No.

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

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?

Patrickcw:

No.

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

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 doesnāt.

Acme

TGW:

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

It is more food efficient to level up ten at a time. And it is quicker because you donāt 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 donāt 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 Iāll 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 cāmon. 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¦

TGW:

Oh, hams. I have plenty of those. And I donāt 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 Iāll 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.

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 donāt 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, thatās what the green leveler gets. If I have 18 red, the red leveler gets 10 red and then 8 redā¦

Acme

Acme

Fizban:

Feeding 10 1* same-color heroes, one at a time, has an expected value of +0.01737, w

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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Gryphonknight:

You table is missing

Yeah, I realized that upon looking at my screenshot againā¦ so I yanked it.

I have a headache. Iām 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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Fizban:

Iām going to mash some yetis into paste now.

Always the correct answer!

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TheAcmeSalesRep:

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 doesnāt.

I THINK youāre correct.

TheAcmeSalesRep:

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.

Now see, that makes sense, and doesnāt require me reading through probability tables and pulling up my calculator app.

Essentially what youāre saying is that it doesnāt 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. Hereās 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¦

4 Likes

Patrickcw:

I THINK youāre correct.

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

2 Likes

Fizban:

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.

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

2 Likes

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 donāt have a doctorate degree. I only have a masterās degree in B.S.

1 Like

TGW:

Wait, wait, waitā¦ so the conclusion is that 10 x 2% actually

isthe same as 1 x 20% (as I had initially believed)? You guys are confusing me here.

This is what Iāve 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 Iām very disturbed that I could have gotten a simple question like this wrong?

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Donāt be. You did correct probability calculations which is something most people cannot do!

Acme

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