Color Stacking Fairness Project

#Updated 29 Jan 2019

Raids 101-300 are here
Raids 301-500 are here

TL;DR (with updated numbers):

Verifying whether raid tiles are random when color stacking.

Current games seen: 500
Current tiles seen: 17,500

Probability of drawing tiles of stacked-into color: 20.02%

95% Confidence interval: 19.4% to 20.6%

Conclusion: Looking completely fair

Detail:

The question of whether SGG adjusts tile probabilities against color stackers in raids is a very common debate on the forum. What there isn’t much of is data.

What exists is here:

And they make two very contradictory findings. What neither poster has done, however, is open their data to examination. We have to take their word for the methodology and conclusions. That’s a tough pill to swallow when the claims are so contradictory.

I’ve started collecting data myself, and I’m going to publish it openly on here so the forum at large can slice and dice it as they see fit. Currently, I’m at 3500 tiles seen, which is 100 raids. I’m doing a 3/2 color stack, so 3 of one color, and 2 of another. I vary which colors I pick depending on the target, but it’s always 3/2.

The results couldn’t look much fairer. The 95% confidence interval is broad enough that there still might be a very mild negative bias. But it’s not looking likely. More data to come.

Data:

Team Red Green Blue Yellow Purple Tile Count Tiles 1st color Tiles 2nd color
3 y 2 P 11 5 8 6 5 35 6 5
3 y 2 p 9 9 3 7 7 35 7 7
3 y 2 p 8 6 3 9 9 35 9 9
3 p 2 r 5 8 9 10 3 35 3 5
3 r 2 p 5 6 7 8 9 35 5 9
3 r 2 y 6 8 11 5 5 35 6 5
3 y 2 p 6 7 9 5 8 35 5 8
3 b 2 r 9 4 8 4 10 35 8 9
3 b 2 y 6 5 9 11 4 35 9 11
3 r 2 b 7 9 10 5 4 35 7 10
3 r 2 b 6 8 7 6 8 35 6 7
3 r 2 b 7 7 4 9 8 35 7 4
3 r 2 b 7 4 10 6 8 35 7 10
3 b 2 p 12 9 4 5 5 35 4 5
3 y 2 p 5 9 5 9 7 35 9 7
3 b 2 y 9 9 9 3 5 35 9 3
3 b 2 y 7 5 6 11 6 35 6 11
3 r 2 p 10 5 9 4 7 35 10 7
3 b 2 r 7 6 7 7 8 35 7 7
3 r 2 p 4 7 7 11 6 35 4 6
3 r 2 p 8 10 8 2 7 35 8 7
3 y 2 p 13 11 7 3 1 35 3 1
3 r 2 y 9 4 4 10 8 35 9 10
3 b 2 y 5 7 10 6 7 35 10 6
3 y 2 r 8 12 2 3 10 35 3 8
3 y 2 p 7 11 5 6 6 35 6 6
3 y 2 p 7 6 10 6 6 35 6 6
3 r 2 b 7 10 5 6 7 35 7 5
3 r 2 y 8 6 7 5 9 35 8 5
3 r 2 b 5 6 9 7 8 35 5 9
3 r 2 p 3 7 3 11 11 35 3 11
3 r 2 p 8 5 8 7 7 35 8 7
3 y 2 r 7 5 10 6 7 35 6 7
3 y 2 r 10 9 5 7 4 35 7 10
3 r 2 y 6 8 9 7 5 35 6 7
3 g 2 r 6 8 9 6 6 35 8 6
3 b 2 p 7 4 9 7 8 35 9 8
3 b 2 g 9 3 12 3 8 35 12 3
3 y 2 p 11 6 3 5 10 35 5 10
3 r 2 p 4 5 13 4 9 35 4 9
3 r 2 b 6 7 11 6 5 35 6 11
3 y 2 r 7 6 6 8 8 35 8 7
