A quick, nerdy statistics problem for those who actually know statistics

Alright guys, I've got another one.

A new item this time, but I have 2 choices of monsters because the monster that drops it has a particular alternate variant where the numbers are spread differently. Anyway, same rules apply in terms of what carving and capturing are. 3 chances to carve per fight, one chance to capture. If it becomes important, this fight is a bit longer than the last one, averaging 25-30 minutes, with capturing shaving about 3-5 minutes off of that time.

Alright, starting with the normal variant of the monster, things aren't too complicated. Each carving attempt has a 16% chance of producing the item I want. A capturing attempt has a 22% chance of success. Going off what's been mentioned previously in this thread, I think it's safe to assume killing this one is better than capturing.

However, with the alternate variant of the monster the numbers are different. Killing the variant has a 15% chance on a carving attempt, with a 23% chance on a capture with an additional 10% chance on a capture that results in 2 of the items I need on top of the chance at one item (meaning in one capture attempt it is possible to get 3 total of the items I need). And that's where I get a bit iffy on what's best. Do I kill or capture this one? Is capturing this one more effective than killing the normal version, or are the chances of those additional 2 bonus items too small to be considered worthwhile?

Going off what's been mentioned previously in this thread, I think it's safe to assume killing this one is better than capturing.

Definitely.  3 carvings at 16% gives you a ~40% (slightly higher) of getting at least 1 item.

Alternate Variant comparison is going to take a little more rigorous stats to make sure, still nothing at a high level, but I'm really rusty.  Let's start with normal variant:

http://stattrek.com/probability-distributions/binomial.aspx?tutorial=stat

b(x; n, P) = _nC_x * P^x * (1 - P)^{n - x}

We need nCx too, found here http://stattrek.com/statistics/dictionary.aspx?definition=Combination

_nC_r = n(n - 1)(n - 2) ... (n - r + 1)/r! = n! / r!(n - r)! = _nP_r / r!

Ick.  What a mess.  Let's just use n! / r!(n - r)! 

P = .16
n = 3
Q = .84
x = number of successes, used below as 0-3
C = Variable since r=x here.  I think.

Plugging in the #'s, with minimal rounding we get:

0 .5927
1 .3387
2 .0645
3 .0041

Expected items/kill on common variant = 1(.3387) + 2 (.0645) + 3(.0041) = .48

Now, the Alternative Variant:

Killing:

0 .6141
1 .3251
2 .0574
3 .0038

Expected items/kill on alternative variant = .45

Now, for capturing we have a different situation again.  This one is actually easier.

Expected items/capture on alternative variant = 1*(.23)+2*(.1) = .43

Expected items/capture on the common is miserably terrible, = .22

Only factor remaining here is time savings.  Let's be aggressive again.

Killing Commons: 2.4 kills/hour * .48 = 1.15 items/hour
Capturing Alternates: 3 kills/hour * .43 = 1.29 items/hour

Interesting.  But what if we're aggressive the other way?  30 minute fights, 3 minutes saved:

Killing Commons: 2 kills/hour * .48 = .96 items/hour
Capturing Alternates: 2.2222 kills/hour * .43 = .9555555 items/hour

Long story short:  This time, your actual time saved in capturing matters.  If it's making fights take 20 minutes instead of 25, capturing is stronger.  If it's making them take 27 minutes instead of 30...well...it isn't.  Killing wins on a "per fight" basis consistently here, but the time/fight has a significant impact on what is ultimately the faster method for attaining this item.  If you really care a lot, it's time to start timing battles  .

Note that if you only need one instance of the item, killing is obviously the way to go.  Capturing only wins out over time due to the odds of proc 2 extra items in one fight.  If you're trying to farm 100 of these and capturing is saving you 5 minutes, you definitely want to capture.

One final thing to note is that because your individual fights take a long time, probability can take a dump on you no matter what you choose.  Even across a day, your sample size is going to be small, small enough that your actual value may differ from the expected value considerably.

You, sir, have impressed me and earned the respect of my mathematically untrained mind.

