I wonder why I was white 20 times.
I read that color=automatic makes stronger player white, that could explain some bias towards white as I estimate I played only approx 6 games against stronger players.
But then profile page says that 10 games were against stronger player.

I like separated blitz and slow ratings and I know it’s difficult to manage them, I don’t want them to be removed. But different routines probably use different code to compare strength and it leads to confusion.

When I select last 21 games on profile page, pie chart shows I was weaker 10 times.
But code that assigns color must think I was nearly never weaker.

The profile page determines comparative strength at the end of the game. The automatic colour selection is obviously determined at the start of the game.

Having said that, I have noticed unexpected behaviour with the automatic option. Perhaps it doesn’t use the overall rank. Maybe @anoek can clarify.

My guess is, that when the rank difference is smaller than 1 rank, the color is assigned random (it’s an even game after all). If rank difference if bigger than 1, the stronger player gets white.

I wrote a script to see your rank at the start of each game.

Ranks of your last 21 games

game_id

creator

your rank

your opponents rank

rank difference

you played white

white was stronger

15042915

opponent

1.3k

0.1k

1.16

yes

no

15041513

opponent

0.9k

0.2k

0.72

yes

no

15041317

opponent

0.9k

2.0k

1.03

yes

yes

15037475

you

0.6k

1.6k

0.98

yes

yes

15027037

opponent

0.9k

0.3k

0.63

yes

no

15024411

opponent

1.1k

2.6k

1.50

yes

yes

15022939

opponent

1.1k

2.4k

1.29

yes

yes

15022479

opponent

1.2k

1.4k

0.16

yes

yes

15021982

opponent

1.2k

2.0k

0.80

yes

yes

15012941

opponent

1.4k

2.1k

0.66

yes

yes

15009488

opponent

1.2k

1.6k

0.39

yes

yes

15008305

opponent

1.2k

1.0k

0.23

yes

no

15008266

opponent

1.2k

1.0k

0.23

yes

no

14999191

you

1.3k

3.3k

1.93

yes

yes

14993822

opponent

1.1k

1.5k

0.35

yes

yes

14952164

opponent

0.9k

0.4k

0.54

no

yes

14818584

opponent

1.1k

2.8k

1.68

yes

yes

14798855

you

0.8k

3.1k

2.35

yes

yes

14796564

you

1.0k

3.3k

2.35

yes

yes

14795897

opponent

1.0k

0.5k

0.42

yes

no

14795682

you

1.0k

2.7k

1.74

yes

yes

14760603

opponent

1.3k

1.1k

0.20

no

yes

14756890

you

1.2k

2.2k

0.92

yes

yes

14756795

you

1.1k

1.7d

1.76

no

yes

14756759

you

1.1k

1.7d

1.76

no

yes

14756554

you

1.1k

1.7d

1.76

no

yes

14755297

opponent

1.4k

12.3k

10.84

yes

yes

14754263

you

1.4k

1.9k

0.44

no

no

14718631

opponent

1.3k

3.3k

2.01

yes

yes

14682967

you

1.0k

0.9k

0.09

no

yes

In 6 of this 21 games was black stronger.
In games with a rank difference <1 the ratio white:black stronger is 7:5 while if rank difference is >1 the ratio is 8:1.

Note: There are some rare cases in which white was the weaker player even though the rank difference was > 1, but that are only rare cases while for rank difference < 1 white in about 50% the weaker player. (It holds for at last 200 of your games)

Thanks for the analysis.
So if all those 21 games had color=automatic, then probability of all 12 games with rank difference <1 giving me white is 1:4096. But some opponents probably forced their color to be black.

This is a common misconception of statistics. It’s the right answer to the wrong question.

If you ask in advance “what is the chance that I’m white in my next 12 games?” then the answer is indeed 1 in 4096.

But you have already played and wonder afterwards “how big is the chance that I’ve got white 12 consecutively?”.

If you got black 12 times you would have asked “why am I always black?” so the probability to get an improbable looking color assignment would be at least 2 in 4096.

You have to get a improbable color assignment in the first place (i.e., you wouldn’t be asking “why I wasn’t white 12 times in a row?” if you haven’t got white for that 12 games).
You could have gotten this 100 games earlier (and would have asked then why I got 12 times white/black) or not before you played another 100 games. So you have to find the answer to the question “how probable is it to get 12 times the same color in a row within my whole history and future of playing go on OGS?”

The probability for that is much lower than 1 in 4096. It would be 1 in 4096 if you would know that you play only 12 games at all on OGS. Each game you play in advance (even future ones) will lower the probability. At some point in time you would have to ask “why I never get the same color 12 times in a row?”

One could even argue that you are not special at all and you have to calculate the probability for “how probable is it for any player to get the same color 12 times in a row?”. And this isn’t improbable at all. Every 4096th player should get 12 times the same color in their first 12 games. Each of them could have asked “why have I got white for all my gamees?”

long story short, I would argue against your assumption, that one of your opponents forced their color to be black. The probabilities is very high that they got black by chance and only that you are looking at especially that games let it seem improbable.

In my middle school homework, I tested multiple hypotheses and then documented only one of them. I realized there is something fishy, it was generic way to get significant result, so I started understanding this class of errors.

When I started wondering why I got nearly 20 whites in a row, it was nearly 1:10^6 which is strange. When I learned that about half of my whites are easily explained by color=automatic, problem dropped to about 1:10^3 which is no longer that strange. But inconsistency in profile page (game list vs pie chart) prevented me from fully understanding what happens here, it felt like something is wrong and I can’t tell what. Thanks for your effort.

It’s even trickier still, because it would be 2:4096 if we were talking about independent, random (as in non-systematically biased) events. These events are neither independent nor random.

Edit: I wrote a quick, slow and extremely dirty R simulation because I’m too lazy to do the maths. Note that 2:4096 is likely an upper bound, because it’s more likely for someone to get the same color 20 times in a row if they’ve had 20 in a row already (and I didn’t bother to sieve for how many individuals would experience this).

2:4096 ~ 0.0005

N players - N games - N sims - Average ‘winners’ (20 colors in a row somewhere) - Observed fraction
1000 - 200 - 10 - 0.6 - 0.0006
10000 - 200 - 10 - 5.4 - 0.0005
1000 - 200 - 100 - 0.34 - 0.0003
10000 - 200 - 100 - 3.25 - 0.0003

simcols=function(nplayers,ngames,nsims){
players=1:nplayers
colorz=matrix(rep(0,nplayers*ngames),nrow=nplayers,b=T)
bingo=0
winners=0
for (k in 1:nsims){
colorz=matrix(rep(0,nplayers*ngames),nrow=nplayers,b=T)
bingo=0
for (i in 1:ngames){
white=sample(players,nplayers/2)
black=players[-white]
colorz[white,i]=rep(1,nplayers/2)
if (i>19) {
for (j in 1:nplayers){
if (sum(colorz[j,i:(i-19)])==20) {bingo=bingo+1}else{if (sum(colorz[j,i:(i-19)])==0) {bingo=bingo+1}}
}
}
}
winners=winners+bingo
}
return(winners/nsims)
}
simcols(1000,200,10)