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

I've got a bit of video-game related math that needs doing, and I haven't had a statistics class since 9th grade so I can't remember squat about how to properly figure this out.

Anyway, I'm farming some gear in Monster Hunter 3 Ultimate, but there's a particular crafting component I need quite a large amount of to finish it off.  I can do one of two things; either kill or capture the monster for the materials.  If I kill the monster, I can carve it 3 times for materials.  If I capture it, I can only get one chance at materials, but the odds of each component are greater than if I carved it.  The particular material I need has a 31% chance of being found while carving, and an approximate 45% chance of being found when capturing (there's a boost involved here that I'm not exactly sure of how strong said boost is, so just assume 45%).  There is also a part of the monster I can break off during the fight for an extra carving chance, though this particular bonus carve only has a 24% chance of yielding what I need.

I need 6 pieces of this particular material.  Assuming I get the bonus carve only every other fight (it's rather difficult to break off consistently), about how many times would I have to kill the monster to get all the materials I need?  About how many times would I have to capture it?

PS:  Anyone who can name the monster and/or materials off of these numbers wins all of my nerdy respect

oh my god the stats are boggling me!

Is it some kind of gravios armour? (for that guy who just does a wild stab in the dark with his very outdated and rusty knowledge)

Serious_Much wrote:oh my god the stats are boggling me!

Is it some kind of gravios armour? (for that guy who just does a wild stab in the dark with his very outdated and rusty knowledge)

And they say video games are bad for your mind (okay, I've not actually learned how to do statistics from this but at least I'm thinking about it  )

And no, nothing so awesome. Just some high-rank stuff while I prep to take on G-rank quests. And since I'm feeling generous, your second hint is that it's for a weapon, not armor

Okay, so I can at least narrow it down.

I'll take a wild stab in the dark and say you're a greatsword monger, cus they're awesome for the most part

Second though, it requires monster drops not ore, so it's a bone based upgrade for it.

Wait a sec- something breaks? Im a noob really compared to everyone else at MH, but that makes me think of the diablos. So maybe it requires diablos horns?

Is it a greatsword of the monster materials upgrade path which you need a *** ton of diablos horns for? (If this is even close to the truth I will have impressed myself)

Serious_Much wrote:Okay, so I can at least narrow it down.

I'll take a wild stab in the dark and say you're a greatsword monger, cus they're awesome for the most part

Second though, it requires monster drops not ore, so it's a bone based upgrade for it.

Wait a sec- something breaks? Im a noob really compared to everyone else at MH, but that makes me think of the diablos. So maybe it requires diablos horns?

Is it a greatsword of the monster materials upgrade path which you need a *** ton of diablos horns for? (If this is even close to the truth I will have impressed myself)

I can help you narrow it down by saying that none of those things are correct  

(also by saying that, while I am indeed a GS user (CURSE YOU RANDOM GUESSES) I am not trying to upgrade a GS)

LOL fail.. Oh well I'll just slink off and let others guess

Serious_Much wrote:LOL fail.. Oh well I'll just slink off and let others guess

Well at least you came here to talk, even if you didn't actually answer the problem

Seriously though, mathy people, I'd like to get some ideas on this. I'm sick of fighting this thing over and over.

Can you cut off the bonus part of the monster in both the kill AND capture scenarios or only when killing it?

 EDIT: yes, Im actuall gonna work this shyt out

Hart wrote:Can you cut off the bonus part of the monster in both the kill AND capture scenarios or only when killing it?

 EDIT: yes, Im actuall gonna work this shyt out

Yes. The bonus cut works in both situations.

Assuming you got the items 2/3 times and the bonus wen u carve it it would take 3-4 trys with out extra carve 5-6 capture would take 7-8. Either way its better to carve it since u get a 1/3 chance with 3 chances.4 if u get the extra

Wolfof Phyrexia wrote:Assuming you got the items 2/3 times and the bonus wen u carve it it would take 3-4 trys with out extra carve 5-6 capture would take 7-8. Either way its better to carve it since u get a 1/3 chance with 3 chances.4 if u get the extra

Bolded the problem. Assuming is not working out in practice. There have been fights where on a kill I get 0/3 carves, and I've actually never once gotten the part I need from the bonus carve yet. I know the percents via various wikis and resource sites for the game, but I realize a 30% chance doesn't strictly mean "if you do this 10 times you'll get exactly 3 items." It's the specifics beyond approximate guessing that I'm hung up on, and I can't mentally diminish the boringness (is that even a word?) of the grinding process on such shaky guesswork.

