On what dataset? How large? With what degree of confidence, and using what statistical measure?
And you can directly calculate the expected distribution of tiles under a permitted starting boards requirement. You don’t need to simulate it.
It runs through exactly 1000 boards currently, but can run through any number.
It checks % of boards with at least one match of the desired color to get a percent, and the avg “desired colored tiles” per board as already stated. With the degree of confidence of “it’s simple math” so 100% since it actually just adds up the boards and tiles that apply.
Sure you don’t need to simulate it (IE; generate actual boards) and go into statistical analysis, but at the end of the day I’d rather see what the 1000s of boards look like and add up the actual numbers.
I can put it online easily enough, yah just gotta enable flash to run it, and I can paste the math on the page so you can see exactly how the figures are calculated.
In the meanwhile, because I’m not here to get into a spat but rather incredibly eager to see how it compares, where is the “very good evidence” that the boards are not futz with? (I know you can’t prove a negative, but I guess there’s some spreads sheets or detailed posts with some numbers that show they are about what one would expect if they are truly random and I’d love to see it.)
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I collected a dataset of 500 boards, which I published to the forum here:
Looking at the number of tiles of the strongest, and then max of strongest two colors across that dataset:
At 500 boards (17,500 tiles seen) it’s a little noisy. But it’s clearly not biased low. If anything, it’s biased a scosh high versus theory. But it seems highly likely that’s noise, since SG has said the distribution the tiles are drawn from is in fact uniform random across the colors.
The 95% confidence interval on strong tiles is within +/- half a percent of the nominal value, so it didn’t seem worth doing a ton more collection.
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Yes, and that matches my simulation, avg. of about 7.1 of desired tile color (if you went mono or what one would call “strong color”).
What interests me more is matches of that strong color on the starting board. Do you have any data related to that? There should, if what I coded up has any merit which again it should because it’s really incredibly simple, has 63% of starting boards allowing you to clear a match of the strong color right out of the gate.
If that’s the case, I’ll happily admit my error. Everything else I said unrelated to any potential rigging, however, remains.
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I didn’t record that, unfortunately. What I recorded was:
- My team composition for each fight
- Counts of each color of tile
From this, I generated the count of my strong and second strong color–whatever that happened to be for a given fight. That data produced the graphs you see, and is fully published in the thread I linked.
And then, because someone asked, there are a few hundred runs where I hunted teams that had more than one hero of some color, and recorded how many tiles of the color strong against that color there were.
That wouldn’t surprise me. Although I haven’t actually calculated it, it’s calculable from the process that lets one figure the number of boards rejected at each tile count. It was never something I was looking at.
It’s going to be heavily biased toward the boards where you have plenty of tiles, though, I suspect.
43% of boards will have fewer than 7 tiles of your main color. Those boards are probably progressively less likely to enable matches as the tile count plummets, making them feel extra useless.
The likelihood that the tiles are drawn from a uniform random distribution and then the boards are somehow tweaked though seems low. There are plenty of boards that do have a 3-match in the strong color right out of the gate, and so the algorithm would have to be a very subtle one.
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Depends on if those six or less can even be matched once, and where the tiles are (under tank v off to the side).
There are plenty of boards that do have a 3-match in the strong color right out of the gate, and so the algorithm would have to be a very subtle one.
This is why I was hoping you might have data. I can recall a ton of boards that did not, and a number of boards that did. Should be 63-64% I might start recording data from wars and raids only. Don’t want to go off memory, because confirmation bias is absolutely a thing.
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I wish I did. It would have been easy enough to record if it had been a question I was considering. Sounds like a worthy project, though. If you want company, I’m willing to count with you. Just let me know where and how you would like me to record data.