Why Players Prefer Draw-Size Scoring

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nopunin10did
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Re: Why Players Prefer Draw-Size Scoring

#41 Post by nopunin10did » Thu Feb 07, 2019 4:20 am

Amateur Statistician Moment

For the sake of argument, I took a sample of 179 games of classic that I'd previously collected from PlayDip. Not a huge sample, but enough to run a primary experiment. These games were full-press, no variants, et cetera.

Keep in mind that all rated games on PlayDip currently use Draw-Sized-Scoring.

I used the SC counts at end-of-game to come up with these variables:
  1. Did the game end in a solo?
  2. What was the board-topper's Sum-of-Squares score for the game?
  3. How many powers were eliminated by end of game?
  4. What was a surviving player's DSS score assuming the game ended in DIAS?
For number 2, I ignored the rule in SOS whereby a soloist gets 100% of the points, as I'm using SOS more as a metric for the time being.

I fed these values into R and produced a few different logistic regressions.

In a logistic regression, the dependent variable is assumed to be a binary or boolean value. A game that actually ended in a solo has a Solo value of 1, and a game that actually ended in a draw has a Solo value of 0.

I found the following:
  1. There was no evidence of a correlation between hypothetical DSS score and the game ending in a solo. The coefficient for this was actually negative, but the p-value was absurdly high.
  2. Likewise, there was no evidence of a correlation between powers eliminated and the game ending in a solo. This is effectively the same test as what was done for (A), just with the independent variable scaling linearly.
  3. There was significant evidence of positive correlation between the hypothetical SOS score and the game ending in a solo. I tried two different regressions for this value, and the p-values were 7.23e-11 and 0.00692 for regressions with nonzero or zero intercepts, respectively.
In layman's terms, this means that a Sum-of-Squares score was a very good measure for closeness-to-the-solo, while draw size was not, even in an environment where draw size is the only system used.

This doesn't necessarily mean that Sum-of-Squares is a perfect scoring system, but it does provide evidence for some of what has already been discussed in this thread.

Code: Select all

> head(games,10)
   Solo Elims    GPI SOS.p.GPI Delta.SC  SOSR Delta.SOSR DSS.Score
1     0     4 131.33      1.29        1 0.429      0.063 0.3333333
2     1     4 150.67      2.15       10 0.717      0.575 0.3333333
3     0     2  61.60      1.96        0 0.393      0.000 0.2000000
4     1     3 115.00      3.14       12 0.785      0.678 0.2500000
5     0     2  62.00      1.61        0 0.323      0.000 0.2000000
6     1     2  84.00      4.30       14 0.860      0.800 0.2000000
7     0     1  38.33      2.61        3 0.435      0.222 0.1666667
8     0     4 136.67      1.65        4 0.549      0.254 0.3333333
9     1     2  91.60      4.37       14 0.873      0.795 0.2000000
10    0     4 132.67      1.48        3 0.492      0.188 0.3333333
> games.dss.glm <- glm(Solo ~ DSS.Score, data = games, family = binomial)
> summary(games.dss.glm)

Call:
glm(formula = Solo ~ DSS.Score, family = binomial, data = games)

Deviance Residuals: 
   Min      1Q  Median      3Q     Max  
-1.202  -1.190   1.156   1.165   1.192  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)  0.09439    0.54201   0.174    0.862
DSS.Score   -0.25661    1.85836  -0.138    0.890

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 246.74  on 177  degrees of freedom
Residual deviance: 246.72  on 176  degrees of freedom
AIC: 250.72

Number of Fisher Scoring iterations: 3

> games.sos.glm <- glm(Solo ~ SOSR, data = games, family = binomial)
> summary(games.sos.glm)

Call:
glm(formula = Solo ~ SOSR, family = binomial, data = games)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.3274  -0.2509   0.0368   0.3240   1.9783  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  -16.399      2.517  -6.516 7.23e-11 ***
SOSR          26.108      3.931   6.641 3.11e-11 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 246.74  on 177  degrees of freedom
Residual deviance:  82.99  on 176  degrees of freedom
AIC: 86.99

Number of Fisher Scoring iterations: 6

> games.elim.glm <- glm(Solo ~ Elims, data = games, family = binomial)
> summary(games.elim.glm)

Call:
glm(formula = Solo ~ Elims, family = binomial, data = games)

Deviance Residuals: 
   Min      1Q  Median      3Q     Max  
-1.300  -1.179   1.060   1.176   1.297  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)  -0.4173     0.4613  -0.905    0.366
Elims         0.1400     0.1388   1.009    0.313

