Pattern in the raids

General Discussion
21

By straight arithmetic, the increased damage you cause to the tank is precisely cancelled out by the reduced damage to the other heroes, assuming all your heroes and troops are equally strong.

Yes, you potentially get the benefit of ghosting, which is good. But this is offset by the fact that you are reducing your expected damage.

Because our assumption above - that all your heroes and troops are equally strong - is almost always false. When you substitute out your best hero and troop of one colour, and bring in your second best hero and troop of another colour, you are usually downgrading. (Even more so if you triple stack.)

So when you’re colour stacking, you are betting on the benefits of ghosting outweighing the detriments of using heroes and troops that are not your best. Sometimes that pays off, sometimes it doesn’t.

Plus, you’re dramatically increasing your volatility. So if you get an advantageous board you can destroy opponents easily - even opponents with much better heroes than yours. But if you get a bad board, you can lose to opponents you should walk over.

For me, the bottom line is that stacking is a great way to raid up - you can beat lots of opponents you’d otherwise lose to, and climb high on the leaderboards. I think it’s a terrible tactic to use when filling your raid chest, though. Instead of collecting 8 easy wins and some lovely ascension materials, you have a good chance of going. 6-2, or even 4-4, and delaying the payoff by many unnecessary hours.

22

I don’t think triple red against a blue hero is weaker than bringing a single green hero fam.

23

Triple red against a blue hero will give you 1.5x damage for every red tile. A single green hero will give you 2x damage for every green tile. (Plus, of course, your green hero will be your best green, using your best green troop. Your red heroes will be your best, second best, and third best reds, using your best, second best, and third best red troops.)

So triple red against a blue hero will be considerably weaker than single green.

This is only one isolated aspect of the calculation, though. Here’s the arithmetic for simple double-stacking, which I’ve posted before:

Let’s say you’re facing a green tank, so you double red and omit blue.

Your expected damage against the green tank will increase by about 27%, because:
(4r + g + p + y)/(2r + g + 0.5b + p + y) =1.27
where we expect that r = g = p = y = b (because boards are random).

Your expected damage against purple and yellow will be unchanged, because:
(2r + g + 0.5p + 2y)/(r + g + b + .5p + 2y) = 1, and
(2r + g + 2p + 0.5y)/(r + g + b + 2p + 0.5 y) = 1
where we expect that r = g = p = y = b (because boards are random).

Your expected damage against the red hero will fall by about 18%, because:
(2r + 0.5g + p + y)/(r + 0.5g + 2b + p + y) = 0.82
where we expect that r = g = p = y = b (because boards are random).

Your expected damage against the blue hero will fall by about 9%, because:
(r + 2g + p + y)/(0.5r + 2g + b + p + y) = 0.91
where we expect that r = g = p = y = b (because boards are random).

So the expected gain in damage against green is exactly offset by the expected loss in damage against red and blue. (Though of course, the situation will usually be worse than this, because the stacked hero and troops you introduce will be weaker than those you substitute out.)

1 Like
24

Although I do usually love reading your posts, this one had too many numbers for me so my eyes glazed over. I’m just going to get straight to my counterpoint. Stacking gives the benefit of charging multiple heroes for the price of 1. For simple reasoning, assuming you have a fast hero, you would need 3 “moves” ~8 tiles to charge them. If you have 3 heroes of different colors, 3 moves would only either charge one of them or 1/3 of each, or 2/3, 0/3, 1/3, etc etc. If you have 3 fast heroes of the same color 3 moves would charge all 3 heroes and your specials are all ready to go. This is the other advantage that stacking gives.

Edit: Of course that is countered by the board not having your tiles but RNG is RNG

1 Like
25

You seem to be assuming that damage scales linearly with attack/defense. This thread suggests differently and includes (a few posts down) documentation accompanied by screenshots. Basically, since damage scales exponentially, the more that attack rises the greater the rate of change in damage. In other words, each successive point of attack has more benefit than the preceding point.

26

Yeah - you made the point I was going to make, before I could make it. With a good board, you’ll charge multiple heroes quickly and destroy your opponent. With a bad board, you’ll charge none of yours and all of theirs, and lose.

You’re right: I have assumed damage scales linearly. I read the thread you link to some time ago and tried to replicate the results a couple of different ways, but I couldn’t. Since then I have just assumed it was wrong.

If the theory of an exponential increase in damage by increased attack is correct, this would certainly change the calculation. Whether it would change the conclusion, I’m not so sure. Infuitively, I’d say it would probably depend on the shape of the curve: it might turn out that the increased damage to the tank outweighed the reduced damage to flanks and wings, or it could well turn out that gains against the tank were more than offset by losses against the flanks and wings. Can’t say for sure.

But this is just speculation: at this stage I’m prepared to stick with the assumption that damage is a linear function of attack, at least until I can generate a non-linear result myself (or see a decent chunk of data from other players to that effect).

27

I still think that just because the boards are random, it is a shaky assumption mathematically to use r=g=p=y=b to the determine damage output for a finite battle.

