Color Stacking: The Odds

I just finished my own simulation. As previously mentioned a binomial distribution does not take the 2 dimentional nature of the board into account, and does not correct for boards that are initialized with a match (and must be rejected).

A 4 million iteration run of my code showed matches in over 3 million of the generated boards. I will post data and graphs in the near future. There is definitely a slight difference between the distributions of match-free boards as compared to a simple binomial distribution. The probabilities are slightly bunched to the center, so the worst and best boards are less likely and the average boards are more likely when you take initial matches into account.

Thanks to the Mod with the Math, I’ve been pondering this subject for months, finally did something about it.

EDIT: 6/30/2021. The X axis of the original chart is off by one (doh!). The data is correct, however. This is the corrected graph.

the raw output:


note: rejected boards are recorded as zeroes, thus the necessity of subtracting the reject count from the zero count.

note 2: since there were no occurences of counts above 17, I’ve truncated the data in the spreadsheet and chart.

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I doubt there exists any pool of boards. Most likely each board is generated in place when it is needed. From other threads we know that server just provides RNG seeds for players and those seeds are separate for different game modes.

22 is the maximum and only occurs in one specific layout.

Proof writing isn’t my strong suit, but I challenge you to fit one more on this board.

Odds: 1 in 6.55 * 10²³

6.55 * 10²³ is the approximate size of the “pool”. This is based on total possible permutations multiplied by the match free rate of 22.5% shown in my computer study.

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Well duh, you’re a mod, not a normal human bean!

:wink: :wink: :joy:

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I’ve just disproved that the board isn’t biased against mono teams. If that was true the following wouldn’t be possible. I tried but it wouldn’t take the video!

I don’t see proof, but I don’t believe the game is rigged either…

Proof would require a statistically significant number of runs. Others have done this, counting tiles in numerous boards.


I think autoplay could have won this

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You may be underestimating the power of stupid.
But that is a dream board.

Here’s mine:

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Agreed, autoplay would have totally fired those three dark tiles in the lower right corner while you sit there all WHAT THE :face_with_symbols_over_mouth::face_with_symbols_over_mouth::face_with_symbols_over_mouth:

At least it would if it were my board :stuck_out_tongue_winking_eye:

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Stupid Question…what is the 1.1 x multiplier in the Kiril and Grimm Attack stat calculation?

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That’s the attack boost due to the combo. You can see it in the screenshot.

Ahh…thank you very much. So each combo multiplier is 1.X; Where X is the combo minus one?

So if a resulting move had 10 combos. The 10th combo would result in a 1.9 multiplier.

Thanks! I’ve played the game long enough to know that mono strategy is fierce. I’ve just recently went down the rabbit hole :hole: of understanding why.

Awesome stuff everyone

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You are absolutely right. :slight_smile:

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omg

1.75 years into the game and I did not know that combos had damage multipliers…

I realizes that this post was some time ago but it is an issue I have been working on for a little while. Let’s start with attack methods. If you line up horizontally (even with a great line view it is a weak hit. Vertical hits are stronger. Your cop match with soldiers is a fickle thing. Sometimes that color match will give you a good hit but you can not take your eye off the board. If you have a red soldier and not making any damage, check the color chart top left. Try the dominant color even if you don’t have a matching soldier. No head way, try using just enough of a soldier’s power to make a dent and go back to tile’s. If you are still not making headway try one of your weakest or strongest weapon if you feel that five minute clock on you. There is never just one right answer, you have to use all tools available remember what you have read, what has worked, and if not working this time there must be another way, close your mind too nothing. You might find something new😎

From my damage analysis I’m 100% certain that the combo bonus boosts damage, not attack, and applies to the damage modifier just like the elemental bonus and crit bonus.

Noob.
20 characters or something like that.

I accept this label with great shame

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Never really expect that zero tiles is a possible setup, till today:

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