Color Stacking: The Odds

[Garanwyn]

@Olmor

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

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 It’s a fun project, and you might be surprised by the result.

[Fizban]

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…)

[KINGDOMCOME]

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.

King

[KINGDOMCOME]

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.

King

[Garanwyn]

@KINGDOMCOME

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.

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…

[KINGDOMCOME]

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.

King

[Gryphonknight]

@Edit

Defense

This also explains why color stacking works so poorly on defense. A.I. Damage is always colorless. So the increased vulnerability is not balanced with an increased attack ( the +20% final damage bonus roughly balanced a rainbow teams attack advantage ).

A.I. Cheats

@Gryphonknight

==20% bonus damage buff==
Players can increase damage by making matches of a color strong against the defending hero. Since the A.I. Cannot, they get a flat 20% bonus ( which is roughly the bonus of a rainbow team against a single color boss due to strong matches versus a team of all neutral colors fighting the same boss ).

You can preview the raid defense team and pick the best colors to attack.

Garbled info

@KnifeWonder

5 reds for example, you get a small bonus to the overall attack too, like basically if your attack power is 100% when having a monochrome team it will be like 105/110%. Is it true or just a myth?

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?

@Kikyo

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.

This.

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

@Garanwyn

So instead of your 3-stacked tile attack being 3x as powerful as a single-hero tile attack, it’s 4.4x as powerful. That’s huge.

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.

But.

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

@Garanwyn

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

or

2. 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 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

@Garanwyn

The simplification here is that 35!/(35-X)! can actually be cancelled down to:

35 * 34 * 33 * … * (35-X+1)

So if X = 3, for example:

35!/((35-X)! * X! = 35 * 34 / (3 * 2 * 1) = 198.333

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.

Edit:
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”).

@Gryphonknight

odds zero mana (and almost zero damage) from:

row on board (7)- 1 / 0.8^7 = 1 in 5
column on board (5)- 1 / 0.8^5 = 1 in 3
Power shard or initial match 5 to create power shard = 4 in 5

@Gryphonknight

For a random match 3 board, every time a shield is removed from the board, it can be replaced by any of the other colors. So removing 5 shield from the board has a 1 in 3125 chance of replacing them with 5 purple shields. If your team does not contain a purple hero, you have 5 shields that do almost zero damage to the boss and generate zero mana for your hero.

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.

[Garanwyn]

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

[CorpseTiller]

I’d probably win 9 out 10 times too if I could go 2-1-1-1-1 … haha!

[Rohn]

I run 5 of one color every fight… I am saying something has changed. I KNOW I averaged 5 wins EVERY war. 50 wars. And I averaged 4.75 wins of 6 raids 75 runs. After last update I now average 1 win every war for 5 wars. Also 2.2 wins of 6 raids from 28 runs. Now before we get into the RNG, my averages are WAY to low. I KNOW there has been MANY MANY people lobbying for SG to do something about color stackers. Do I think they would admit to this change NO I DO NOT, because that would be telling certain people HA HA we stopped you. We have ALL seen the same things being said over and over about color stacks no longer working the same,maybe its time to start listening to these people. I DO think it has changed.

[Kerridoc]

Data, please.

In particular, do you think you are seeing:

• skewed boards
• less damage from a stack per tile
• both

The second point is pretty easy to check, so please do so. This is easiest in raids/wars where the defense score of each foe is known. If you prefer, post screenshots so others can do the math.

If the first, that’s harder. The Color Stacking Fairness Project has been collecting data about this, but we haven’t seen and bias or trends there—at least to date. Please add your data to help improve our collective knowledge.

[Rohn]

Kerri skewed is the way I am leaning. I will start getting screen shots if I remember LOL. All of my stats are just wrote down like this war I won X amount of fights. I ALWAYS attack stronger teams.

[nevarmaor]

Hmmm, current war is VERY small sample size but,

First two flags I went 3-2 and one-shot teams 2-300 TP higher. Third flag I went mono because all blue tanks and I had no strong green left. I one-shot a team 300+ TP higher using neutral colour stack (yellow fwiw).

The next 3 flags will also be mono, I’ll report back how that went. The sixth will likely be around 1000 TP difference. I always aim at the 3900+ opponents.

Yes, I have had wars with horrible boards. I have had wars where I one-shot no one. I have had wars where my first flag was a whopping zero points. And I have had wars where I one-shot a team 1000+ TP higher with a neutral mono stack. It has all happened in the past, it is all happening in the present, and it will all happen in the future.

I don’t see a change for the worse though.

[Kerridoc]

It’s not your outcomes that matter, it’s the frequency of tile drops by color and the damage effect of each tile. Outcomes depend on hero choice and skill in board manipulation, which is outside of SGG’s control.

[Mothra]

Well, I used to do okay with color-stacking, but I have reason to believe that Small Giant is purposely shutting down color-stacking techniques in raids. Every single puzzle for over a month straight has literally been littered with colored tiles for heroes that are unrepresented in my line up. On the flip side in all of those raids, it was like pulling teeth for tiles of the hero colors that were stacked. The chance of an upset made the raid arena interesting. Now, the lousy rewards in the raid chest can no longer make up for the mental toll that aspect of the game has by ensuring less wins by lower team power teams. I’ve quit raiding. I’ve quit trying to fill raid chests. It’s not worth it unless you are one of the top players in the world, who pours their life-savings into this game.

[nevarmaor]

It would not make sense for them to simultaneously shut down colour stacking while also encouraging colour stacking with elemental links on the newer heroes being introduced.

Also, I do quite well in raids now, and my total expenditure on the game is $17.55.

[Cvs]

@Mothra

but I have reason to believe that Small Giant is purposely shutting down color-stacking techniques in raids

What reason is that? Assuming you have proof that goes against the math @Garanwyn has shown and tested in the op.

[Mothra]

Well, obviously I can’t prove it other than that I was winning 60% of raids against teams with as much as 700 points of power on defense more than my offense. For the past month, I’ve won less than 10% and have lost well over half of raids against teams with an inferior team power.

[ffphier]

I’ve been doing really well recently going either mono or 4-1. Most of my raids are against teams in 4000-4300 range with a 3600 range team and I’ve been winning well over half, probably more like 2 out of 3.

[Mothra]

But how many 5-star heroes are in that 3600 team? Star class makes a difference regardless of team power.