Feeding Heroes: One at a Time vs. Ten at Once

Ever since I started playing this game I’ve heard the suggestion that when feeding your heroes, it’s best to do 10 cards at a time to maximize the chance of bumping up their special skill. But I’ve never understood the math and statistics behind that theory, and rather than continuing to torment my team and peer support with my stubborn questions, I asked a friend (a physics professor) to lay it out for me. Turns out everyone’s right, sort of!

For this example, let’s say we’re feeding 1* heroes to the same color hero. Individually, the chances of increasing special skill is 2%. Feeding ten at once increases this to 20%.

It might be easier to imagine this as physical odds instead of percentages. In option one (feeding ten at once), you can pick from a jar with 5 tickets, and one is a winner. In option two (feeding ten one at a time), you pick 10 times from 10 different jars - each containing 50 tickets, with only one being a winning ticket. That is, one 1/5, or ten 1/50s.

In option one, you clearly have an 80% chance of not drawing a winner. In option two, the math is a little trickier - it’s 49/50 to the 10th power, or 81.7% chance of failure. So, the difference in risk is 1.7%, and option one seems better, if not significantly so. But, my friend still insisted you should take option two - and here’s why.

The math above doesn’t account for the chance of multiple wins in the 10-jar scenario. That is, the potential reward is significantly higher. You could, however unlikely it may be, feed 10 heroes one at a time and get a special skill bump on every single one (well, the first 8, at least). This potential reward factor compounds almost exponentially over time. Considering we’re feeding heroes not just dozens, but sometimes hundreds of cards - doing it individually appears to be the way to go.

Before I posted this I searched the forum to make sure this hasn’t been discussed before, and it seems it has several months ago in a comment on the post linked below. Full credit to this contributor for getting there first, but I wanted to bring this topic to full light again:

Thanks for reading all the way through this boring math stuff, and if anyone sees fault in the logic here, please let me know! If there is an advantage one way or another, I think it’s important we all know about it!

UPDATE 1/17/19 Due to the latest game update, MAXED 3s now have a 5x chance to level up their special. That is, feeding five 2s of the same color or ten 1*s of the same color will produce a 100% chance of special level up. While I believe my math still stands for how best to get them TO that point, it’s now very quick and easy to save up the 5/10 at the end and make up for any missed special leveling - and in such cases SHOULD be fed all at once. (Incidentally, awesome update, thank you SG!)

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mathematically it looks right. technically, yeah, you have the possibility of getting multiple raises by going one at a time, and once or twice it might work out that way in your favor, but practical experience will likely tell you that its not worth it.
for instance, i play DND and i can say that i do not get a 20 5% of the time. nor do i get a 1 5% of the time.
i still try to go with 10 at a time when possible and most of my 4* are at 8 well before i hit the 3/60 mark. i’ve only had one 3* not make it either.

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So what you’re saying is the math is right… =)
Everyone will of course have differing personal experiences, odds are the opposite of guarantees. It’s easy to see patterns where you expect them, and as far as I’ve seen the 10-at-a-time theory is frequently espoused in E&P chatrooms. I don’t have any problem maxing my specials either - and I’ve always fed one by one. I don’t know DND well enough to understand your comparisons there, but I do appreciate the fact that the difference may be so little that it doesn’t matter which way you do it. If this is true, though, I’d still recommend my way: it’d save players a lot of roster space, and avoid plateaued hero strength while they’re needless waiting to collect ten to feed. Do appreciate your feedback though, thanks!

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the only reason i still vouch for the 10 altogether method is my lack of faith in RNG’s. despite their intended randomness, i have rarely found them to really be that random. i just don’t trust that 10 2% chances will succeed as well as a single 20%. maybe its just superstition.
my DND reference is regarding 20 sided dice. technically you should have a 5% chance for any of the numbers 1-20, but practical experience has shown i don’t hit a 20 or a 1 at that rate. often thats because of lopsided dice, which is how i feel about RNGs, i feel they are lopsided.
but, if the 10 separately still works the same then maybe the RNG is fairly accurate here.

