We can’t possibly compete on ELO against 2-player games.

[Fiora_Laurent]

This is my first time to use the forum of Board Game Arena. Thanks Wreckage for inviting me to give some comments to this issue.
After reading his post, i totally agree with him. I eventually realize that, why some players top the list who get so high ELO are so unfamiliar. I never play with them. I know the reason now. Although the ELO is not so important for me. I still support Wreckage for a fair ELO system about the # of player in the game.

既然是是香港人那就和你說華語。你的ELO比較高(495)，所以如果算法變了，多人遊戲時候的ELO波動幅度變大，那麽有可能你的ELO可以提高幾百。但是你要知道，受益的可不止你一個。所有之前玩多人遊戲，且能暫時維持50%以上勝率的人，他們的ELO多多少少都會提高。
這意味着，如果把以下兩種人剔除掉：

• 只玩1V1的玩家。

• 玩多人遊戲但水平較差，勝率達不到50%的玩家。

再把剩餘的所有高於50%勝率且玩多人遊戲的玩家視為一個國家，ELO視為貨幣，這意味着在這個國家里，發生了通貨膨脹。
顯然，如果只看他們內部的話，ELO的提升毫無意義。
但是對於1V1玩家（譬如我），他們的ELO上漲，有意義嗎？正面还是负面？讓我來解答這個問題。
麻煩您看看我的對戰記録，我作為一個1V1玩家，我的對手可談不上是徹頭徹尾的菜鳥吧？他們的ELO都是200以上的，並且：

• 他們中間的絶大部分，其實是以玩多人遊戲為主的。只不過，與此同時他們也不介意玩1V1。

• 他們之間的很大一部分，紙面上的勝率都高於50%。

所以，答案是：
假設1V1的ELO算法不變，而多人遊戲變了，1V1玩家的ELO，同樣也會加速增長，是有利的。
以我為例，假設我有600 ELO：

• 原先我只能和平均250 ELO的玩家對戰（不是因為我欺負弱小，而是更高ELO的人實在是難以匹配到，否則我為什麽不去和菜鳥對戰？）。每次獲勝平均可獲得2 ELO，每次失敗平均會損失20 ELO。

• 算法變化后，我可以輕輕鬆鬆匹配到平均400 ELO的對手，而他們的實力，其實和之前250 ELO的玩家在同一水平，或者說根本就是同一批人，所以我的真實勝率會和之前一樣，但是系統可不會這樣認為，因為雙方的ELO相比之前接近了，它會判定我的勝率降低，所以每次獲勝平均可獲得多達6 ELO，而每次失敗僅會讓我損失12ELO。

顯然可知，我的ELO增速會比現在快得多。
你快我也快，你高我也高。工資漲一倍但物價貴一倍，意義何在？
當然啦，如果算法變了之后，<Chadmild>這位玩家仍然沉迷於只和零ELO的菜鳥對戰的話，他的ELO會被包括我在內的很多玩家超越。不過人家也不是傻子，如果真的算法變了，他為了保住第一名的位置，也不可能只和菜鳥對戰。

English Version:
You are a high ELO(495) player who only plays <multiple players set>, So if the calculation system changed, the ELO variation rate becomes bigger in <multiple players set>, yes you can increase your ELO for several hundred maybe. But please remember, you are not the only beneficiary. Any player who play <multiple players set> and can keep his win ratio >50% temporarily, their ELO will also increase more or less.
It means, if we ignore these following 2 kinds of players:

• The players who only play 1v1 set.

• The players who play <multiple players set> but have low skill, not able to keep their win ratio >50%.

Then we assume all the other players(win ratio >50% and play multiple players set) as a country, ELO as money, it means an inflation happened in this country.
Obviously, if we only discuss about this part of players in the "country", the increase of ELO is absolutely worthless between themselves.
But for 1v1 players(such as me), is the increase of "their" ELO valuable? positive or negative? Let me answer the question.
Please check my game history, as a 1v1 player, my opponents are not rookies, their ELO are higher than 200. Besides:

• Most of them are <multiple players set> players, they just don’t mind playing 1V1 either.

• The win ratio of many of them are >50%.

So, the answer is:
If the calculation system of 1v1 does not change but the system of <multiple players set> changes, the ELO of 1v1 player, will also increase, it is positive.
For example, I have 600 ELO:

• Formerly, I can only play with opponents who have average 250 ELO(it doesn't mean I am a coward, just because it is almost impossible to encounter a high ELO player, otherwise, why don't I play with rookies?).I earn average 2 ELO per win, and lose 20 ELO per loss.