3 y 2 p 13 6 5 6 5 35 6 5
3 y 2 p 8 3 10 8 6 35 8 6
3 r 2 b 8 5 6 9 7 35 8 6
3 r 2 y 7 7 7 5 9 35 7 5
3 b 2 r 7 10 6 4 8 35 6 7
3 b 2 r 6 6 8 7 8 35 8 6
3 b 2 p 4 5 6 8 12 35 6 12
3 r 2 b 6 7 10 5 7 35 6 10
3 y 2 r 8 7 4 11 5 35 11 8
3 y 2 b 5 12 6 4 8 35 4 6
3 b 2 p 10 5 5 8 7 35 5 7
3 b 2 y 2 6 9 11 7 35 9 11
3 b 2 y 9 5 8 6 7 35 8 6
3 b 2 y 7 10 5 9 4 35 5 9
3 b 2 y 10 7 5 5 8 35 5 5
3 b 2 r 6 7 8 6 8 35 8 6
3 y 2 r 5 5 13 7 5 35 7 5
3 y 2 p 7 5 7 6 10 35 6 10
3 r 2 p 10 5 6 6 8 35 10 8
3 b 2 y 13 7 4 6 5 35 4 6
3 y 2 p 4 7 8 7 9 35 7 9
3 r 2 p 12 7 3 7 6 35 12 6
3 r 2 b 6 7 9 6 7 35 6 9
3 y 2 b 9 6 6 7 7 35 7 6
3 y 2 b 8 9 5 5 8 35 5 5
3 b 2 p 6 8 9 8 4 35 9 4
3 b 2 p 7 10 6 6 6 35 6 6
3 b 2 p 7 3 7 9 9 35 7 9
3 b 2 y 6 4 9 7 9 35 9 7
3 b 2 y 6 11 5 2 11 35 5 2
3 r 2 y 9 9 8 3 6 35 9 3
3 b 2 y 8 5 8 7 7 35 8 7
3 b 2 r 9 9 5 8 4 35 5 9
3 r 2 y 11 10 1 7 6 35 11 7
3 p 2 b 7 6 6 5 11 35 11 6
3 y 2 r 7 8 5 7 8 35 7 7
3 p 2 b 5 6 9 7 8 35 8 9
3 y 2 r 1 7 6 11 10 35 11 1
3 b 2 r 9 10 5 4 7 35 5 9
3 r 2 p 9 5 7 7 7 35 9 7
3 r 2 p 5 5 9 5 11 35 5 11
3 y 2 r 8 4 9 10 4 35 10 8
3 b 2 p 6 10 5 9 5 35 5 5
3 b 2 p 7 6 5 7 10 35 5 10
3 r 2 b 9 9 8 7 2 35 9 8
3 b 2 p 8 9 7 9 2 35 7 2
3 r 2 y 5 9 7 7 7 35 5 7
3 r 2 g 12 6 4 5 8 35 12 6
3 r 2 b 7 7 5 9 7 35 7 5
3 b 2 r 6 6 8 7 8 35 8 6
3 r 2 p 7 6 9 7 6 35 7 6
3 r 2 b 7 6 10 6 6 35 7 10
3 r 2 y 6 5 8 10 6 35 6 10
3 b 2 p 7 5 9 8 6 35 9 6
3 b 2 r 5 6 8 8 8 35 8 5
3 r 2 b 7 6 9 10 3 35 7 9
3 b 2 y 4 7 8 7 9 35 8 7
3 b 2 p 8 13 7 2 5 35 7 5
  728 694 710 672 696 3500 707 702
Est % 20.80% 19.83% 20.29% 19.20% 19.89%   20.20% 20.06%
Est Tiles 7.28 6.94 7.10 6.72 6.96   7.07 7.02
44 Likes
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I think someone has created a fake forum account, @Garanwyn, to mock me.

I have noticed this account more than once since my return from my most recent sabbatical. I believe its purpose is to titillate me with its wit, to shame me with its numeracy, and to seduce me with its transparent data collection and analysis. To date, I have resisted temptation.

This thread might finally have crushed me.

I give up.

Please marry me, @Garanwyn. I don’t care what your gender is - you’re better than me and if we were together I could be better than I am.

You think I’m kidding. I’m not.

34 Likes

OMG HAHAHAHA! FK EPIC!
LOL

3 Likes

I very much enjoy your posts and your dry wit as well, and I’m really happy you’re back from sabbatical. I’m glad that, at least in some small measure, my posts and analysis have found favor with you.

