# Special refuses to level up - whats the worst you have seen?

I agree 100% with Fizban. You have a slightly better chance when feeding one at a time, because you can level up multiple times using the same number of heroes. Occasionally you get lucky and level the same hero’s special 2x in a row.

I’m not really sure where Patrickcw is getting the idea that feeding them one at a time has a lower chance than 10 at a time…

It’s been a long time since I had a math class, but I’m pretty sure 10 x 2% is the same as 1 x 20%. Unless something has changed since my school days with “new math” and all. Entirely possible, kids these days do their homework on ipads, in my day we used stone tablets.

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The expected time to max is exactly the same either way. You are correct that the odds of leveling up EXACTLY once is 18.3% in your scenario. But you could level up twice…or three times…or even ten times. (Well not ten because it stops at 8!)

If you feed ten 1* heros, you have a 20% chance of leveling up the special. Do that 5 times and you EXPECT to level up once. You might not level at all… You might level more than once. But you expect to level once.

If you feed single 1* heros, you have a 2% chance. Do that 50 times and you EXPECT to level up once. Again, it might happen more or less, but that’s what you expect.

In both cases, you used fifty 1* heros to expect one level up of the special.

Acme

10x2% is absolutely not the same as 1x20% when you are talking about probability.

I’m not talking about the probability of any given level up though. I’m talking about the EXPECTED time to max the hero. And that is the same either way.

Ah, okay. That is one class I didn’t take, and one that still baffles me. The whole flipping a coin thing, 50% heads vs. 50% tails. So flipping the coin 100 times is supposed to, on average, land 50 times on each (but usually doesn’t follow exactly due to margin of error). So in that case… is the coin 49% likely to land on heads and 51% tails, or vice versa? Or is that a case where probability doesn’t apply?

correct.

It reminds me of Wu Kong. Really good chance of x2 damage with tiny chance of x0.1 damage.

see notes.

I really need to learn how to use a binomial calculator.

### Notes

Click for notes

FIN

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How can you determine expected time to max a special skill without considering the probability?

Probability applies. The expected value of something is the probability it will occur times the value if it does occur. The expected value of multiple events add together.

The expected value of leveling up a hero using ten 1* heros is…

20% * 1 = 20%

The expected value of leveling up a hero using one 1* hero ten times is…

10 * 2% * 1 = 20%

So either way, after fifty 1* heros, you expect to level up the special once. Expected value is a long-term average, however, while actual results very heavily on both sides of the curve

This is why I love Wu Kong. You don’t have to be a math expert to see him kill everything and conclude that he is good in spite of the many misses.

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So… okay. You seem to be confirming what I already thought to be true. Where does this 18.3% figure come from?

I didn’t say you don’t consider the probability. But there probability of a single feed is only one part of the calculation. See my last post for more detail.

Acme

If you feed one 1* hero at a time, there is an 18.3% chance you will level up the special EXACTLY ONCE after 10 heros have been fed.

You could level up less (zero times) or more…

Acme

No.

1 - (1 - 0.02)^10 = 18.3%

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LOL… so you mean… the 1.7% difference includes the possibility that it will level up MORE than once?

In that case, how could anyone possibly argue AGAINST feeding one at a time?

Wrong. This is the probability of leveling up EXACTLY ONCE. You can level up more than once feeding them one at a time. The expected value takes that into account. Your calculation doesn’t.

Acme

It is more food efficient to level up ten at a time. And it is quicker because you don’t go through the animation as much. So those are two strong arguments against one at a time!

Acme

Oh, hams. I have plenty of those. And I don’t mind animations if it gives me a better chance at leveling a special skill. Hell, if I can watch a 30 second mystic vision on some really dumb product that I’ll never buy in exchange for a gem and some arrows, I can wait 5 extra seconds for a slightly better chance to level up a special skill.

I mean c’mon. This is a game where it takes months to pull decent heroes and get ascension mats, I would think most players have the patience to deal with some animations…

But either way, you expect to max out the skill after the same number of heros fed. One at a time gives you a much higher variability in when it happens. But if you maxed out 1,000,000 heros each way, on average they would hit their max special skill at very nearly the same level.

Because of this, I just don’t worry about how many heros I am feeding. When my hero storage is full, I feed. If I have 7 yellow, I feed my yellow leveler 7 heros. If I have 2 green, that’s what the green leveler gets. If I have 18 red, the red leveler gets 10 red and then 8 red…

Acme

Acme

You table is missing

00000 00010
00000 00100
00000 01000
00001 00000

00010 00000
00100 00000
01000 00000
10000 00000

etc.

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Yeah, I realized that upon looking at my screenshot again… so I yanked it.

I have a headache. I’m going to mash some yetis into paste now.

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