XR57

Here's a math test (well, question), because a lot of people seem to think they're good at math

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As stated in the title, "Here's a math test (well, question), because a lot of people seem to think they're good at math." I'll probably deffer people over to here mid-conversation if they claim to know math. This question is what I consider to be a "fair" amount of difficulty for people discussing videogame math. It's about a ~15 minute question at worst, you could put a couple of these on a real exam.

Question:

Suppose you're playing a videogame. In this game, you have some integer-amount of hearts, which get subtracted from (by one) when you take damage. However, there's a passive item you can equip (a ring, or something) which has a chance to stop you from losing a heart when struck by an enemy. The odds start at 0%. Taking damage once raises them to 20%, twice to 50%, and three times to 90%, at which point additional hits will not raise the odds further. The odds are set back to 0 once the item activates.

  1. Over an infinite series of hits, how often does this item activate? (what is the proc rate)
  2. Over any finite series of hearts, what is the %-increase in lifespan?

Assume odds always start at 0%, i.e. that the item is not "gamed" in advance before a fight to start at 90.

Show your work (nothing trivial) and include at least 4 digits behind the decimal if the decimal extends beyond that :)

Edited by XR57

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2 hours ago, forc3dinduction said:

mmmm bait.

 

image.png.de76d0ddcb63c0741792d1ec7c95ac

Bzzzzt! Wrong answer!

Oh, and posted two hours ago, but edited one hour ago? Say, is this really your first answer?

Edited by XR57

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1 hour ago, XR57 said:

Bzzzzt! Wrong answer!

Oh, and posted two hours ago, but edited one hour ago? Say, is this really your first answer?

His message was edited only 2 mins after posting. You can see the exact time if you keep your mouse over the time.

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I don't know infinite series, but I like to challenge myself.

Suppose player has indefinite hearts, and an indefinite amount of hits have been evaluated. 

A "subseries", as used here, is a series of successful hits inflicted upon a player ended by a negation, or death of player.

A hit is negated, and subseries n starts.

Attack 1: 0% negation. All subseries thus must be at least one hit long.

Attack 2: 20% negation. Thus, 20% of subseries are 1 hit long, with a negation or death following.

Attack 3: A third attack in this subseries requires attack 2 to succeed (80%) There is a 50/50 chance of hit or negation. Thus, an additional 40% chance of subseries n being 2 hits long.

Attack 4+: There is a remaining 40% that the first 3 hits have struck. from here, the odds of negation are 90% There is a 36% chance of subseries n being exactly 3 hits long. 

There is a 3.6% chance of it being 4 hits long, 0.36% chance of it being 5 long, and so on. Thus, a further hit chance (applies only after the first 3 attacks,) of 36*10^-(x-3), where x is the amount of prior successful hits, and x equals or is greater than 3. 

Each subseries is begun by a hit and ended by a negation (the first hit taken in general cannot possibly be negated)

Thus, 20% of subseries have 50% effectiveness,

40% of them have 33% effectiveness,

36% have 25% effectiveness...

3.6% have 20% effectiveness 

0.36% have 16.666...% effectiveness

0.036% have ~14.2857% effectiveness

0.0036% have 12.5% effectiveness

0.00036% have 11.111...% effectiveness.

Continuing, (36*10^-(y-3))% of subseries have (100/y+1)% item effectiveness for y greater than or equal to 3.

Q1: Fiddling with weighted percents, I came up with about 33.1176% effectiveness. This makes sense (but may be a slight underestimate). Most negations will occur on the third or fourth attack, following 2 or 3 hits. Some negations may occur on the second strike, sometimes player might have a really unlucky streak.

Q2: This results in roughly +51.7856% hearts count.

Or maybe I'm completely wrong. I'm no mathematician, and I won't even pretend that anything I did was proper. I probably should have used limits or stuff like that, but... eh.

Oh, and BTW: this topic belongs on r/gatekeeping. You're gatekeeping math literacy.

PS: Math AP exams and the math SAT section, in my experience, generally ask for 3 places past the decimal.

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Clarification: All subseries have the same odds of outcomes, so a hypothetical subseries n is being used to generalize other subseries which make up the infinite series, and find the occurrence rates of subseries of certain lengths, and thus localized effectivenesses, which are weighted and combined into the overall item effectiveness throughout the infinite series.

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8 hours ago, PurdooSix said:

His message was edited only 2 mins after posting. You can see the exact time if you keep your mouse over the time.

Coulda sworn it was different when I last looked, maybe it rounds up to the nearest hour. Either way, still a bzzt.

4 hours ago, DominusPericulum said:

I don't know infinite series, but I like to challenge myself.

Ah, if you get them in principle you can just try and do what forc3 was doing, where you just evaluate it far out enough for the decimal not to matter. Though it's set up so that you can find a pattern and pull a fraction out.

4 hours ago, DominusPericulum said:

PS: Math AP exams and the math SAT section, in my experience, generally ask for 3 places past the decimal.

You think I haven't taken those? I'm past having taken my GRE's mate. 4 places was just what I felt like asking for.

4 hours ago, DominusPericulum said:

Thus

Sorry, that's a bzzt.

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On 7/25/2019 at 9:11 AM, XR57 said:

Bzzzzt! Wrong answer!

Oh, and posted two hours ago, but edited one hour ago? Say, is this really your first answer?

i was awake for about 20 minutes (after sleeping exceptionally bad due to the hot weather) when i saw the topic, and my statistics is like 10 years unused rusty.

post was edited bc i moved some fields in the screenshot to where i liked them better, done like 3 min after posting.

maybe i'm gonna give it some more thinking, i noticed some small details i found better solutions for.

Edited by forc3dinduction
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3 hours ago, forc3dinduction said:

better solutions for.

Yeah really cool to phrase "being wrong" as merely an "inferior solution"

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I feel like you are disguising your school homework with gaming terms to lure your fellow wastelanders to do it for you.

 e4a829e2-502a-42d4-898f-f3169442026b-bes

  • Haha 3

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On 7/25/2019 at 3:12 AM, XR57 said:

because a lot of people seem to think they're good at math

hah, beat your problem right there. I suck at math :P

  • Haha 1

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