Maximum number of tiles

Hi everyone, a question for our fellow mathematicians/statisticians:

What is the maximum number of tiles of the same color a board can start with ?

Apologies if there already is a similar topic

I don’t know the answer but I quickly came up with an answer of 24. Someone should fact check this.
Table below represents the 5x7 board where 1 is the color you want and 0 is something you don’t want.

1 2 3 4 5 6 7
1 1 0 1 1 0 1
1 0 1 1 0 1 1
0 1 1 0 1 1 0
1 0 1 1 0 1 1
1 1 0 1 1 0 1

Edit: this is incorrect

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Problem with your example is that it already includes matches, and you can’t have a starting board with matches already on it.

22 would work…

numbers

Believe 23 works also…

numb2

I don’t think you can have more than 23 of the same color on the board without having 3 in a row match.

EDIT: not that I think it would ever happen, but if you do happen to ever get a board that looks that good, please take a screen capture and bring it back to us to salivate over. :grin:

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Thank you guys for your time. I will definitely screenshot if ever !

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I still think it is funny that you cannot get an opening board with matches, but you can get an opening board that is so bad it immediately rearranges itself :joy:

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The game will generate some number of boards to try and guarantee:

  1. no starting matches
  2. available moves

After X number of attempts (don’t know how many… ISTR a dev saying 30) it’ll give up, and allow a board with no moves to occur, which will immediately shuffle.

You are mistaken, my friend, because you are only concentrating on rows :slightly_smiling_face:
If you column-think, instead, you will see that you have started with a 2-zeroes array.
That is being unnecessarily generous with zeroes.
If I shift left your matrix I get:
IMG_20210329_062201
to which I can append the least expensive column in terms of zeroes (aka my first or you last):
IMG_20210329_062344
Thus resulting in:
IMG_20210329_062857
or 24 tiles of the same colour with no moves.

This setup also includes the minimal number of 3-zeroes rows, so my guess is that 24 is indeed the maximum.

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There we go: proof boards are not purely random, yay!
Because if they were after 30 attempts you could either get a board with no possible moves or a board with starting matches.
So boards are

  • either somehow constructed on previous tiles
  • or discarded under certain circumstances
  • or both

Does that bias random?
Most likely yes.

[It’s very hard to operate deterministic selection on pure random keeping it pure random]

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Yep, looks like you got me.

In my defense, I didn’t put a lot of time into exploring every possible combination. I just identified the first proposed board as having matches on it, and tried a couple of different combinations. Came up with 22 on the first, 23 on the second. But shifting the numbers as you did does increase the maximum possible to 24.

Well done!

You have no need for defense, I was mostly kidding while trying to spread interest for linear algebra :slight_smile:

Also… I have a condition that makes extremely easy for me to see patterns and number inconsistencies (yup, looking at you PRNG) :wink:

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I used to be good at math, but I’ve been out of school for nearly 20 years now. :laughing:

18 pieces. Seemingly little, but I never saw more.

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Now that is a beautiful board.

Would be 1000x better if any of your opponents were actually red, but… well that’s probably the only reason you got so many blue tiles in the first place.

Oops… sorry, didn’t mean to subtly suggest that boards are ever rigged at all…of course they’re not. Other players have compiled thousands of spreadsheets to prove that they’re not. :slightly_smiling_face:

The board can start with no moves available. It is extremely rare to happen but it happen once in my 3 years of playing this game.

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It’s not that rare, it has happened to me probably at least a dozen times.

But it has not happened to me in a really long time, which makes me think that maybe they fixed it?

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I’m very unlucky for something that have low probability. I play this game for 3 years but never get any heros of the month. I’m free to play but in 3 years, I should get at least 1.

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I believe @Rook was in the same situation for a very long time. She did finally get one (actually, 2 I believe).

I’m usually pretty unlucky myself, but I’ve done better than you in the HotM department. I hope your luck changes!

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Got my first HOTM when almost entering my fourth year.
Obviously: slow, of a colour I’m flooded and one I didn’t really want.

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I actually covered that.

And @TGW it’s not something that can be fixed while still generating random boards. The algorithm changes that would be needed to avoid it simply aren’t worth it. Far easier to generate boards without matches and then eliminate ones that end up with no moves, or give up and instantly shuffle.

Yeah, I got Clarissa at 3+ years, then Zocc.

Anyway, back to topic… :grin:

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