As for your very gracious proposal, I am afraid that my wife would likely be generally against the idea. Worse, the bigamy laws both here and in England would tend to weigh against the idea as well.

18 Likes

Your posts are always my favorite. Thank you for doing this leg work!

I considered doing it myself, but I am clearly more lazy than you are!

1 Like

Thanks! You’re very welcome. I’m glad you enjoy them. I was actually too lazy to do it myself, right up until someone claimed a 25% decrease on the stacked into color. Then, I just had to see for myself.

7 Likes

I’m crushed. Hell hath no fury like me scorned. I now wish nothing but death upon you.

On the other hand, you never needed my proposal or my approval. Your statistical knowledge clearly equals and probably exceeds mine, so I’ll just go back to squabbling on backwoods threads and leave you to this one.

(You add value by being here. I hope you stay for a while.)

8 Likes

Another pair of expert feline eyes is always appreciated. You’re welcome on the thread any time.

4 Likes

This is great work, but I’m afraid it won’t convince many people. People that complain that random isn’t random necessarily have no idea what random is. If they don’t know what random is then how can they understand statistics? If they don’t understand statistics then your data shouldn’t convince them. The rest of us appreciate it though.

5 Likes

I’m glad you find it interesting/useful!

Some people will at least be contented to know that someone has looked at the data, has published it, and has concluded that it really is random. If someone is both not knowledgeable about statistics and not willing to listen to those who are, then yeah, they certainly aren’t going to change their minds based on this.

Honestly, it was less about convincing the incurably superstitious and more about actually knowing the answer myself though. I made it open because I think that’s the right thing to do.

7 Likes

Oh…you already posted a foto of your proposal of marriage!
brobb

and the answer was: YES!

4 Likes

Somewhere in one of those threads someone stated that the tile placement was not random, but that it had to do with the DEFENSE team color stacking, and not the attacking team.

I took a look at it, ran a SMALL number of raids (maybe 20?) and the numbers held up… that if I could find non-rainbow teams to raid, the Strong tile against their stacked color showed up less frequently.

Unfortunately… I can’t find the post :frowning: gonna see if I can… memory might be serving me wrong… but certainly that could have some useful implications with team building :slight_smile:

Thank you for your excellent work here as well, of course. And if you go missing we will start the search at brobb’s house :))

Edit:

I never did provide any data for THAT little idea… and I couldn’t find what in the thread made me think that the idea had merit.

Interesting. So, sort of a backstop for those lethally bad at planning a defense?

Since I generally stack against the doubled color, the effect ought to be present in my data. But I’ll start tracking it explicitly and see what happens. Thanks for the (remembered) idea.

:rofl:

You mean if it’s not the CIA that got me, right? :wink:

1 Like

Funny counter-example, complements of SWEG. Of course, the whole thing is low probability with that zero red tiles, and proves nothing. Just thought it was interesting to see it after the discussion:

I’ve started collecting enemy stack data. Rolling to find them takes a fair amount of food, since they’re not all that common.

Through 7 boards, the enemy’s stack color is 21.2% of tiles. But 7 boards is approximately zilch statistically. I’ll keep you posted on what I find. Thanks again for pointing me to this hypothesis!

1 Like

Up to 10,500 tiles seen. That’s 300 raids.

