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.
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.
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.
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 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.