Tracking times isn't actually that hard to do since the game itself records each individual hunt's duration and tells you precisely how long it was down to a tenth of a second upon completion, as well as having a clock next to your health bar that ticks down every 5 minutes of the hunt (hunts typically have a max time of 50 minutes, any longer and you automatically fail, so this is to show a quick estimate of how much time you have left as well as what I use to get timeframes like 25-30 minutes). It would just be a matter of actually writing down the results of a few hunts and finding an average based off the exact numbers rather than the estimates from the clock if we want specifics

So I guess for this instance it sounds like killing the normal and capturing the variant are about on par with each other, give or take a few minutes on a per-hunt basis. I actually don't need too much of this item (only 3), so I guess I'll aim at capturing the variant and hope the timecards play in my favor. If it runs long, I won't have lost much time total since I shouldn't be needing many fights anyway.

Lastly, I'll admit to posting this one more for the fascination of the thought experiment rather than actual desire to speed things up like last time. For your amazingly detailed response I'm deeply grateful on that front (and am going to spend a good while still after posting this to try and fully understand the equations and links you used ), but if you'd rather me save my inquiries and your brainpower for when it's of actual impact I can understand. Since this looks like a lot of effort you put in I feel obligated to officially ask though; do you mind me asking these videogame-related word problems purely out of curiosity or would you rather save your mental effort for when it will be of actual use?

Haha I don't mind.  I can't promise I'll ALWAYS be the one answering, but I was in the mood for it.  The only frustrating thing is how much my once-solid ability in statistics has eroded.  I barely remember anything.

Part of the reason I did this is to shake off rust.  That said, do try to understand my approach at least.  It's far from impossible that I made an error, especially with the nCr portion of the equation.  Still, the numbers seem to check out for me.

Ah, but if it's just doing the 3 kills iteration, I made an excel sheet that handles that automatically (calculating .45 instead of .48 for killing alternative I only listed because it involved literally 10-keying in one cell to get the different result).  That would literally be effortless now.  This whole thing took less time than you're probably imagining.  The only real snag is that I had to read up and try to remember how to do it at all, which took a little time, and then type it up, which took less (I'm a fast typist, probably 80-100 words/minute comfortably, though it's hard to come up with what one wants to say at such a rate).

There are usually methods in any academic setting that will greatly improve the time it takes to both learn and implement things.  So few of my peers even considered that when I was in school, and it's still rare today.  Ones approach can mean the difference between struggling and getting a B on a graduate elective microenomics final, or making/studying off notecards for an evening test the day of the exam only and getting the highest score in the class.

Alright, here's another one. This time it's to find out just how ridiculously lucky I managed to get on a recent hunt.

No fancy buildup this time just numbers. I had killed a very large monster who grants a large number of carves, 6 carving attempts rather the normal 3. Now while not the item I was searching for on this particular hunt, this monster does have 2 very rare items you can carve from it. One only has a 5% chance of being found on a carving attempt, and the other only has a 3% chance. On this particular kill I found not one, but two of each of these rare items. Since this is a Dark Souls forum I'll assume most people will get this reference, but this felt like going to New Londo to farm for titanite Chunks and to come out of a single run with multiple Slabs.

What exactly were the odds of finding as many of these items as I did in a single run?

this is monster hunter, you do one farming method till it gets boring then you do the other, also every one of the MH games seems to have a desire sensor which makes it that much harder to get what you want, I say this from experience having tried to collect 10 of a common(50%+ drop rate) item and not picking one up for 3 runs straight.

also not many monsters in 3 ultimate only have one breakable part, thus the choices are... arzuros, volvidon, lagombi and... the bird wyverns (G Jaggi, G baggi, G wroggi)

sparkly-twinkly-lizard wrote:this is monster hunter, you do one farming method till it gets boring then you do the other, also every one of the MH games seems to have a desire sensor which makes it that much harder to get what you want, I say this from experience having tried to collect 10 of a common(50%+ drop rate) item and not picking one up for 3 runs straight.

also not many monsters in 3 ultimate only have one breakable part, thus the choices are... arzuros, volvidon, lagombi and... the bird wyverns (G Jaggi, G baggi, G wroggi)

Are you responding to the opening post, the most recent issue in my last post, or just speaking about the issue of drops in a general sense?

first post I think? seriously though which monster is it? or did someone guess it and I didn't see it?

