Color Stacking: The Odds

One major problem that I have with this proposal is that it has the unintended consequence of nerfing the damage done to titans. Not exactly something that should be taken lightly consider the possibility of stronger titans returning.

Furthermore, the way the current formula works gives player with shallower benches (mostly 4*, some 5*) an opportunity to defeat very good defenses (players with mostly 5*). I think you would see far more cup droppers to avoid having to deal with Guin/Grave. Rainbow doesn’t really help you if you are outgunned. A color stacked 4* team can beat a full 5* team. A rainbow 4* team will get thrashed by a full 5* team.

I’m not discounting that rainbow offenses with good synergy. All I’m saying is that the current color stacking formula provides an increase in the number of offenses that can beat a given defense. Changing the formula is a boost to defensive teams by eliminating some of those possibilities. If SG thinks that such a boost is necessary to fit their desired model, then I’d agree this is the way to go. Personally, I like the way the system is now, but would not be upset to see it change. I would simply ask them to also adjust titan defenses to account for this change.


The titan, of course, should not change, but about the other is that’s what it is about. Do you think it’s normal for a 4 * team to beat the Top? And what is the effort or talent worth if you have a bug that allows everything. Why grow? Another solution that would help a lot in this, given how unpopular it would be to remove it and would also favor the new ones would be to change the raids, to put only 100 above or below, or 250 maximum of level, would equal the challenges.

I don’t see a problem with a 4* team beating the top if they make the gamble to color stack a 3/2 or mono team. It’s not that much different than using Wu Kong’s Gambler’s Stance in my eyes. Sometimes they miss, other times it is a rousing success.

Why grow? Because instead of beating them 1 out of every three times, eventually you’ll be strong enough to beat them 2-3 times out of every three attempts. Improving your roster will improve your success rate on offense and defense in raids. I think it is misleading to call it a bug. It is simply the mathematical result of the damage formula the game uses.

Thinking about it, it affects all aspects of the game, not just raids. Pushing for completion of rare quests, challenge events, titans. I simply worry about making a game-wide change because the top 1000 don’t like losing on raids to players they feel are inferior.


So, I wasn’t expecting this degree of surprise at my statement. I thought this was the general understanding. Since it isn’t, I’m currently collecting data to verify that my understanding of the combination rule is how it actually works. Let me make sure I’m not getting it wrong before we worry too much about the in-game implications.


4 against sniping or mana busting tanks and the 5th opposite to the own stack works nice.

2 against the tank and 3 against the hardest hitter, if it’s a weaker tank.

If the tank buffs hard, take a rainbow.

@Kerridoc, @Kikyo, @KnifeWonder, @Ber

I’ve looked at this question a bit now, and I still don’t have a satisfactory answer. It’s clear from @SolemnWolf’s examples section that the attack stats used to be added together and then the exponential applied, exactly as I described above:

But in running my own tests on PvE, this doesn’t seem to be holding up. I can’t tell yet if the problem is:

  1. They split out the attacks individually at some point, like Kerridoc suggested


  1. There really is some linearization of the X^1.35 calculation as damage increases.

It looks, after about 80 sample points, as though #2 is more likely than #1. More research is definitely needed.


I thought I’d throw in a few color-stack screenshots I took recently.

Here’s a blue 5-stack I used as a desperation move trying to knock out the tank in a recent war. The team was significantly stronger than mine, but because of the (very!) good luck on the starting board, I was able to not only kill the tank, but wipe the whole team. :slight_smile: (Things like this are why I really enjoy this game!)

Here’s a red 5-stack I used, same as before, just looking to punch a hole in the middle for my allies to work down the rest of the team. I didn’t fare as well here, but Skittleskull was hurting after the second move and I think I knocked out 2-3 of this team.

And since there was some talk about stacking defensively, here is a team I faced. I built a stacked green team but then accidentally clicked to start with my usual rainbow team - I managed to win anyway. :slight_smile:

Make of these what you will. I think the first clearly shows that the game isn’t designed to screw over people for color-stacking, as obviously I had a very good starting board on that one. :slight_smile:


Very nice! Thanks for sharing these. :grinning:

I know you mean well and want to provide the best feedback to us all. The numbers look great, the stats and so on. My last 2 wars I used 6 color teams each, 75% of my teams never got to fight due to unbalanced boards. Yesterday I did 12 raids of which 10 had no color tiles/diamonds and ended with the same results.

Most of our Alliance says the same thing. It’s not about whining or claiming the game is unfair. It’s about loading a 5-0 team, and the tiles and diamonds don’t show. I change to a 4-1 team and a few more show up. I then move to a 3-2 team and it starts to balance a bit.

These are factual results, on our end of the game, as well as the games moderators stating their factual numbers. You have yours, we have ours.

I can take a loss, it’s just a game, but numbers being provided to us don’t always reflect the actual board results when playing.

