Color Stacking: The Odds

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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.

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Numbers are always apreciated, thank you.
That really hit the mark on what it means color stacking in an opening board.

What’s more, pretty much a good or very good opening board at some point onwards means only 1 thing: instant victory.

Even a board with NONE tiles of the color you are stacking means you have to lose, cause you probably have another massive color you can use to clean the board.
Actually (now i’m gonna say something quite rude) a good player is someone that transform bad boards in good ones.

Top players has not more good boards of the others.
They just win using even the bad ones.

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You’re dead right about transforming a bad board Elpis! It’s a real art, and I know I’m only so-so at it. When I get them, I try to dump useless tiles into the opposing healer. At worst, they’re going to heal an already full team, and with luck I’ll get some actual combos of the colors I need.

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Color stacking is a better bet than rainbow teams! Why?
If you stack 3/2 your tiles are much stronger. You can take down 5* heroes with 4* heroes by tile damage alone, additionally all your specials charge around the same time. You can get bad boards sometimes but even a good board with a rainbow team isn’t that good… how much damage will your green tiles do with a single green hero against a blue defender? Idk I haven’t done it in a while, like 50 or 75 points of damage? Seems impossible to win like that. 3 green heroes turns a single tile against a blue hero into like 300 damage, 450 with a critical hit. Stacking colors also means weak color tiles still hit decently.

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Again about specials charging roughly around the same time, I can’t imagine trying to raid and charge 5 different color specials especially when my tiles are doing basically no damage and I’m charging the defending team

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It’s less about charging 5 specials than about having at least one special that’s chargeable on any given board. But I color stack too when I can. I just acknowledge that it’s risky and I’m going to get some crap boards.

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I think it’s more risky bringing a rainbow team because you are gauranteeing yourself low to mediocre damage. I did an experiment in the top 100 where I defeated teams of all 5* heroes (many of them with Guin and GM as tank) with only 4* heroes and color stacking. A rainbow 4* team is not good enough when attacking in the top 100 without incredible luck.

Also consider how damage is calculated. If you bring a rainbow team, you’re not taking advantage of the somewhat exponential increase in tile damage. This increase in tile damage allowed me to win raids in the top 100 with only 4*'s even when I had bad boards to begin with. Disclaimer: it’s still really hard to win in the top 100 with only 4* heroes but you have better odds when color stacking.

Also, I don’t think in terms of probabilities of the starting board because boards change quickly. You can start bad, but can get a really good board in just a couple of turns. With good foresight, you can turn bad boards into good ones or you are just experienced enough to make the best boards possible in your favor. Of course, there’s always bad luck, but same can be said with rainbow teams.

So I don’t see it as a 60/40 gamble, and I think it’s better than having guaranteed low/mediocre damage with a rainbow team. But thanks for the numbers, it was interesting to know.

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I guess this shows getting no tiles happens.

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That board isn’t bad there’s a lot you can do there. Why did you bring a blue though? Anyways this is a bad board

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image640×1136 1.19 MB

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Brought the blue just for attack down

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@Scrape Yup. There are over 1.2M active daily players of E&P. If each of them uses just 12 flags a day, then I’d expect about 6,000 boards with no tiles of the desired color every day. Sucks to be one of the ones pulling it though.

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Screenshot_2018-12-05-20-59-42
Screenshot_2018-12-05-20-59-42720×1280 1.27 MB

You also can have good board like this (I got this diamond after one move😉)

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If you want a long win streak the best way is to use a rainbow team plus cup dropping. A mono or two color team will eventually lose with an abysmal board. I’ve raided a lot with rainbow teams and I like the ability to be able to have a chance at least with every board (except the rare case where every board is hosed when you can only make a 3-match in a singular place for 4 turns in a row and of course in different colors).

That said I raid 95% with a 2-1-1-1 team, too lazy to switch teams. Heavy color stacking is a good idea though with a weaker team, rainbow is for equal matchups or weaker opponents.

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Numbers mean nothing… Just like in TP’s case. Just think how many times did you dispose of a 4000+ TP team using a 3400 TP team. I do it all the time, so I guess it’s not a big deal.
A good board when stacking colors is not about the number of tiles, it’s about their placement on the board. 6 direct red tiles under a green tank, while stacking three reds, mean pretty much you won the fight, while 10 red tiles shuffled all over the table with chances to hit some blue hero are a desolate sight… Pushing it a bit further, a bad starting board might turn in a great one in a matter of seconds, if the right tiles kick in.

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3 / 2 stacking system works. I can vouch for that.

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I raid around 2600-2800 with a single rainbow team and almost never lose. I skip Guin though, she’s the only hero that requires stacking against.

Because war aid adds an incentive to win in less moves, unfortunately rainbow teams don’t work as well in wars.

Do the stats in OP account for the fact a starting board can’t have a gem match?

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This is the main reason: color stacking gives you better chances to charge & fire your specials before the defense would charge their and chopping attacker’s heads.
Also, color stacking increase the “burst damage”…
helping the attacker to not let the defending teams recover the tile damage taken.

More damage/n° tiles means more damage with higher attacker’s and lower defending team’s mana gain… winning with a rainbow team seems impossible nowdays due to tank’s punishing specials or their high resistance/recovery skillset.

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It must be some godlike rainbow team “almost” never to lose in diamond… would you share your line-up with us, mortals?

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I’ve used the word impossible to describe raiding with a rainbow attack team I think every single time I’ve talked about raiding with a rainbow team lol. Players are concerned that you’ll get bad boards with a color stacked team but I don’t even think there’s such a thing as a good board for a rainbow team. Not when you’re attacking maxed defenders with good team synergy. It’s like impossible to beat that with any rainbow team.

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The only rainbow team I could see working would be one with plenty of mana ticks as Hel - Proteus, Hansel - Peters, Gretel - Chao, and a strong buffer/debuffer as Wu Kong or Isarnia ('cause reasons).