• After the change, I can encounter opponents whose ELO are average 400 very easy. And their ability, actually in the same level with <250 ELO players> in before, or in other words, they are the same people. So my true win ratio will be the same as before. But the system does not think so, because the ELO of both sides is closer than before, it will judge that my win ratio is lower, then let me earn average 6 ELO per win, and let me lose only 12 ELO per loss.

Obiviously , the increase speed of my ELO will become much faster then before.
You fast I also fast, you high I also high. Salary becomes double but commodity price also becomes double, anything useful?
Certainly, if the calculation system changes and <Chadmild> still only play with rookies(zero ELO)，his ELO will be easily surpassed by many other players including me. But of course he is not foolish, if one day the system changes, in order to maintain his 1st place, it is impossible for him to continue playing with rookies.

[Chadmild]

I just discovered the topic, what an exciting subject !

I may believe in you Wreckage about the fact you just mentionned me for your example but it inevitably entails some bad/wrong comments about me, that's not very pleasant to be targeted without any reason !

In view of all the messages, it seems that i must defend myself about my way of playing 6nimmt huhu, so i'll tell you i have always played 1 vs 1 game, IRL and on BGA (except when i discovered the game and with family/friends). You can say that mode doesn't represent the essence of the game, that's boring etc, no problem, i perfectly understand ! I prefer duals for all the games generaly, and about 6nimmt,my preference goes to tactic more than fun. Can you admitt this kind of strange people exists and please let me play with my favorite mode ?! Saying that i'm playing 2p games only for the ELO, that i'm afraid to face 5p/tactic mode or some other notices like that are clearly wrong/off topic

As said, everybody knows that's different kinds of play, and i've no problem with that : i can say i would surely finish at the last place during a game including Wreckage and i could lose a 5p game against 150 elo players Each person has his speciality.
But i'm not sure making different standings is a good idea, in this case, we should change it for all the games which allow different modes, different number of players...

Now, about my Elo, to be clear, i began to take a look at the standings when i saw i grow up quickly, top 50, top 20 etc, i wanted to reach the 1st place, that's natural, isn't it ?! And so, i tried to face low ELO/bad players, that was calculated, yes, a strategic choice but i wanna say i always took pleasure with each game and without any cheating, of course
To people who think i'm a chicken (don't want to play against good players), i answer i love KFC ( ) and took part (and won) to many tournaments, as #1 and before, with high elo opponents,
To people who say that it would be easy to reach that level like that, be honest, who would accept to play a game to win 0,3 pt vs -20 pts for a loss ?! Almost nobody.
Come on, let's try and we'll see after 100 games if you improved your elo. You need to stay focus all the time not to lose, be very very patient and, as said before, you could usually face fake beginners (mostly for that well known game) ! So that's much more risky than you can think, trust me
As a gambler, i also follow this way about sport betting, prefering the very low odds, that's the same case here with the elo system ! Do bookmakers refuse low odds tickets because it would be easier to win ?! Is this the right method ? I don't think so but here is my favorite. No fair/unfair, no better strategy, just different ones.

So please guys, let me have fun playing the mode i want and against who i want, without silly comments, thanks


Wreckage, i just ask myself why you talk about that now while you play 6nimmt and know that elo system since a very long time No link to the fact you were very close from the #1 and you turn around many times without reaching it ? No provocation here, nothing against you, i hope you could do it one day but that's my guess (i know you'll say it's wrong ^^).

About people agreed with you (lots of newbies on the forum huhu),i really doubt they took a look at the calculation and made simulations before judging objectively...You know as me that lots of them just complain seeing 2p players "polluate" the standings, all that story is only a 2p vs 5p strife, what a pity

I didn't really look at the points system to be honest, i'll try, so no definitive advice about your request but i trust BGA to have established a +/- fair system. I didn't see complains for the other games and don't forget a lot of 5p players reached the 6nimmt #1, so...
I'm a statistician and the way you proved your thesis from the stats you mentionned seems to be wrong..."Wreckage has more % wins and faced higher elo opponents but Chadmild owned much more elo points, so the system is unfair", average persons could think that's the truth regarding this way but that's not so easy, they are more components to take into account !

