Color Stacking Fairness Project

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

Just wanted to follow up with you on this hypothesis. I’m about 150 raids (about 5300 tiles) in now on my counts for enemies who color stack on defense. The results suggest that it’s pretty unlikely that there’s any bias to protect the enemy’s stacked color(s) either.

95% confidence bounds
Upper 21.67%
Mid 20.59%
Lower 19.51%

So I’m actually seeing about 7.2 tiles of the color that is strong against the enemy’s stacked color, on average. I don’t believe that it’s representative of a genuine bias in favor of hurting the enemy, though. Probably just a bit of statistical noise.

At this point, I’ve stopped rerolling with intent to find color stacking enemies, but I do still record data when they pop up.

8 Likes

Thank you for taking that extra step. I appreciate it :slight_smile:

Feel like this little guy can altogether be put to sleep now lol

4 Likes

Wow. You have so much patience. Well done.

2 Likes

Thanks! It adds about 30 seconds a raid, so it’s not too bad. I’m just about to post my 500 raid update. Still looking perfectly fair/unbiased :slight_smile:

5 Likes

Up to 17,500 tiles seen. That’s 500 raids.

Updated probability of seeing a tile of the stacked into color: 20.02%

95% confidence interval: 19.4% to 20.6%

Conclusion: looking perfectly fair

Data for raids #301-500 below

Team Red Green Blue Yellow Purple Tile Count Tiles 1st color
3 r 2 g 8 9 3 6 9 35 8
3 r 2 g 6 5 10 6 8 35 6
3 r 2 g 5 6 8 7 9 35 5
3 r 2 b 8 7 11 4 5 35 8
3 r 2 g 7 6 5 9 8 35 7
3 b 2 r 10 4 6 9 6 35 6
3 b 2 g 6 10 10 6 3 35 10
3 y 2 b 9 7 6 5 8 35 5
3 y 2 b 6 11 1 4 13 35 4
3 y 2 b 3 14 7 5 6 35 5
3 y 2 b 4 7 9 8 7 35 8
3 y 2 b 8 5 11 4 7 35 4
3 b 2 y 6 6 9 5 9 35 9
3 y 2 r 8 7 5 8 7 35 8
3 b 2 y 8 10 6 7 4 35 6
3 r 2 b 5 8 10 7 5 35 5
3 r 2 b 8 10 9 4 4 35 8
3 y 2 b 8 8 8 7 4 35 7
3 y 2 r 6 6 9 6 8 35 6
3 b 2 p 9 8 5 8 5 35 5
3 b 2 p 7 7 7 9 5 35 7
3 b 2 p 8 3 6 9 9 35 6
3 y 2 b 9 11 2 8 5 35 8
3 p 2 b 4 7 8 10 6 35 6
3 y 2 b 10 7 8 3 7 35 3
3 y 2 b 9 6 7 6 7 35 6
3 y 2 r 8 3 9 11 4 35 11
3 b 2 r 7 3 9 6 10 35 9
3 y 2 b 8 4 2 10 11 35 10
3 b 2 r 7 4 9 5 10 35 9
3 b 2 r 9 6 3 8 9 35 3
3 b 2 r 5 8 6 9 7 35 6
3 g 2 b 3 8 7 7 10 35 8
3 r 2 b 7 5 8 6 9 35 7
3 r 2 p 9 6 7 7 6 35 9
3 g 2 r 6 4 8 6 11 35 4
3 b 2 g 7 9 7 7 5 35 7
3 b 2 p 10 7 9 5 4 35 9
3 r 2 y 8 9 4 7 7 35 8
3 r 2 y 12 5 5 5 8 35 12
3 b 2 p 8 6 5 8 8 35 5
3 b 2 r 4 2 7 12 10 35 7
3 p 2 b 7 7 11 6 4 35 4
3 p 2 b 3 8 7 8 9 35 9
3 g 2 b 11 5 8 8 3 35 5
3 b 2 r 8 7 10 5 5 35 10
3 b 2 g 3 12 5 6 9 35 5
3 r 2 y 6 9 8 7 5 35 6
3 r 2 y 6 8 9 8 4 35 6
3 r 2 y 8 10 5 9 3 35 8
3 b 2 y 12 5 11 5 2 35 11
3 y 2 b 7 12 3 6 7 35 3
3 p 2 b 10 9 5 5 6 35 6
3 y 2 r 10 11 5 6 3 35 6
3 y 2 r 4 10 6 7 8 35 7
3 y 2 r 7 6 5 10 7 35 10
3 g 2 r 8 7 11 6 3 35 7
3 g 2 r 5 7 6 9 8 35 7
3 b 2 y 5 4 10 8 8 35 10
3 b 2 r 8 10 4 5 8 35 4
3 r 2 g 3 9 8 8 7 35 3
3 b 2 r 7 3 6 9 10 35 6
3 r 2 y 8 7 4 6 10 35 8
3 g 2 r 8 8 9 7 3 35 8
3 g 2 r 9 6 6 8 6 35 9
3 b 2 r 9 9 5 6 6 35 5
3 g 2 b 4 8 7 9 7 35 8
3 g 2 b 6 7 6 9 7 35 7
3 b 2 r 8 7 8 6 6 35 8
3 g 2 r 6 10 7 5 7 35 10
3 r 2 g 9 10 5 7 4 35 10
3 b 2 r 7 9 6 8 5 35 6