I did refer to the same phenomenon here:

The bug is not in the code but the percentages displayed that get quite distorted when you are talking about 25% chances.

I have a vague recollection of a character advancing two levels when I fed it 10 heroes but I cannot be sure. If so, then it won’t matter. Based on my experiences above, I think the program runs the same routine 10 times rather than one routine with a variable number of cards.

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I’ve been trying to level my heroes faster by feeding them faster, less interested in the % skill increase than increasing the stats. With Kelile I would feed as many as I had when leveling, anywhere between 1-10. She reached max skill around 3rd ascension, faster than my other heroes, some of which aren’t at max skill.

It seems I usually get a skill increase when ascending to, not sure if just lucky or if higher chance when ascending. Also, it’s easier to max skill the higher *s because you have so much more leveling you have to do.

You always get a skillup when ascending (assuming the hero wasn’t max skilled already).

The math is right; that said, I don’t find much practical value in it. I’ve leveled a lot of heroes to 70 and never ran into an issue even on 4* (I’d suggest it’s absurdly unlucky on a 5* given how much exp is required).

3* or level 60 on either 4 or 5*, yeah that can be hit or miss as to whether I max it in time… but the time consuming nature of doing 1 at a time leaves little to recommend it in my estimation when you’re feeding 50 cards.

Valid point, and I do occasionally feed multiple cards at once to save time. I guess my real issue is how often I hear people insisting 10 at a time is the statistically best way to do it, and practically insisting newbies do so, when, at best, it doesn’t seem to significantly matter.

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I think the 10x version was better for 3*s in the “olden days” since you couldnt continue upgrading the skill once you hit max level. So it probably just an mantra that stuck.

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Ah, interesting point, didn’t know it used to be that way. Good to know!

so is it confirmed that 4 X 25% does not equal a 100% chance to increase and is actually 4 separate 25% chances?

No 4 x25 =100% guaranteed special increase

@Talisax You’d need to clarify interpretation here… what you say is either incorrect or not depending on this.

Are you going to stack (add) the percentages and only have 1 event? Then it’s 100%. Or 4 separate events at 25%, then it’s just a decent probability of being 100%.

(4x 25% chance over 4 separate events does not equate to 100%. It just equates to something close to 100% on average over time over a sufficiently large sample set, but in that set you may well have several runs that are significantly longer than 4 where the event does not occur… with other runs of the event occurring several times in succession.)

I think I was clear, but yes I meant 4 x 25% at once will guarantee you a special increase. Using it separately would not guarantee an increase. Hence 4x25

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Except 4 individual 25% chances gives a total of 4 skillup chances so you can get more than one.

The math comes out so close either way it doesn’t really make much difference when we’re talking either 4 or 5*'s, 3*'s are really the only problematic ones as someone alluded to above.

I did the math on this and found that one-by-one feeding has worse chances of gaining a special skill level. Feeding ten 2* heroes of the same color at once gives a 60% chance of not gaining a level (0.6^1). Feeding the same ten heroes one by one gives a 66.5% chance of not gaining a level (0.96^10).

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Huh? I don’t think what I see is what you mean. I feed ten of same color and have always maxed special skill before final assencion. I recently tried mixed colors and less than ten crunchy heroes. Now I am stuck with a Bane that’s fully leveled with a special skill of 4. Yuck!

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That sucks, Azure. I was looking at the specific situation of having ten 2* heroes of all the same color to feed to a same-colored hero. My question is whether it is better to feed all at once or one at a time. All at once gives a 60% chance of NOT gaining a level, while one at a time gives a 66.5% chance of NOT gaining a level. If you’re happy with feeding 10 to get one level, then all at once is the better option (40% chance of success). However, as others have pointed out, the one at a time method gives the chance of getting multiple levels since each single feed provides a 4% chance of getting a level. The trade-off overall with one at a time is a greater chance of getting nothing with a possibility of getting more than one level.

If you’re stuck with Bane at full ascension and max leveled, just keep feeding him heros to max out his skill.

If you cant do that, write a support ticket. :slight_smile:

Thank you. I appreciate your help.
You made my day better, hope yours is good.

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