There are a TON of posts complaining about how the game engine is somehow biased against those of us who color stack. I’ve seen lots of screen shots of 5 or 10 or 20 games, along with complaints that the engine can’t possibly be fair based on these (small) samples.
What never seems to get talked about are the actual probabilities, and what we should really expect to happen when we color stack. Which is unfortunate, because the actual probabilities are really informative. Assuming that the game is truly random (which is what the devs claim), then for any color you choose to stack:
1 boards in 5,000 (0.02%) will have no tiles of the color you want
2 boards in 1000 (0.17%) will have only one tile of the color you want
9 boards in 1000 (0.94%) will have only two tiles of the color you want
31 boards in 1000 (3.1%) will have only three tiles of the color you want
77 boards in 1000 (7.7%) will have only four tiles of the color you want
131 boards in 1000 (13.1%) will have only five tiles of the color you want
178 boards in 1000 (17.8%) will have only six tiles of the color you want
So if you’re color stacking, 42.8% of your boards will be EXPECTED to have 6 or fewer tiles (max of 2 matches) of the color you want, assuming everything is really random.
Worse, most of those boards will actually have your color tiles all over the place, meaning you won’t be able to make ANY matches at all in the color you’re stacking. So you should expect that, on average, 4 games out of every 10 are going to be really sucky for the color you’re stacking. And getting three or four really sucky games in a row when color stacking isn’t surprising at all.
We should expect that heavy stacking into a color is at best a 60/40 gamble, and it’s really easy to get burned on a 60/40 gamble.
Note: Math has been updated to account for rejection of all starting boards with one or more matches.