3 b 2 r 3 10 5 11 6 35 5
3 b 2 r 10 5 7 7 6 35 7
3 b 2 r 10 7 7 6 5 35 7
3 r 2 g 11 7 3 7 7 35 11
3 b 2 p 5 7 10 4 9 35 10
3 b 2 p 4 8 4 11 8 35 4
3 b 2 p 7 11 7 7 3 35 7
3 r 2 y 8 8 8 6 5 35 8
3 g 2 b 3 9 8 7 8 35 9
3 b 2 r 8 7 6 8 6 35 6
3 b 2 r 9 6 2 6 12 35 2
3 b 2 r 5 8 7 9 6 35 7
3 p 2 r 9 7 10 6 3 35 3
3 b 2 y 8 5 7 6 9 35 7
3 r 2 p 9 5 8 5 8 35 9
3 r 2 b 5 10 9 4 7 35 5
3 b 2 p 6 7 10 7 5 35 10
3 r 2 g 9 10 4 4 8 35 9
3 r 2 g 3 9 10 8 5 35 3
3 r 2 g 8 6 5 10 6 35 8
3 g 2 b 4 6 8 6 11 35 6
3 g 2 b 10 4 7 8 6 35 4
3 b 2 r 6 6 8 8 7 35 8
3 b 2 r 8 8 9 3 7 35 9
3 b 2 r 8 6 7 4 10 35 7
3 y 2 r 8 9 3 8 7 35 8
3 b 2 r 7 10 7 7 4 35 7
3 r 2 b 11 8 4 4 8 35 11
3 r 2 b 6 8 4 8 9 35 6
3 b 2 r 8 7 8 6 6 35 8
3 y 2 r 7 10 5 6 7 35 6
3 y 2 r 6 9 6 6 8 35 6
3 y 2 r 7 6 12 7 3 35 7
3 r 2 g 10 4 4 10 7 35 10
3 p 2 r 3 5 10 9 8 35 9
3 y 2 b 6 10 6 4 9 35 4
3 b 2 r 9 5 9 8 4 35 9
3 r 2 g 8 5 4 7 11 35 8
3 r 2 g 11 7 3 7 7 35 11
3 r 2 b 9 9 6 7 4 35 9
3 g 2 p 6 7 7 7 8 35 7
3 b 2 r 7 6 7 5 10 35 7
3 r 2 g 10 9 4 8 4 35 10
3 b 2 g 6 11 2 8 8 35 2
3 y 2 g 6 7 7 7 8 35 7
3 y 2 b 8 5 7 11 4 35 11
3 g 2 p 8 6 8 6 7 35 6
3 b 2 y 11 6 6 6 6 35 6
3 b 2 y 4 8 10 6 7 35 10
3 g 2 b 7 6 8 8 6 35 6
3 g 2 b 5 8 8 6 8 35 8
3 y 2 r 7 8 6 10 4 35 10
3 r 2 g 2 6 8 9 10 35 2
3 g 2 r 7 9 6 8 5 35 9
3 r 2 y 7 4 6 11 7 35 7
3 r 2 y 6 7 8 6 8 35 6
3 p 2 r 6 8 11 6 4 35 4
3 b 2 r 7 4 12 6 6 35 12
3 r 2 g 7 4 11 8 5 35 7
3 r 2 b 9 8 10 2 6 35 9
3 b 2 g 8 7 8 5 7 35 8
3 g 2 b 5 7 8 9 6 35 7
3 b 2 y 8 6 7 5 9 35 7
3 r 2 g 4 10 9 6 6 35 4
3 r 2 g 5 7 7 9 7 35 5
3 r 2 g 8 7 10 4 6 35 8
3 b 2 r 6 8 4 8 9 35 4
3 g 2 b 6 6 9 5 9 35 6
3 g 2 b 10 4 8 4 9 35 4
3 b 2 y 8 9 7 8 3 35 7
3 y 2 g 8 7 3 10 7 35 10
3 b 2 p 5 5 6 8 11 35 6
3 r 2 y 5 7 10 7 6 35 5
3 r 2 y 8 6 8 5 8 35 8
3 r 2 y 6 13 9 1 6 35 6
3 g 2 y 6 8 7 9 5 35 8
3 r 2 p 8 7 6 7 7 35 8
3 b 2 y 7 6 6 4 12 35 6
3 b 2 y 8 6 8 7 6 35 8
3 r 2 g 11 3 7 9 5 35 11
3 r 2 g 9 8 5 9 4 35 9
3 b 2 r 4 7 9 10 5 35 9
3 b 2 y 3 12 4 6 10 35 4
3 b 2 y 10 6 7 5 7 35 7
3 g 2 y 5 6 10 7 7 35 6
3 g 2 b 4 6 10 9 6 35 6
3 y 2 b 11 8 4 6 6 35 6
3 y 2 b 3 5 13 8 6 35 8
3 b 2 g 11 7 5 5 7 35 5
3 b 2 g 16 5 4 6 4 35 4
3 b 2 g 4 9 8 5 9 35 8
3 b 2 r 10 7 6 7 5 35 6
3 r 2 g 2 6 8 11 8 35 2
3 r 2 g 3 11 5 10 6 35 3
3 r 2 g 7 10 4 5 9 35 7
3 b 2 p 3 7 11 5 9 35 11
3 b 2 r 6 5 8 4 12 35 8
3 b 2 g 6 10 5 11 3 35 5
3 b 2 g 7 7 11 4 6 35 11
3 b 2 p 6 8 9 7 5 35 9
3 b 2 p 4 8 8 9 6 35 8
3 b 2 r 9 4 4 9 9 35 4
3 y 2 r 4 10 8 4 9 35 4
3 y 2 r 6 7 10 9 3 35 9
3 b 2 g 8 4 4 10 9 35 4
3 b 2 g 7 6 7 9 6 35 7
3 y 2 r 9 8 7 7 4 35 9
3 p 2 b 7 7 5 8 8 35 8
3 p 2 b 5 10 4 6 10 35 10
3 r 2 y 4 6 7 11 7 35 11
3 y 2 r 7 8 6 6 8 35 6
3 y 2 r 9 7 3 7 9 35 7
3 y 2 r 7 5 5 8 10 35 8
3 r 2 b 8 6 6 11 4 35 8
3 r 2 b 6 12 6 5 6 35 6
3 r 2 b 7 6 10 4 8 35 7
3 r 2 y 6 7 7 9 6 35 6
3 p 2 g 11 7 6 6 5 35 5
3 b 2 r 7 7 6 7 8 35 6
3 b 2 r 6 3 10 7 9 35 10
3 b 2 r 7 6 6 7 9 35 6
3 b 2 p 9 8 4 7 7 35 4
3 b 2 r 7 4 9 7 8 35 9
3 r 2 p 4 11 9 9 2 35 4
3 r 2 p 8 5 6 7 9 35 8
3 r 2 p 2 13 8 7 5 35 2
3 b 2 r 7 6 7 7 8 35 7
3 y 2 b 6 3 12 7 7 35 7
  3521 3458 3550 3529 3442 17500 3503
Est % 20.12% 19.76% 20.29% 20.17% 19.67%   20.02%
Est Tiles 7.04 6.92 7.10 7.06 6.88   7.01
10 Likes