For the input, this is true. However, we are interested in the output, which is determined by the input and the behavior of the player (sorting the tiles in order to obtain the highest value of damage). The better the player is at sorting, the more efficient they become using both rainbow and stacked teams. The stacked team has an added multiplier (strong color stack) that would change the player behavior toward favoring tiles that have this increase in output value, thus tending to overcome the deficiency of having a weak color hero to defeat. Even against neutral heroes, the damage per tile is increased, attracting the player to match the stacked color(s). This leads to less mana for the defense if the player can ghost the missing colors and hit with stacked ones.

In short, I think this analysis is correct if you remove the skill of the player controlling what tiles are played.

28

If we assume that boards are random (I think everyone sensible does), then we also assume that players can’t cause more (or fewer) tiles of any particular colour to drop. So while r=g=p=y=b will never (well, hardly ever) be true, it will always be our expectation.

And just as we might reasonably assume that a skilful player with a colour stacked team would outperform the AI, say, so we might also reasonably assume that a skilful player with a rainbow team would outperform the AI. Under both circumstances we might assume that a player will do better than random matches would, probably even better than a simple algorithm would.

But we have no reason to suppose that a skilful player has more opportunities to exploit their skill with a stacked team than with a rainbow team. A skilful player with a stacked team will manipulate tiles to eliminate opponents, to charge their own specials, to avoid charging their opponent’s specials, or to charge their opponent’s specials tactically. Exactly the same is true of a rainbow team, except the rainbow player may need to make more complex colour prioritisation decisions.

(Brief digression: it might actually be reasonable to suppose that a skilful player has more opportunities to exploit their skill with a rainbow team than with a stacked team, because there are more routes to victory with a rainbow team. For a stacked team there’s really only one way to win: get enough tiles of the stacked colour. End of digression.)

The bottom line is that we have no reason to suppose player skill is more of a factor with a stacked team (and some reason to suppose that player skill might actually be less of a factor).

29

Interesting. So your attempts to replicate the results indicated that damage scaled linearly? I’m always frustrated when games (or any other entity, for that matter) give us stats but don’t tell what they mean or how they interact. We naturally assume that attack is related to damage inflicted and defense to damage received, but how? How much better is 729 attack than 715? It really impairs our ability to make good decisions. I wonder if reverse engineering the hero power formula would yield any insight. Does power scale with the practical value of a stat or the numerical value?

Yeah we absolutely can assume that and in fact the developers have done so as well, which presumably is why defensive teams receive a stat bonus.

I’m not sure I agree with that. Color stacking players have to work around the unrepresented color, while rainbow teams don’t. Assuming that color stacking teams avoid hitting opposing teams with unrepresented color tiles then rainbow teams have to deal with, on average, lighter hitting tiles, which means feeding the opposing team more mana. I think both philosophies have their weaknesses that require players to develop skills and strategies to compensate.

or with a rainbow team. :wink:

30

I agree with much of what you say, but I think that it is leading you to the wrong conclusion. If the tile drops are immutable leading you to assume r=g=b=p=y in the damage output and there are minimal opportunities to exploit player skill, then why do you say that a player is better than the AI in terms of tile damage? For the record, I agree that a player is better than the AI, I just want to know why you think that is the case given this analysis. I’d like to see where that is mathematically taken into account.

31

The short answer: yes. The longer answer: at times not quite, but close enough to being linear as not to matter, and without a deviation I could reproduce consistently.

But I think successful rainbow teams do have to work around colours. The tactics behind a successful rainbow attack are similar to a successful stacked attack - use tile damage to kill opponents and charge your own specials, while avoiding or managing your opponent’s specials. Rainbow attacks will usually want to maximise tile drops of particular colours sequentially, while avoiding or carefully managing drops of some other colours. The difference is that a stacked team will know the target tiles before the game even starts - the rainbow team will have to decide based on the board, their own specials and their opponent’s specials. I think there might be an extra aspect of skill to that decision making.

Yes, this is the safer conclusion: all my ranting above about decision making is just an idea, really - I have no real evidence that extra skill can be exploited when running a rainbow team. Without such evidence, it is sensible to assume that player skill has the same effect on both strategies.

No - this is sort of the opposite of what I assume. I think there are very considerable opportunities to exploit player skill (although as @Z-B points out, it’s not really reasonable to assume there are more associated with a rainbow team). But player skill won’t in any way impact our assumption that r=g=b=p=y. Randomness is immutable.

Do we need to take into account player skill, mathematically? Only if we think it is likely to impact one strategy - rainbow or stacking - more than the other. If we expect the impact on both to be the same (and I guess we should - see above) then we can ignore it, for the purpose of our calculations.

32

Except: When making a diamond or a bomb, the player is actually making one more tile of that particular colour. Hence, player’s choice and skill to set up diamonds and bombs in the right colours (and pass up on the opportunity in wrong colours) will modify the composition of boards.

1 Like
33

i have an account loaded with 5s and good 4s on my alt and i just lost twice to a guy and only killed 1 hero beteeen the two raids; it happens. (got him the third time though).