It could be interesting to invite a guy from BGA to come here to reply.
That's all, sorry for my bad english

[Chadmild]

And win percentage means nothing. If you play 1 game of something with 5 players in it, and win it, congratulations you now have a win percentage above 200%

True, the % doesn't go from 1-100 like we usually understand % to mean, but it still means the player with the higher number is winning a higher percentage against opponents than someone with a lower number.

Be serious Wreckage, this could be true only for people who always play with equal number of players!

That's however simple :
- 1 vs 1 : if I win 99/100 games => 99% wins
- 4p : if you win 50 games and finish bottom of 50 other games => better ratio (100%) but individually, you only have beat 50% of your opponents vs 99!

So the comparison about our respective ratio in your starting reasoning is a little bit dishonest and disqualifies it :-p

Finally, I wanna say I'm not a big fan of Fiora (I clearly told him I didn't agree/like its multiple accounts) but we could admit he seems spending long time about that question, I didn't read any stupid things in its long long long messages ^^
We're still waiting for a guy who can prove mathematically he's wrong, that this system is unfair (not only a feeling looking at a piece of stats about me). Wreckage tried but what about all other guys?

Thanks!

[Fiora_Laurent]

After reading the reply of <Chadmild>, I think if <Chadmild> and I live in the same city, we can be good playmates in real life. There are too many commons between us:

so i'll tell you i have always played 1 vs 1 game, IRL and on BGA

Me too, in real life, it is much easier to find only one valuable opponent than 4 of them. So it is easier to start gaming in <1v1 mode>. And without rookies, it can give everyone a better experience.

I prefer duals for all the games generaly, and about 6nimmt,my preference goes to tactic more than fun.

Me too, I think for almost every kinds of board game,
only <1v1 mode> can forever keep all the participants in a fair environment during one whole game from the beginning to the end.

• Since you decide to start the game, the only target in every single round is to "beat your opponent".

• No matter how strong your opponent is , or how huge numbers of scores your opponent leaded currently.

• If your opponent thinks no hope to win and gives up, it has no influence to the final ranking.

• The only choice is to beat one opponent by your own hands, otherwise you will be beat. Nobody else can help you achieve it.

• You can make a long term plan for several rounds even for a whole game, try to control the situation. Because less player, less uncertainty.

• At least in my opinion, that means <active attack> is usually a better choice than <passive defense>. Even if your plan fails, you can also disrupt the opponent's plan if he has.

• For example in 6nimmt! , <active attack> can make the situation complicated, create a game with more wonderful and less boring.

• You must keep foucs and think more. If you try to muddle through a round, or only think of the benefit of current single round, you will be more closer to lose the game.

Now look at <Multiplayers mode>:

• "Beat your opponents" is not the only choice, sometimes you can wait them fight with each other and you can be the final winner very easily.

• If one of the players has too much behind in scores and give up, his following choice will maybe become unreasonable and seriously affect the final ranking.

• In 6nimmt! this problem is not very serious because it is hard to target a specific player. But in some other games, if one player don't want to win, he can easily determine who will be the winner or at least who can not be the winner.

• Each opponent makes a choice, and these choices affect each other. Yes you can try to predict the situation but sometimes it's too complicated and unpredictable, so maybe you will find that "Do Nothing Prediction" is also a not bad idea.

• It is already very hard to control the situation and let it tends to what you want if all your opponents' level is equal to you. But at least nobody will make a foolish decision and break the balance.

• If one of your opponents is a rookie with some incredible behaviors, much harder. Don't tell me you can also predict some suicidal behaviors.

• For example you set a trap for John and John has no choice have to jump into it, but the rookie jumps before John although he can avoid the trap.

So, as a normal level player in <multiplayer mode> of 6nimmt!, the best strategy for me, is to <passive defense>, just consider which choice has the minimum possibility to be trapped at the current round, almost no need to consider the following rounds.
Let me take a reasonable risk at the current round in order to take advantage in the following rounds?

• In 1v1 mode? I will do this.

• In multiplayer mode? No way.

About 6nimmt! , maybe <multiplayer mode> also has a higher strategy & tactic than <1v1 mode>, but in my currently skill level, I can hardly feel it. I can only feel much "FUN"(Uncertainty), and this "FUN" only makes me uncomfortable.

be honest, who would accept to play a game to win 0,3 pt vs -20 pts for a loss ?! Almost nobody.