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 246.74  on 177  degrees of freedom
Residual deviance: 245.71  on 176  degrees of freedom
AIC: 249.71

Number of Fisher Scoring iterations: 3

> games.sos.zero.glm <- glm(Solo ~ SOSR + 0, data = games, family = binomial)
> summary(games.sos.zero.glm)

Call:
glm(formula = Solo ~ SOSR + 0, family = binomial, data = games)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.4166  -1.3173   0.9383   0.9809   1.0273  

Coefficients:
     Estimate Std. Error z value Pr(>|z|)   
SOSR   0.6507     0.2409   2.701  0.00692 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 246.76  on 178  degrees of freedom
Residual deviance: 239.28  on 177  degrees of freedom
AIC: 241.28

Number of Fisher Scoring iterations: 4
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Claesar
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Re: Why Players Prefer Draw-Size Scoring

#42 Post by Claesar » Thu Feb 07, 2019 12:31 pm

nopunin10did wrote:
Thu Feb 07, 2019 4:20 am
...
I found the following:
  1. There was no evidence of a correlation between hypothetical DSS score and the game ending in a solo. The coefficient for this was actually negative, but the p-value was absurdly high.
  2. Likewise, there was no evidence of a correlation between powers eliminated and the game ending in a solo. This is effectively the same test as what was done for (A), just with the independent variable scaling linearly.
Interesting, thanks!
  • There was significant evidence of positive correlation between the hypothetical SOS score and the game ending in a solo. I tried two different regressions for this value, and the p-values were 7.23e-11 and 0.00692 for regressions with nonzero or zero intercepts, respectively.
In layman's terms, this means that a Sum-of-Squares score was a very good measure for closeness-to-the-solo, while draw size was not, even in an environment where draw size is the only system used.
I don't fully understand what you're saying here. Are you suggesting that a large difference between the biggest power and the second-biggest increases the chance of a solo?
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nopunin10did
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Re: Why Players Prefer Draw-Size Scoring

#43 Post by nopunin10did » Thu Feb 07, 2019 4:20 pm

Claesar wrote:
Thu Feb 07, 2019 12:31 pm
  • There was significant evidence of positive correlation between the hypothetical SOS score and the game ending in a solo. I tried two different regressions for this value, and the p-values were 7.23e-11 and 0.00692 for regressions with nonzero or zero intercepts, respectively.
In layman's terms, this means that a Sum-of-Squares score was a very good measure for closeness-to-the-solo, while draw size was not, even in an environment where draw size is the only system used.
I don't fully understand what you're saying here. Are you suggesting that a large difference between the biggest power and the second-biggest increases the chance of a solo?
Not exactly. I don't want to overstate my claims here, especially since by definition SOS for a board topper in a solo has a higher possible range than for a board-topper in a draw.

A followup experiment would look at snapshots of game states midgame to get the SOS of the board-topping player, then see whether that's a good predictor of an eventual later solo.

But I don't think it will be all that controversial to say that you're much more likely to clinch the solo the higher the lead in SC count you have over other players.

More important is my finding that there was no evidence of correlation between eliminations and achieving the solo.
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Re: Why Players Prefer Draw-Size Scoring

#44 Post by ghug » Thu Feb 07, 2019 5:20 pm

nopunin10did wrote:
Wed Feb 06, 2019 7:20 pm
ghug wrote:
Wed Jan 30, 2019 12:40 am
Carnage also encourages allowing a draw to happen without oneself over throwing a solo.
In Carnage, draws must include all survivors. That's the case for SOS too, though I'm less familiar with specifically how your site implements it. Do you allow people to vote themselves out of a draw in an SOS game?

This is one small point where Carnage & SOS tend to adhere to the printed rules better than typical DSS systems, since the concept of approving a draw that you're not a party to isn't supported in the rules.

(Not that I particularly think that the rulebook should be treated as gospel when it comes to draws, but that's a bigger issue.)
All webDip draws include all survivors. What I was getting at is that it's better to be eliminated and have the game end in a draw without you than it is to allow a solo in Carnage, which is weird.
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Re: Why Players Prefer Draw-Size Scoring

#45 Post by nopunin10did » Thu Feb 07, 2019 5:59 pm

ghug wrote:
Thu Feb 07, 2019 5:20 pm
All webDip draws include all survivors. What I was getting at is that it's better to be eliminated and have the game end in a draw without you than it is to allow a solo in Carnage, which is weird.
Gotcha. It is a little strange, but it's in line with one goal of Carnage's designer: that the solo should be the most important part of the system. Regardless of what you do, you only win the most points if you solo, and you only win the least points if someone else gets the solo.
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Re: Why Players Prefer Draw-Size Scoring

#46 Post by Restitution » Thu Feb 07, 2019 6:24 pm

Is there any reason Carnage scoring wouldn't work in webdip?

