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

No.

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

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LOLā¦ so you meanā¦ 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 doesnāt.

Acme

It is more food efficient to level up ten at a time. And it is quicker because you donā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 donā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 Iā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 cā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 animationsā¦

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 donā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, thatās what the green leveler gets. If I have 18 red, the red leveler gets 10 red and then 8 redā¦

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 againā¦ so I yanked it.

I have a headache. Iām going to mash some yetis into paste now.

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Without looking closely, you have an error somewhere. The odds of exactly one level-up are way below the theoretical odds.

Acme

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I THINK youāre correct.

Now see, that makes sense, and doesnāt require me reading through probability tables and pulling up my calculator app.

Essentially what youāre saying is that it doesnāt really make a significant difference either way, so just level however you like. Sounds good to me!

OK, I did my math right this time: I thought it seemed odd, but I was in too much of a hurry to concede that I was initially incorrect, so I rushed it.

I neglected to factor in the number of times each possible combination could come in. Hereās the updated chart.

Without really explaining too muchā¦ feeding 10-at-a-time (1* same color) has an expected value of 0.2ā¦ and so does feeding 1-at-a time ten times.

EDIT: DANG ITā¦ I still have 98% and 2% shown on the bottom, that should be 80% and 20%ā¦ /sigh/

EDIT 2: fixed the screenshot aboveā¦ whewā¦

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You are moving in the right direction!

If it helps convince youā¦I have a PhD in Chemical Engineering and spent years as a consultant before I left the field 13 years ago to teach high school math. This is stuff I live for!

Acme

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Perfect. You added in the number of combinations that lead to each occurrence. I like the approach you took to this.

Nice work, sir!

Acme

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Worst I have had is a 3* at 3-50 with 5/8.
I have never had a 4* or 5* not at 8/8 before max, all but one before final ascension.

3* I feed only 1* on-colour. Rest whatever I get (but on-colour).

My Khagan at 2-60 is 8/8. At 2-1 he was 2/8. I was up to that point strictly 10x 1* on-colour. After 2-1 I decided whatever ā¦

Wait, wait, waitā¦ so the conclusion is that 10 x 2% actually is the same as 1 x 20% (as I had initially believed)? You guys are confusing me here.

Forgive me, I donāt have a doctorate degree. I only have a masterās degree in B.S.

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This is what Iāve said all along. You expect to max out the special skill at the same point either way. They are not the same, however, as one at a time has far more variability in the results.

Acme

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I had a midterm in my dynamic modeling class earlier this year that included probabilities and Iām very disturbed that I could have gotten a simple question like this wrong?

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Donāt be. You did correct probability calculations which is something most people cannot do!

Acme

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