I am one of the exceptions hahaha.
Although the win ratio against a rookie is extramely high, so what? Don't ignore the risk. If the risk and the profit are balance, it is still fair.
We accept the a common but tiny profit and a rare but horrible risk at the same time.

you could usually face fake beginners (mostly for that well known game) ! So that's much more risky than you can think, trust me

Agree. After several times I win a game against a fake rookie by a very close score and earn only a bit ELO, or lose the game and lose plenty of ELO, I decide to never play against rookies anymore. Now I only play against players whose ELO is 200+ and reputation is 100% for the instead.It can totally avoid encountering fake rookies.
So, why don't you(Chadmild) also accept my advice?

As a gambler, i also follow this way about sport betting, prefering the very low odds

I am also a gambler, but I only follow this way about E-sport betting. I think in traditional sports, the bookmakers are too professional so they can set a very reasonable odds so almost every options have negative expectations, especially for a <unbalance match>, the payout is much lower than a close match in the same league, I think it is absolutely no chance. So I guess, you have lost some money in gambling in the whole process.

After all, I found——

• You are trying to prove that the current ELO system is fair, no need to be changed.

• I am trying to prove that even if the ELO system changed, we can still occupy the high rankings sooner or later.

Two different ways but the same purpose.

[Bids]

Hi All!
I have been in a similar situation in carcassonne as Chadmild in 6 nimmt (respect for your answer), although I opened all tables always for anyone to join, assuming I could beat anyone in 1-1 with the expansions.

So why did I stop playing multiplayer games in carcassonne, and this also answers for me the problem with ELO: there is always an extreme risk of kingmaking especially when they see that you have an ELO above 700. So if you have a 90% chance of winning against players of ELO 400 (this is more or less what BGA estimated for me), the chance of winning against them both together in a 3 player game is not 81% ! And this is where it goes wrong in my opinion in the calculation of ELO. I would say that my chance of winning the game is around 50% (maybe BGA should calculate these percentages depending on the number of players) , so I should get a reward of 10 ELO for winning the game instead of 4 or 5 ELO and likewise for losing it should be only 10 instead of 20. But then the sum of ELO's wouldn't add up, so that creates another problem of an exponential growth.
Maybe this could be solved by rewarding less points for the second place.

Like in that case: +10 ELO for me as a winner, -3 for the second and -7 for the third. If one of them wins, they would get 15 , second -5 and me as a third -10. My chance of ending last is not 10% * 10 % (=1%) but rather 20% !

So for me the conclusion is: ELO is not wrong, percentages are wrong

[Chadmild]

Let us compare:
Chadmil
91% wins …this keeps him at an average of about 710 ELO
Average opponent = 115 ELO (from Sept 1, last 50 games)
Lowest opponents = 20% of his opponents have only 1 ELO
Highest opponents 429, 348, and 4 players in the 200s, the other 44 are apprentices or average.

Wreckage
100% wins…this keeps him at an average of about 570 ELO
Average opponent = 460 ELO (against the same number of opponents)
Lowest opponents = 20% in the 300s , none lower
Highest opponents = 30% are experts, 70% are above Chadmild’s highest opponent, 94% are above his second highest opponent.

Another message, sorry but i have a delay to catch up

I looked attentively, here are more objective stats about that last 50 games :
- Chadmild : 49 wins /50 => 98% ratio => +15 pt elo (+2,1%)
- Wreckage : 117% wins ratio but you beat 76% of your opponents (155/204) => +29 pts elo (+5,4%)

I could say : that's not fair, i have much better % wins but owned less elo points while i risked to lose more points each game (note that i should have moved back with only 1 additional loss)

Don't mix stats from the start and from the last 50, that's not honest. As you wrote, we could presume it's possible to reach 710 elo with "only" 91% wins against 115 elo average opponents each time but that's false. Impossible.


After research and calculations (not perfectly corrects), BGA system gives about 97% probability win for a 710 elo against a 115 elo opponent (+0,6 pt/-19 pts) and 65% chances for a 570 elo to beat a 460 elo opponent (about +7 pts/-13 pts).

So now, let's just take a look at the mathematical expectation (mean value) :
- Chadmild : (0,6 * 0,97) + (-19 * 0,03) = 0
- Wreckage : (7 * 0,65) + (-13 * 0,35) = 0

OK it means a 5p game is seen as 4 individual 1 vs 1 games, maybe that's not so true as Bids said, that's the key, but saying it can't be possible to compete against 2p is clearly abused.