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Re: Why Players Prefer Draw-Size Scoring

#47 Post by nopunin10did » Thu Feb 07, 2019 10:52 pm

Restitution wrote:
Thu Feb 07, 2019 6:24 pm
Is there any reason Carnage scoring wouldn't work in webdip?
Funny you should ask:
https://www.playdiplomacy.com/forum/vie ... =6&t=57975

Short answer is Yes, it can work, but with modifications. Standard Carnage doesn’t scale well with variants, and it’s not great when used in this sort of zero-sum environment where players can pick a scoring system game-by-game.

I developed a formula that alters Carnage to scale with any game of 5 players or more and keeps its payouts in a draw comparable with those of DSS. We’re currently using a version of this Fibonacci scoring system for an online forum/Discord tournament.
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Re: Why Players Prefer Draw-Size Scoring

#48 Post by swordsman3003 » Thu Feb 21, 2019 12:02 am

As promised, I posted captainmeme's response essay to my blog. It's absolutely awesome to get a guest post, and I love that the blog now has an argument against my perspective.

Thank you captainmeme!!

https://brotherbored.com/guest-post-dra ... s-scoring/
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Re: Why Players Prefer Draw-Size Scoring

#49 Post by Tibarius » Wed Feb 27, 2019 12:23 pm

I followed the discussion here and i would add a few thoughts:

1. I do not agree to the statement that the game with 7 experienced and skilled players will always end in a draw, because the other players will recognize early enough if that threat arises and unite their actions to prevent it. The point when it is clear that one player or an alliance has the chance to gain 18 centers is sometimes very hard to determine, even for skilled players. And then there is always the option of a stab against an alliance member in the late game which makes it pretty impossible to determine a solo win threat.
2. An aspect completely missing in the artice is the question of repetition. If you like the game you play it usually more than once. Then it becomes a very important game setup criteria if you play anonymously or with your account name visible to other players. Skilled and experienced players will usually have an idea about how you play, if you play with your account name visible to other players. And if you are known as lyer and/or backstabber your challenge will be higher with each game.
3. While the game creator has created a game which was most likely intended to be played to win. This is not the perspective of a player. The motivation of players to participate in a diplomacy game is the only thing that matters for that certain player - and the other players can make no impact on that attitude at all (because it is not part of the game).
4. Diplomacy can be treated as game - and the purpose of a game is to entertain its participants (and observants). You (one) can see something else in diplomacy, due to his repetative nature you can see it as simulation on how to behave in conflicts.

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Re: Why Players Prefer Draw-Size Scoring

#50 Post by Tibarius » Wed Feb 27, 2019 12:34 pm

Another important point:
5. Luck PLAYS a major role in Diplomacy.
(a) The random nation selection can fit or not fit your interests and playing styles.
(b) The behavior and attitudes of the other six players have a major impact on the game and can be in-line with your expectations or go against them. For example: are they reliable ... give orders each move, do not NMR out of a game if they perform poorly, play for a stalemate line if able or throw the game away. Play 15 turns to eliminate powers or just prefer to start a new game and draw this one, etc.
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Re: Why Players Prefer Draw-Size Scoring

#51 Post by MajorMitchell » Wed Feb 27, 2019 1:21 pm

I do like the post from nopunin10ded. That's a cracker. The cracks about PPSC are mostly lame imho.

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Re: Why Players Prefer Draw-Size Scoring

#52 Post by swordsman3003 » Wed Feb 27, 2019 3:19 pm

Tibarius wrote:
Wed Feb 27, 2019 12:34 pm
5. Luck PLAYS a major role in Diplomacy.
I think this statement is just plain wrong. Luck plays a major role in Poker (randomized card drawing), Axis and Allies (rolling cupfuls of dice), Settlers of Catan (again, dice), and even Magic: the Gathering (again, randomized cards).

When people are talking about "luck," they're referring to how the game has randomized information that controls the outcome of the game. Luck play a role in Diplomacy. But that role is trivial compared to these other games I've mentioned.