No sarcastic replies needed like in the past. This issue has been closed in the forum, but still exists in the game whether you agree or not.

Thanks for all you do for the game, us and the experience of playing.

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I’m not really sure who you’re addressing your post to. If you mean me–and I’m the one who calculated those numbers–then you should know that I’m just a player like you. These numbers weren’t provided by Small Giant. They’re the correct numbers for a true random distribution of boards, though. I’d be happy to show you how to do the calculation, and you can do it yourself.

In your post, you keep mixing the words “tiles” and “diamonds”. It makes it somewhat hard to tell just what went on in those matches you’re talking about. I assume you’re not trying to say you literally got zero tiles of your strong color in 9 war matches.

If you’re saying instead that you had trouble making diamonds, though, that’s less surprising. It would also not be surprising that you had trouble filling your mana bar. That takes a lot of tiles to do when heroes aren’t Very Fast mana. A randomly distributed board is much less likely to have big clumps of a particular color. Mono stacking is a risky strategy precisely because of this. I wouldn’t recommend it.

Just to prove a point about what these boards tend to look like, though, I went and grabbed the first revenge-able enemy out of my watchtower and stacked mono against him. Here’s the opening board:

Then I grabbed the second revengeable-opponent. Here’s that opening board:

And then the third. Here’s that board:


I didn’t cheat or cherry pick. Those are pretty average boards.

I’d invite you to start taking screen-shots of your own boards and counting up tiles. If you do a large enough sample, I bet you’ll find that you have an average of 7 tiles of the color you’re stacking into. If you’re not counting tiles, then you don’t really know whether you’re averaging 7 tiles of your strong color or not.

Monocolor teams demand very accurate, careful tile play. You have to be much more careful, because there’s no second color to save you like there would be when you stack 3/2. It’s easy to get frustrated, or to get caught charging your opponent’s mana without making much progress on your own.


color stacking is an option for high defense heroes or very fast mana only to me. my leader runs 3 -2 color stack pretty much every fight and being that he has a 4 k team he stays in high diamond with this strategy, but in wars he either wins big or loses big leaving a high team amost full health with none of our low guys able to clean that up which is not good in my eyes.

in my personal experience i only color stack RIGARD AS TANK, GRAVE AS TANK, RICHARD AND AZLAR AS TANK, AND KASHREK AS TANK. occasionally lianna and sartana need to be stacked against.

i understand color stacking benifits with tiles damage and i also understand how quickly your lineup can suffer immensly in wars because u have stacked yourself out of usable heroes round 1. this latter is why i try to teach players how to use their skills vs stacking as having 6 solid teams is better than one big kill.

my highest team is 3800 and we war with teams where 5 or 6 people are 39 plus and another 10 are around my level yet i finish top 5 of every war but 1 for the last 6 months.

i am an avid believer that constant color stacking reduces actual learned skill and can be more detrimental in learning counters and develop a heavy reliance on gem damage. me and Anchor from 7DD had a nice convo about this topic, but hey to each his own.

the only person i always stack against is gravmakers as tank, every one else i may go 2 2 1 or 2 111 but my main goal is to win with the most character avaiable in my roster to be lethal in both rounds of the war not just one.

you will also notice the more you stack in raids to beat teams 2 and 300 points higher which feels good intil every one of them owns you on revenge attacks.

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The startboard seems to depend a little on the stacked colors, but afterwards it seems to be rnd, I think.

A stack almost charges at one time and that’s the advantage imho.

I run through S2 with 4-1 green red abd it works great.

I’d encourage you to keep a log of tiles in the starting boards for a while to verify whether your impression matches the data :slight_smile: It’s a fun project, and you might be surprised by the result.


In the last war, I did 5-color stacks in I think 5 of my 6 attacks… might’ve been all 6 (I didn’t record it). But I do know that I intentionally did 5-color stack against some pretty tough tanks to try to knock out the center so that other alliance members could have a hole to work through and finish off the team.

I was pleasantly surprised that I managed to full-wipe several of those teams, against the odds. I scored 250 total, second-highest of everyone in that particular war.

I’ve gotten to the point where, if I want to knock out a tank, I don’t hesitate to 5-stack against it and roll the dice. Last war, it worked like a charm. It isn’t always that way. But I can anecdotally say that the game doesn’t stack the odds against me each and every time I do it. (I posted some screenshots in my previous post in this thread, see above…)

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I apologize if I sent this out incorrectly. It was meant as a General reply to the discussion. Not one individual.

I’ve read all the input, feedback, math, stats and so on.

The game results daily state otherwise, at least from what I observe daily as well as my Alliance. 5-0 stacked color teams are less likely to get their perspective color tiles regardless of the math and stats.


It’s all good. The game program determines everything regardless of what we say.

It’s not worth the complaining about anymore.

Thanks for all your feedback.


If you really believe that, “put your money where your mouth is” and start collecting data. Heck, if you just want to screenshot the boards, I’ll do the tile counts and collation for you.