Hey @Garanwyn

First of all thanks for putting in the effort and the hours for doing the analysis. As an IT professional I love looking at numbers and stats.

One quick question… would it not be better to use one stack colour say 3 dark 2 yellow and do a lot of raids using that and see how well the tiles generate. Right now we are analyzing stacking but the colour stack is varying. If tile generation algorithm is truely random then you could just be getting lucky with the boards being given.

I am not statistician by any means but I would love to hear your thoughts on this.

1 Like

You’re welcome! I’m glad you find it interesting.

With respect to your question about color stacking:

The hypothesis we’re trying to test here is whether the tile engine has a bias against color stacking, not whether it produces equal numbers of tiles of each color (I’ve never heard any theories that there might be a literal color preference in the tile engine, and I certainly don’t see one in my data).

To test this hypothesis, we can think of every tile draw on a board as falling into one of two categories:

  1. Tiles of the strong stacked color (whatever it might be)
  2. Tiles of a non-stacked color

Then each board gives us a binomially-distributed sample.

Unless you’re hypothesizing some sort of roving color bias or roving color-stacking bias, there’a no change in our chance of getting lucky across the samples by changing colors versus by sticking with a single color.

If you’re interested in the per-color estimates, here they are. The confidence interval bounds are pretty loose on some of them, though, since I don’t stack them often.

Color   95% Low Mid 95% High
Red        
Total Strong Tiles 1224 19.33% 20.35% 21.37%
Games 172      
         
Blue        
Total 1549 19.15% 20.04% 20.93%
Games 221      
         
Green        
Total Strong Tiles 239 16.90% 19.06% 21.23%
Games 36      
         
Yellow        
Total Strong Tiles 608 18.37% 19.78% 21.18%
Games 88      
         
Purple        
Total Strong Tiles 248 17.10% 19.24% 21.39%
Games 37    
3 Likes

Thanks man. I kinda reached the same conclusion after thinking about it last night. Your a legend. Keep up the good work and thanks for an awesome explanation.

3 Likes

In the theme of peer review:

Have you/others looked at distribution of color across the board (ie color stacking may produce the same quantity of X color, but are evenly distributed across the grid reducing possible early matches)?

Have you/others looked at the generated tiles beyond the initial board? No game is won on the opening board, does color stacking impact the tiles beyond the initial tiles spawned?

You should also run a rainbow control to confirm that you are receiving the expected 20% / color generation.

Edit: Very interesting and well executed. This is definitely a benefit to the community and something that I have yelled at my tablet numerous times for. I may owe it an apology.

2 Likes

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