Nobody says that a game involves a lot of "luck" because there are a lot of differences in "behavior and attitudes" of your opponents. That stuff is beyond your control as a competitor, but something being outside your control does not make it "luck" -- and in fact, in Diplomacy you have a far greater ability to affect your rivals' psychology than almost any game ever made. So even if this is a metric for "luck" (it isn't), luck plays a diminished role in Diplomacy compared to other games.

By your reasoning, "luck plays a major role" in Chess, Go, and Tic-Tac-Toe, because you don't know what kind of opponent you will get. Nobody talks like that.

Virtually every time I have described Diplomacy to someone who I want to encourage to play, I describe the game as "Risk, but with almost zero luck involved." That conjures up in the other person's mind that Diplomacy will not involve dice rolling, coin flipping, or card-drawing to decide who wins or loses. And that is an accurate portrayal of the game.

If I were to say "Luck plays a major role in Diplomacy" then they would think Diplomacy is like Backgammon, Yahtzee, or Monopoly. It isn't.

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Re: Why Players Prefer Draw-Size Scoring

#53 Post by Claesar » Wed Feb 27, 2019 4:18 pm

swordsman3003 wrote:
Wed Feb 27, 2019 3:19 pm
Tibarius wrote:
Wed Feb 27, 2019 12:34 pm
5. Luck PLAYS a major role in Diplomacy.
I think this statement is just plain wrong. Luck plays a major role in Poker (randomized card drawing), Axis and Allies (rolling cupfuls of dice)
...
In my opinion, A&A should be played with "low-luck dice" i.e. you tally up the total combat strength and divide by 6. The integer plus a single die roll determines your hits.

Example:
You attack with 4 Infantry (attack of 1 each), 2 Armor (attack 3) and 1 Fighter (attack 3). Total attack is 13, so you score 2 hits plus another if you roll a 1 on a d6.

Still more luck involved than in Diplomacy, obviously.

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Re: Why Players Prefer Draw-Size Scoring

#54 Post by bunp » Wed Feb 27, 2019 4:24 pm

Relative to other games you can say there is no randomness in the rules of diplomacy. However you are playing with 6 humans. Humans are unpredictable and irrational. I'd especially like to draw attention to the fact that they each have a life outside of this game that will greatly impact how they play.

Is it a busy time at work? Will they be available for back and forth press multiple times each phase or will they only have time to exchange 1-2 brief messages?

Are they tired when they enter their moves for a crucial phase? Misorders or missed tactics can and do happen.

Did they just play a game where they were X power and got stabbed by Y power? If they get X and you get Y in their following game you can bet they will be less likely to trust you.

Did your steadfast and brilliant ally get hit by a bus and sent to the hospital forcing NMRs?

To an extent you can try to assess and react to these factors in your press and strategy, but you can't control them completely. You will be making a lot of decisions using intuition and even if you make the "correct" decision based on the available information it is not guaranteed to have a beneficial result each time.
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Re: Why Players Prefer Draw-Size Scoring

#55 Post by dargorygel » Wed Feb 27, 2019 4:52 pm

Doesn't it depend on your definition of luck?
If by luck you mean, "Things that happen outside of anyone's control whatsoever..." then luck is not a factor in Diplomacy. Even the random choice of nation/position is only a factor if YOU are unskilled or untrained in playing, say, Italy. Every situation can be prepared for, and given enough information, predicted.

If by luck you mean, "Things that happen outside of MY control..." then there might be luck. Things DO happen outside of my control or I would always win. The secret alliance behind my back, the ally who forgets to enter orders (for the first time in her history,) the inexperienced player who neglects a stalemate line on the other side of the board. These things happen in Diplomacy, and these things protect the game from being tic-tac-toe.

My football coach used to say, "We make our own luck." We do that in Diplomacy, too.
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Re: Why Players Prefer Draw-Size Scoring

#56 Post by swordsman3003 » Wed Feb 27, 2019 6:41 pm

To everyone who is disagreeing with me: please read my post again, then read on.

I didn't say there is zero luck in Diplomacy. I said that it defies a common sense use of the English language to say that luck plays "a major role" in Diplomacy. English speakers, especially ones who have played a board game, understand "luck" to refer to the rules and components of the game (such as cards, coins, dice, and other RNG). Diplomacy has almost none of those things, and that's why the game involves little luck.

If "luck" encompasses all possible things that could happen in the universe outside of your control (e.g., players getting injured or killed during matches by happenstance), then every thing under the sun depends on "luck" and it's a misleading statement to point out that Diplomacy in particular is somehow based on "luck." If we were having a conversation about the nature of human ambition, I'd be perfectly happy to agree that everything depends largely on luck. That's not the conversation we're having.