Updated probability of seeing a tile of the stacked into color: 20.05%

95% confidence interval: 19.3% to 20.8%

Conclusion: looking perfectly fair

Data for raids #101-300 below

Team Red Green Blue Yellow Purple Tile Count Tiles 1st color Tiles 2nd color
3 b 2 r 3 6 8 8 10 35 8 3
3 p 2 y 10 4 7 9 5 35 5 9
3 b 2 r 8 4 4 11 8 35 4 8
3 b 2 r 8 7 6 5 9 35 6 8
3 b 2 r 5 3 9 9 9 35 9 5
3 p 2 y 10 4 9 8 4 35 4 8
3 r 2 b 9 6 8 3 9 35 9 8
3 y 2 p 7 5 6 8 9 35 8 9
3 r 2 y 9 5 9 7 5 35 9 7
3 p 2 y 7 8 5 4 11 35 11 4
3 r 2 b 7 6 7 9 6 35 7 6
3 r 2 p 5 10 6 7 7 35 5 7
3 r 2 p 8 10 8 4 5 35 8 5
3 p 2 y 8 7 6 9 5 35 5 9
3 r 2 b 8 7 10 5 5 35 8 10
3 r 2 b 7 4 8 8 8 35 7 8
3 b 2 g 9 5 6 8 7 35 6 5
3 b 2 g 7 6 10 8 4 35 10 6
3 b 2 r 6 7 3 10 9 35 3 6
3 b 2 r 8 8 7 5 7 35 7 8
3 y 2 r 6 8 9 7 5 35 7 6
3 y 2 b 5 8 5 10 7 35 10 5
3 b 2 p 9 5 6 8 7 35 6 7
3 y 2 r 7 6 10 4 8 35 4 7
3 b 2 y 5 6 10 6 8 35 10 6
3 b 2 r 4 6 8 11 6 35 8 4
3 r 2 b 5 8 7 6 9 35 5 7
3 r 2 y 9 5 8 6 7 35 9 6
3 r 2 y 10 6 7 9 3 35 10 9
3 r 2 y 5 7 10 6 7 35 5 6
3 r 2 y 7 6 6 5 11 35 7 5
3 b 2 y 6 9 7 8 5 35 7 8
3 r 2 b 8 6 5 7 9 35 8 5
3 b 2 r 8 6 12 1 8 35 8 12
3 b 2 p 7 8 5 11 4 35 5 4
3 r 2 b 6 4 6 10 9 35 6 6
3 b 2 g 7 8 4 10 6 35 4 8
3 b 2 g 9 5 7 7 7 35 7 5
3 r 2 b 9 7 5 9 5 35 9 5
3 b 2 y 6 9 5 8 7 35 5 8
3 b 2 y 12 4 8 4 7 35 8 4
3 b 2 y 8 6 8 7 6 35 8 7
3 b 2 y 7 7 7 4 10 35 7 4
3 r 2 b 6 8 3 10 8 35 6 3
3 r 2 b 6 10 10 4 5 35 6 10
3 r 2 y 6 8 8 6 7 35 6 6
3 r 2 y 8 5 6 6 10 35 8 6
3 r 2 p 6 3 7 13 6 35 6 6
3 b 2 r 10 9 5 6 5 35 5 10
3 b 2 r 8 6 4 8 9 35 4 8
3 b 2 r 9 9 3 8 6 35 3 9
3 b 2 p 8 10 7 5 5 35 7 5
3 r 2 b 5 6 6 6 12 35 5 6
3 b 2 r 6 8 8 6 7 35 8 6
3 r 2 b 12 4 8 7 4 35 12 8
3 r 2 g 9 9 8 5 4 35 9 9
3 p 2 r 5 14 7 4 5 35 5 5
3 p 2 r 4 10 7 7 7 35 7 4
3 b 2 y 5 8 8 8 6 35 8 8
3 b 2 y 9 6 5 6 9 35 5 6
3 b 2 y 6 7 7 8 7 35 7 8
3 r 2 y 7 5 9 5 9 35 7 5
3 p 2 g 6 9 11 4 5 35 5 9
3 p 2 g 6 4 10 8 7 35 7 4
3 y 2 p 10 4 5 9 7 35 9 7
3 p 2 b 6 7 10 5 7 35 7 10
3 p 2 b 4 7 8 10 6 35 6 8
3 r 2 p 8 7 4 8 8 35 8 8
3 b 2 y 10 3 8 7 7 35 8 7
3 r 2 y 2 8 7 12 6 35 2 12
3 r 2 y 6 6 12 6 5 35 6 6
3 r 2 b 7 6 11 3 8 35 7 11
3 b 2 p 4 6 10 4 11 35 10 11
3 y 2 p 8 7 8 6 6 35 6 6
3 y 2 p 7 6 8 4 10 35 4 10
3 b 2 p 9 10 6 6 4 35 6 4