[Bids]

Maybe some kind of general 'luck correction' can be included which lowers the precalculated chances in multiplayer games.
Like 50% of the game is luck , so you divide 50 % of the points ignoring the current ranking + 50% skill, so there you take into account ELO

Which would give in my previous example of a 3 player game 700 ELO vs 2 players of 400 ELO (more or less):
0,1 (chance of losing against player 2) * 10 (50% of 20 ELO you can win) + 0,1 (chance of losing against player 3) * 10 (50% of 20 ELO you can win) = 2
+
0,5 (random chance of losing because of luck) * 10 (50% of 20 ELO you can win) + 0,5 (random chance of losing because of luck) * 10 (50% of 20 ELO you can win) = 12 points

Player 2 would get +4 for ending 2nd
Player 3 would get -16 for ending 3th

And then you can vary the percentage of luck depending on how much luck there is in a game and the number of players. For 6 nimmt this could go from 10% for 2 players to 70% for 10 players for example

[Silene]

ELO in general is a System to evaluate strength in 2-player games.

Adapting it to more players is kind of artificial - not completely impossible though. But it isn't expected to lead to very good results. Maybe could be done better than it is now. But I think to be accurate, the site could only switch off the computation of any ELO-number for 3+ player games and only change the number after 2-player-games. So if you are playing 3+, you just cannot expect to get very accurate ELO - so there's nothing to complain about here ^^

[Chadmild]

Hi All!
I have been in a similar situation in carcassonne as Chadmild in 6 nimmt (respect for your answer), although I opened all tables always for anyone to join, assuming I could beat anyone in 1-1 with the expansions.

So why did I stop playing multiplayer games in carcassonne, and this also answers for me the problem with ELO: there is always an extreme risk of kingmaking especially when they see that you have an ELO above 700. So if you have a 90% chance of winning against players of ELO 400 (this is more or less what BGA estimated for me), the chance of winning against them both together in a 3 player game is not 81% ! And this is where it goes wrong in my opinion in the calculation of ELO. I would say that my chance of winning the game is around 50% (maybe BGA should calculate these percentages depending on the number of players) , so I should get a reward of 10 ELO for winning the game instead of 4 or 5 ELO and likewise for losing it should be only 10 instead of 20. But then the sum of ELO's wouldn't add up, so that creates another problem of an exponential growth.
Maybe this could be solved by rewarding less points for the second place.

Like in that case: +10 ELO for me as a winner, -3 for the second and -7 for the third. If one of them wins, they would get 15 , second -5 and me as a third -10. My chance of ending last is not 10% * 10 % (=1%) but rather 20% !

So for me the conclusion is: ELO is not wrong, percentages are wrong

I paied attention to your example

700 elo vs 400 elo => 85% probability of a win according to BGA.
So, we're near 72% than 81% about a victory in a 3p game.

Let's calculate the mean value for the 700 elo player with the following simulation. 1st : 3+3 pts, 2nd : +3-17 pts, 3rd : -17-17 pts.
And finally, after reducing the 75% : 1st : +4,5 pts, 2nd : -10,5 pts, 3rd : -25,5 pts.
With supposed probas of 72%/25%/3%, we get : E= 4,5*0,72 - 10,5*0,25 - 25,5*0,03 = 0. Looks perfectly fair in this way.

You think 50/30/20 is more realistic but i'm not so sure you get as much proba to finish 1st as not finish 1st against 2 guys you should beat at 85% individually.
Whatever, you proposal with the associate elo points doesn't work. You award 10 pts for the win, -10 for the loss and i suppose you'd award nothing for the 2nd place => E= 10*0,5 + 0*0,3 - 10*0,2 = 3 ! So, you highly overestimate the win pts, it couldn't be established like this.
The sum of all your potential elo pts won depending on your place can't be 0 here ! Why would you get both balance (+10/-10) while you're the huge favorite of the match ?
You'll always lose much more points than you could win if you play against worst players !

[Bids]

I think the only way to answer this is to check the data and calculate how often the higher ELO wins in multiplayer games

You think 50/30/20 is more realistic but i'm not so sure you get as much proba to finish 1st as not finish 1st against 2 guys you should beat at 85% individually.

I can tell you, if they work together to beat the higher ELO in carcassonne, your chance of winning is almost 0% and from a pure game-theoretical points of view that's probably even a dominant strategy for them

I can rephrase the questions: if you would play that game in 6 nimmt, do you really think you only have 3% chance of ending last? If you play 33 3-player games, are you telling me that you would only end up last in 1 of them?