So if we're saying that things like whether someone has access to a computer or whether they're intelligent enough to make good moves counts as "luck," then it's a trivially-true statement to say that Diplomacy depends on luck because you're coming from the position that literally all things human beings experience depend on luck.

If you want to play a college-freshman-philosophy game about how words can mean anything, people can define them at any time, words have subjective meanings, then I encourage you to finish your degree. Communication is possible and words mean things. People do understand what the heck I am conveying when I say "Diplomacy involves almost no luck" and would be confused and misled of I told them "Luck is a major factor in Diplomacy."

To say it's "true" that "luck" is a major factor in Diplomacy by defining "luck" as anything players are capable of doing or thinking, or anything that's possible to occur in real life outside the game itself, makes the statement "true" at the expense of its intelligibility (and meaning).
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Re: Why Players Prefer Draw-Size Scoring

#57 Post by David E. Cohen » Wed Feb 27, 2019 6:52 pm

swordsman3003 wrote:
Wed Feb 27, 2019 3:19 pm
Tibarius wrote:
Wed Feb 27, 2019 12:34 pm
5. Luck PLAYS a major role in Diplomacy.
I think this statement is just plain wrong...
Ding!
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Re: Why Players Prefer Draw-Size Scoring

#58 Post by nopunin10did » Wed Feb 27, 2019 7:01 pm

My own preference is to think of the "luck" in Diplomacy instead as happenstance.

The specific circumstances of a given game can indeed be driven by factors mostly (or completely) outside of the players' control. It might be a coincidence (rather than a deliberate strategy), for instance, that your press sent at the beginning of a turn didn't receive a crucial reply to until the very end of a turn, simply for the fact that each player had very different schedules of availability.

In this way, Diplomacy is very much a game of happenstance, especially when playing it asynchronously online.

But with reference to luck, I prefer to think of it as elements in a game which are designed specifically to be fair and random: rolled dice, shuffled cards, and tokens picked blindly from a bag. This type of Luck is an independent blind arbiter of possibility. In Diplomacy, only the initial player assignments might fall under Luck's jurisdiction.

I imagine this is all in line with what swordsman is saying.
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Re: Why Players Prefer Draw-Size Scoring

#59 Post by mhsmith0 » Wed Feb 27, 2019 7:12 pm

Luck plays a non-trivial part of standard diplomacy; if nothing else, there are plenty of times where a situation will boil down to coin flip type attack/defense positions, where it really is basically just RNG who "wins" an action

Gunboat multiplies that by a LOT since you're 100% at RNG risk in spring 1901 since there's ALWAYS a chance you'll get ganged up on early and well that's how it goes, and even without that, there's much more RNG throughout the game given lack of communication and the variety of potential opponents who could have done what power X has done during the game.

Diplomacy was designed to minimize the inherent aspects of luck in a game state (and to remove anything at all that explicitly/deliberately relied on luck), and while I think they succeeded in shunting it off the side, I definitely don't think they succeeded in eliminating it altogether.
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Re: Why Players Prefer Draw-Size Scoring

#60 Post by nopunin10did » Wed Feb 27, 2019 7:24 pm

MajorMitchell wrote:
Wed Feb 27, 2019 1:21 pm
I do like the post from nopunin10ded. That's a cracker. The cracks about PPSC are mostly lame imho.
I don't know if it's the case for you personally, but most of the folks I've found that enjoy PPSC outside of narrow tournament contexts are using it as a workaround (without necessarily realizing it).

A popular context for PPSC on vDip, for instance, is using it with a defined-max-length game. However, in such a game, the terminal board-topper is counted as a winner equivalent to a solo, and there's zero incentive for that person to accept a draw (which is currently always handled as DSS). It is understandable that other players would find that result frustrating and would want some credit toward their efforts; they were beaten by an incomplete victory.

Because an end-of-game-board-topper incorrectly equals a solo winner according to vDip's adjudication engine, PPSC provides a needed workaround to make term-defined games seem a great deal more fair.

I think said players would be better served by dumping PPSC for either an SOS or Fibonacci/Carnage system, either of which work nicely inside games with defined max lengths. Accordingly, hitting the end-year of the game would result in an unequal draw, not a win.

Then, each player has greater incentive to strive for the real winning conditions and to stop others from achieving them; satisfying the requirement for a solo would still grant the full 100% of points. But if the clock runs out, or if players voluntarily terminate the game early, points are divided along the lines of the scoring system.

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