3 b 2 p 9 6 7 5 8 35 7 8
3 r 2 b 7 6 8 6 8 35 7 8
3 b 2 r 8 5 3 13 6 35 3 8
3 b 2 r 7 6 8 8 6 35 8 7
3 b 2 r 5 12 7 6 5 35 7 5
3 b 2 r 6 6 5 11 7 35 5 6
3 b 2 r 7 5 8 7 8 35 8 7
3 r 2 y 8 3 9 8 7 35 8 8
3 b 2 g 5 10 5 5 10 35 5 10
3 r 2 b 6 9 6 8 6 35 6 6
3 r 2 y 8 6 12 8 1 35 8 8
3 r 2 y 12 4 5 9 5 35 12 9
3 b 2 g 8 6 7 6 8 35 7 6
3 r 2 p 5 8 8 8 6 35 5 6
3 r 2 p 9 4 8 9 5 35 9 5
3 b 2 p 4 12 4 8 7 35 4 7
3 b 2 y 5 7 8 7 8 35 8 7
3 r 2 b 4 8 8 8 7 35 4 8
3 r 2 b 6 6 6 12 5 35 6 6
3 r 2 b 13 2 6 4 10 35 13 6
3 b 2 r 7 3 7 5 13 35 7 7
3 b 2 r 5 6 7 9 8 35 7 5
3 r 2 b 8 7 8 6 6 35 8 8
3 r 2 b 9 9 6 5 6 35 9 6
3 r 2 b 8 8 7 6 6 35 8 7
3 r 2 b 9 5 7 9 5 35 9 7
3 p 2 r 8 9 6 6 6 35 6 7
3 r 2 b 4 9 7 5 10 35 4 7
3 r 2 p 10 5 6 5 9 35 10 9
3 r 2 p 6 9 8 7 5 35 6 5
3 b 2 r 8 7 4 8 8 35 4 8
3 b 2 r 3 8 10 9 5 35 10 3
3 r 2 y 7 8 7 7 6 35 7 7
3 b 2 y 4 11 7 7 6 35 7 7
3 b 2 y 7 7 7 8 6 35 7 7
3 y 2 b 10 9 4 3 9 35 4 3
3 y 2 b 9 10 6 7 3 35 7 6
3 y 2 b 7 10 7 3 8 35 7 3
3 b 2 p 9 2 11 10 3 35 11 3
3 b 2 y 7 9 4 6 9 35 4 6
3 b 2 y 7 9 4 9 6 35 4 9
3 r 2 p 6 7 4 8 10 35 6 10
3 r 2 p 6 7 9 6 7 35 6 7
3 r 2 y 7 7 7 7 7 35 7 7
3 p 2 y 5 4 10 7 9 35 9 7
3 r 2 b 8 8 4 10 5 35 8 4
3 r 2 b 7 6 5 10 7 35 7 5
3 r 2 b 9 7 6 9 4 35 9 6
3 r 2 y 6 8 11 4 6 35 6 4
3 p 2 y 6 10 6 6 7 35 7 6
3 p 2 y 7 3 11 5 9 35 9 5
3 r 2 y 7 4 8 8 8 35 7 8
3 b 2 p 8 9 3 7 8 35 3 8
3 b 2 p 10 7 7 4 7 35 7 7
3 b 2 p 6 6 8 7 8 35 8 8
3 b 2 p 8 8 6 5 8 35 6 8
3 p 2 y 8 9 9 6 3 35 3 6
3 p 2 y 9 6 4 7 9 35 9 7
3 b 2 r 6 9 7 5 8 35 7 6
3 b 2 r 5 11 4 7 8 35 4 5
3 b 2 r 9 4 10 8 4 35 10 9
3 p 2 r 7 6 10 9 3 35 3 7
3 b 2 r 8 5 10 4 8 35 10 8
3 b 2 p 7 5 8 10 5 35 8 5
3 b 2 p 7 9 5 7 7 35 5 7
3 b 2 g 9 5 6 10 5 35 6 5
3 r 2 b 5 5 9 6 10 35 5 9
3 b 2 g 5 10 7 8 5 35 7 10
3 b 2 r 2 5 8 10 10 35 8 2
3 y 2 r 8 5 6 8 8 35 8 8
3 y 2 p 9 5 6 8 7 35 8 7
3 b 2 p 8 7 8 6 6 35 8 6
3 r 2 b 6 10 9 6 4 35 6 9
3 r 2 b 6 5 11 6 7 35 6 11
3 r 2 b 6 10 6 7 6 35 6 6
3 b 2 r 8 4 5 9 9 35 5 8
3 b 2 r 6 5 11 4 9 35 11 6
3 r 2 g 6 7 4 9 9 35 6 7
3 b 2 r 6 6 8 9 6 35 8 6
3 b 2 p 7 7 3 12 6 35 3 6
3 b 2 g 5 6 8 8 8 35 8 6
3 y 2 r 10 1 7 10 7 35 10 10
3 b 2 g 6 8 9 5 7 35 9 8
3 b 2 g 5 10 7 7 6 35 7 10
3 p 2 g 7 6 7 5 10 35 10 6