Well in the OP you say it has a breakable part for an extra carve chance. Taking that literally then the only monsters it could be are the Barroths but the carving stats don't match. Unless you meant 'breakable' and you meant a tail but thats' a different story

Well since you seem versed in MH I can be specific, but I'll say that I was using vague language in the OP to convey concepts to those unfamiliar with the details of the games.  With that said, the specific part being broken off was actually me describing cutting off a tail, and I was not including inherent questing or wound rewards in that instance, so use that to widen your search parameters

Imma keep you guessing for a few posts for the fun of it though, and will say that nothing you guessed in your first post was the correct monster

a tail cut huh? most likely would be one of the rath's (los or ian) if you were going for a rarer part but as you're going for a middling rarity item for entry into g rank... im going to guess lagicrus as lightning is effective against the boss required to enter g rank, either that or zinogre...

sparkly-twinkly-lizard wrote:a tail cut huh? most likely would be one of the rath's (los or ian) if you were going for a rarer part but as you're going for a middling rarity item for entry into g rank... im going to guess lagicrus as lightning is effective against the boss required to enter g rank, either that or zinogre...

Keep in mind the opening post was made quite a while ago and has been resolved. I've already beaten the Goldbeard Caedeus and have been working in G-rank for a while (Normal Shot Lv3 tears him to pieces, btw)

That said to further narrow it down if you're trying to guess what weapon it was, I wasn't making it to use it as a main weapon since it's rather weak in solo play (though when I get access to multiplayer I have ideas for it). Also, the monster part I needed was not the main ingredient in the weapon and rather a secondary part (like how sometimes a Gobul-based weapon may require a Nibelsnarf part, despite still being a Gobul weapon). As a further hint, Gobul and Nibelsnarf were used entirely as examples and had no part in the particular weapon, so you can eliminate anything with them in it as possibilities

hmm... well status weapons tend to do better in multiplayer rather than solo and you do use bow guns... but the gun im thinking of doesn't use the right parts... maybe that sleep element lobster hammer? or something froma purple ludroth? im lost, too many weapons...

sparkly-twinkly-lizard wrote:hmm... well status weapons tend to do better in multiplayer rather than solo and you do use bow guns... but the gun im thinking of doesn't use the right parts... maybe that sleep element lobster hammer? or something froma purple ludroth? im lost, too many weapons...

Alright, the main ingredient of the weapon is a plant rather than a monster or wildlife part and the weapon itself is a lance.

plegis needle (mighty plegis)? soo.. brachydios for the ebonshells?

sparkly-twinkly-lizard wrote:plegis needle (mighty plegis)? soo.. brachydios for the ebonshells?

I figured that was too much narrowing down

You are correct sir

But seriously, desire sensor aside what are the odds of getting 2 Deep Dragongems and 2 Dark Dragongems in a single Goldbeard Ceadeus run?

it happened the only time I killed Gold beard... so probably not too bad, also, a suggestion, you can use the mini uragaan event quest to farm g rank uragaan parts prior to hr 7 where you'd normally encounter them, s'what I did to get my maxed out uragaan hammer with 1500 dmg and 400 slime at purple sharpness! maybe you could use t to get the armor as that stuff lets you tank quite a bit.

Reaperfan wrote:Alright, here's another one.  This time it's to find out just how ridiculously lucky I managed to get on a recent hunt.

No fancy buildup this time just numbers.  I had killed a very large monster who grants a large number of carves, 6 carving attempts rather the normal 3.  Now while not the item I was searching for on this particular hunt, this monster does have 2 very rare items you can carve from it.  One only has a 5% chance of being found on a carving attempt, and the other only has a 3% chance.  On this particular kill I found not one, but two of each of these rare items.  Since this is a Dark Souls forum I'll assume most people will get this reference, but this felt like going to New Londo to farm for titanite Chunks and to come out of a single run with multiple Slabs.

What exactly were the odds of finding as many of these items as I did in a single run?

Making life a little harder hehe.

For the 5% item you have a ~3% chance to get two of them in six carvings.  For the 3% item, you have about a 1.2% chance.  But that's for finding two of one alone.

If two of the carvings are one item, that leaves four carvings to get the other one twice.  Even if we don't factor that, we're already in the territory of less than a tenth of 1%.  You might actually have a higher probability of getting multiple slabs.  What's the slab drop% at max item discovery?

By the way, your odds of getting at least one item per run are pretty decent given six carvings, especially if you consider the 8% of getting at least one useful item (you could realistically expect one out of a 5% or 3% item on about 40% of runs if I'm not mistaken).  Once you need only one of them specifically, however (probably the 3% one), it falls to roughly 17% per kill.