). There have been several times when I considered quitting this ladder, and the only reason is that the tie-break forces me to do every puzzle. Sometimes I'm tired, or drunk, or don't have a spare hour, or am hopeless at the puzzle, and I'm happy to just concede it to my opponent. But avoiding it means I would also lose any eventual tie-break (in the championship match anyway). So at times I have to choose between what's best for my crocopuzzle rating, and what's most likely to help win my ladder match. I hate having to make that choice.

So can we have a tie-break system that matches crocopuzzle's assessment of good versus bad? They already give + and - scores to say how well you did, which is what we're (I'm) aiming for anyway... which gives:

Tie-break rule: In the event of a tie, the winner will be whoever gained the most rating points during the match period.

It's simple. There's no bias toward fast or slow. And it encourages actions that we want to do anyway - improve our rating. Skipping a puzzle is not a huge deal any more (although you still concede it if your opponent did it obviously). So I think it would be more 'fun' again.
Sure this gives a small advantage for lower ranked players, but I think that would actually be good for the competition (it's only a tie-break rule after all, why not give the underdog a hand?).

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Re: Reflections on the croco-puzzle ladder?

Post by PuzzleScot » Thu 22 Sep, 2011 11:43 pm

Like it all.

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Re: Reflections on the croco-puzzle ladder?

Post by dickoon » Fri 23 Sep, 2011 5:38 pm

James, thank you! That's a killer point about the geometric mean. One route would be to resolve how we deal with Fehlversuche; a possibility would be to use a penalty other than the default five-minute penalty applied on the high-score table, but this would add to my processing time. With eight players, it's a small deal; with eighty players, rather bigger.

I really like your proposal for a tie-break regarding changes in rating; it's simple and elegant. The fact that you can go back and look at old ratings pages means that it's also practicable. The "skipping puzzles" issue does not bother me in the least, as there's such a disincentive to avoid skipping puzzles already.

The "small advantage for lower-ranked players" is a bit bigger of an issue, though; if a 2000 plays a 1600, and the 2000 performs at 1900 to drop to 1995 and the 1600 performs at 1800 to rise to 1610, but the match ends up 5-5 (and isn't resolved on the Extra Time day), it does seem strange to reward the 1600-rated player ahead of the better-performing 2000-rated player. Other people have suggested manually calculating perfromance levels for the week in the past, which I have previously considered difficult.

If player A has rating a' at the start of a week and a at the end of a week, and player B has rating b' at the start of the week and b at the end of the week, is it possible to deduce the performance levels over the week using a' and a, and using b' and b? My assumption is not quite, as performance at the end of the week is marginally more important than performance at the start of the week, but it would be possible to deduce a reasonable approximation: a' + (a-a')*(60/#days) and b' + (b-b')*(60/#days) respectively.

One disadvantage of this approach is that it takes account of your performance on bye days in the tie-breaker, as well as your performance on non-bye days. That would feel a bit weird, but would be in keeping with a goal of rewarding performance at solving croco-puzzle puzzles, even if not quite rewarding performance at solving croco-puzzle puzzles on the days in the match. That doesn't feel like a stopper flaw to me.

Needs more thought, but at this point I'm tempted to track lots of different things and try to see which ones give us results in practice that seem sensible.

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Re: Reflections on the croco-puzzle ladder?

Post by ronald » Sat 19 Nov, 2011 3:50 pm

I have spent most of the ladder on one half of the draw - and in finally managing to win the champs I switched to the other half of the draw. I observe this half to be much, much "easier" - I am currently way more likely to get to the final as I can bypass 2 out of 3 of drsteve, kiwijam and detuned and stay (on average) in a much higher position. (Although oenomel can still beat me, it's less likely)

So, over a short to medium term, I am facing the same regular opponents. I think this has been observed here previously.

I don't think this is a bad thing, as a nice rivalry can build up... as long as people are mostly able to move between the halves of the draw every now and then. But, it's likely that making the ladder even one step bigger enforces this "I always face the same opponent" problem, as people get more stuck in the middle of the ladder on one half. (people can only change halves by reaching the very top or bottom of the ladder)

I don't have any suggestion on whether anything should be done about this, it's just an observation.

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Re: Reflections on the croco-puzzle ladder?

Post by kiwijam » Sun 20 Nov, 2011 9:48 pm

Quick idea based on Ronald's post: instead of having a perpetual ladder, should we have ladders that last 3 months or 6 months? After that time we reset/shuffle and start again.

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