3 y 2 b 6 6 11 9 3 35 9 11
3 b 2 p 8 7 8 6 6 35 8 6
3 b 2 p 6 7 10 8 4 35 10 4
3 b 2 g 9 5 6 6 9 35 6 5
3 b 2 g 5 5 6 11 8 35 6 5
3 b 2 g 11 3 10 3 8 35 10 3
3 p 2 g 7 8 4 8 8 35 8 4
3 b 2 y 3 6 9 8 9 35 9 8
3 y 2 p 6 5 7 8 9 35 8 9
3 y 2 p 7 5 6 6 11 35 6 11
3 r 2 p 7 2 9 8 9 35 7 9
3 r 2 p 6 4 11 10 4 35 6 4
3 r 2 p 7 4 7 10 7 35 7 7
2 g 3 b 8 4 8 6 9 35 8 4
3 b 2 p 5 10 5 9 6 35 5 6
3 r 2 p 8 7 7 6 7 35 8 7
2 g 3 b 6 6 8 9 6 35 8 6
2 g 3 b 4 9 6 10 6 35 6 9
3 b 2 y 7 10 3 8 7 35 3 8
3 b 2 y 6 3 8 11 7 35 8 11
3 r 2 p 8 7 7 7 6 35 8 6
3 r 2 y 4 7 9 9 6 35 4 9
3 r 2 y 4 5 7 12 7 35 4 12
3 y 2 r 10 7 7 5 6 35 5 10
3 y 2 r 6 5 6 9 9 35 9 6
3 b 2 r 7 6 9 9 4 35 9 7
3 r 2 g 7 5 6 12 5 35 7 5
3 r 2 g 13 8 5 3 6 35 13 8
3 b 2 y 9 5 4 7 10 35 4 7
3 y 2 b 4 6 6 12 7 35 12 6
3 b 2 r 6 4 7 9 9 35 7 6
3 b 2 p 4 8 9 10 4 35 9 4
3 b 2 r 4 9 9 8 5 35 9 4
3 r 2 b 8 5 8 9 5 35 8 8
3 r 2 p 7 7 8 8 5 35 7 5
3 r 2 p 5 7 13 7 3 35 5 3
3 r 2 y 3 7 12 5 8 35 3 5
3 r 2 g 7 6 4 9 9 35 7 6
  2121 2020 2151 2132 2076 10500 2105 2063
Est % 20.20% 19.24% 20.49% 20.30% 19.77%   20.05% 19.65%
Est Tiles 7.07 6.73 7.17 7.11 6.92   7.02 6.88
7 Likes

@Garanwyn.

There are bigamy laws in England!!! What is the punishment in jail time if i… sorry, the friend, i am asking for, is guilty?

4 Likes

Up to 7 years in prison, apparently. But there are lots of places without extradition treaties with the UK, so your… ahem… friend is probably fine. I hear Moscow is nice this time of year… :wink:

http://bloomsbury-law.com/criminal-defence/bigamy-uk/

3 Likes

You have both way more patience and apparently time than I do. Well done!

1 Like

Speaking of odd things…I did a three horizontal blue tile match at the top of the screen the other day, and it was replace 3x times by 3 blue tiles. That has got to be very rare. Just wish I had brought blue!

2 Likes

The recording adds about 30 seconds a raid, so it’s not that bad. Honestly, I burn through all my energy so quickly that stretching out my 6 raid flags by 3 minutes doesn’t seem so bad.

Your 3x blue 3s should be about a 1 in 2 million event. So yeah, that’s definitely one for the rarities trophy wall!

3 Likes

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