At this point, though, I’d agree there’s no point in complaining, because there’s no evidence that the tile engine has any biases. You can’t fix what isn’t broken…


It was not my intention to offend you or anyone else.

Lot’s of screenshots and data have been shared by others already so adding more is redundant. I’ll just leave it there.

It’s just a game so I’m going to move on from this and just try to enjoy playing it rather than complain about it.

All games have their ups and downs and are not perfect. I appreciate you taking the time to interact with me concerning this.

Thanks for your feedback @Garawyn.


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A.I. Cheats

Garbled info

That sounds like a garbled version of 5 red doing double damage versus a green boss and neutral damage versus a red boss in a stage with two bosses.

Or HotM with Elemental link +5% attack +5% defense for heroes of a matching color.

Where is your happy?


I repeat it over and over and over, but attacking always has to be better than defense from a human factor point of view. Who wants to beat their head against a stone wall every day in a game.

Current research on color stacking is headed towards the conclusion that is is a very strong strategy. This is almost identical to the actually broken haste mechanic in Book of Heroes - even the Devs realized Haste was broken and should have used a linear formula. After several failed attempts to reverse course, Book of heroes just learned to live with it and move on. In fact it became a driving force for several seasonal events and seasonal event loots. Taking life’s lemons and making a lemon orchard, to mangle a common expression.

Similarly in Empires, color stacking is now a fundamental mechanic of roster building and defense planning.

Missing link

Fudge. Totally missed this. But it follows from the base design of MMOs. Usually in MMOs a 5* hero does exponentially increased damage versus 1* enemies to encourage updgrading heroes.

Color stacking just turns this effect up to 11. Further increasing the euphoric rush.

From a game design point of view it further reinforces the use of color specific 3*/4* ascension items making rosters of five rainbow 5* teams even more powerful and desirable than two rainbow 5* teams.


Missing heroes doing a fixed 1 HP damage does balance this out especially with the 90 seconds of terror known as titans.

I will now change how I assign 3*/4* troops and class nodes for heroes I usually color stack.

This piece of info appears to be the missing link for Gryphonkit’s insanely powerful Obakon, Rigard, Tiburtus, Cyprian, Hansel attack team ( the largest factor being how their specials interact ).


Aside, Gryphonkit is really annoyed at me for being on the forums when I should be resting. Oh well, that is what weekends are for, bad choices.

MMO stat curve soft cap

I am not surprised by this result. Most MMOs have a base stat curve then a soft cap or a hard cap. This sounds like Empires implemented a soft cap where they swap out a second equation ( or a second set of constants for the core equation ) once a stat value reaches X.

In Book of Heroes the soft cap increased with the number of stars, which required us to solve the soft cap equation before we could confirm the core stat curve. Empires appears to use the same equations for 1* heroes and for 5* heroes. More research is required.

Trying to track down the value of X for the soft cap, if it exists, will dramatically simplify your research since your are trying to solve for one equation when the data results from two very different equations in an “if then” situation.

Move along, move along

You probably want to skip this if not Garanwyn”

Simplification of Complex Dynamic Systems

Your a wizard Harry, Er, Garanwyn.

If I understand half your math here, you are brute forcing the total tiles for small number of X tiles per 35 replacement spaces on the assumption that 3 tile will most likely not be continguous because math is not really set up to deal with the probabilities of a colored topological problem. Simplify, simplify, simplify- may be the unofficial motto of math.

This would seem to leave a large number of replacement conditions out such as combos. Due to real world versus ideal setting the Devs have several times nerfed A.I. Mana gain from combos due to defense topological conditions - mainly centers and flanks - and that would seem to indicate perceived reward versus actual mechanical odds are an important factor in game play especially mono team play.

I am bringing this up for peer review because my past experience with these game mechanic analysis lead me to believe this exponentially compounds the feeling of euphoria and rage with a mono team without significantly effecting your base mathematical model.

But might indicate that you have simplified too much and underestimated the player impact on use and reuse of mono teams.

Actually the exponential effect of color stacking appears to be a big factor mitigated by the RNG of boards.

Analyzing replacement conditions

I tried to simplify a colored topographical program problem by examining a small sub section of the topography problem involving normally high gain conditions- power shard formation. A condition already highly charged emotionally for a player. Further magnified by a mono team ( “Yay purple power shard” or “Boo not a purple power shard”).

Reaching the same conclusion

There seems to be missing work to be done here but both approaches appear to be sound, if limited, analysis of boards and mono teams. Which as far as I know is a unique field limited to Empires and its clones.

The conclusion being rainbow teams and mono teams have checks and balances that make class and special skill synergy more important than color of hero.

Note: the forced exception is Elemental shield enemies where heroes can do negative damage based on color.


Excellent post! Regarding the note for me… setting my coffee maker on “stun”, and firing up the word processor. This may take a while. :slight_smile:


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