Reaperfan wrote:I realize a 30% chance doesn't strictly mean "if you do this 10 times you'll get exactly 3 items."

I've always found that observation interesting. Consider this:
If you have a 30% chance of getting a successful drop each time you try, then you have a 70% chance of failing. If you try 10 times, then you have a 0.70^10 chance of failing entirely and not getting a single drop. This translates to roughly below 3%. That means that you had over a 97% chance of getting at least one drop. So, it's really unlikely that you won't get a drop if you attempt it 10 times. People like to say that each roll of the dice is independent of the previous rolls, but I've always felt that regression to the mean will always play its part.

It's not guess work I noe how this stuff works. U have a better chance of getting it carving than capturing since u have more chance. It's the same situation capturing it just depends on luck as is the case with most games involving farming

OK, so I have voided the bonus 24% since it applie to both scenarios and it sounds lik its unreliable to get.

To get 6 of the items you need, it will take APPOXIMATELY 14 captures or 19 kills.

I have only used the initial values of 45% and 31% respectively because the probability of consecutive carvings yielding items is 0.096 (for 2/3 items) and 0.030 (for 3/3 items). As the probability of this happening is less than 0.1/10% in a practical scenario its easier to disregard that information.

Hopefully all that helps, although I might not have explained it too well

BrotherBob wrote:I've always found that observation interesting. Consider this:
If you have a 30% chance of getting a successful drop each time you try, then you have a 70% chance of failing. If you try 10 times, then you have a 0.70^10 chance of failing entirely and not getting a single drop. This translates to roughly below 3%. That means that you had over a 97% chance of getting at least one drop. So, it's really unlikely that you won't get a drop if you attempt it 10 times. People like to say that each roll of the dice is independent of the previous rolls, but I've always felt that regression to the mean will always play its part.

And that's the kind of detail that's reassuring

"At a 30% chance with 10 attempts, there is a 97% chance of at least one success and only a 3% chance of zero successes."

Now just change the variables up: "At a 31% chance of success, repeated 3 times per trial, how many trials will it take to reach 6 successes?"

Hart wrote:OK, so I have voided the bonus 24% since it applie to both scenarios and it sounds lik its unreliable to get.

To get 6 of the items you need, it will take APPOXIMATELY 14 captures or 19 kills.

I have only used the initial values of 45% and 31% respectively because the probability of consecutive carvings yielding items is 0.096 (for 2/3 items) and 0.030 (for 3/3 items). As the probability of this happening is less than 0.1/10% in a practical scenario its easier to disregard that information.

Hopefully all that helps, although I might not have explained it too well

I got bits and pieces of the explanation, or at least I think I did (0.030 for 3/3 carves and 0.096 for 2/3 means there's only a 3% chance that every carve will give the item I want and a 9.6% chance of two carves?). Still not sure I fully understand though. Maybe I really do need to go back to school  

Can't say I'm happy about the 14 or 19 numbers (these fights can take 15-30 minutes each), but at least it's something to start with. I'll just have to go at it again and hope it ends up not being quite that much  

Like I said man it just based on luck

Reaperfan wrote:
I got bits and pieces of the explanation, or at least I think I did (0.030 for 3/3 carves and 0.096 for 2/3 means there's only a 3% chance that every carve will give the item I want and a 9.6% chance of two carves?).  Still not sure I fully understand though.

It means that there is less than a 10% chance that when you kill the enemy and carve it three times, that you will get 2 items--and less than 3% that you will get all 3 possible. This is basically the same as what BrotherBob said about dice rolls.
When you compare these probabilities to the 31% chance of successfully carving an item (the FIRST successful attempt only) the difference is so large that I think its fine to disregard the other carving attempts when comparing the efficiency of capturing vs killing.
So IMO capturing would appear to be the better method because of its higher probability, but bear in mind that killing still has the POTENTIAL to be faster due to the other factors, but since they have a relatively low chance of occuring I would choose the more reliable method: capturing.

Also just FYI the equation I used to get the number of times is

e=n*p

e=expected number of successful attempts
n=number of trials
p=relevant probability

So to calculate the number of trials needed to get 6 items with a 45% chance of success (capturing obviously) the equation reads

6=n*.45 then reorganise it to find n

n=6/.45

n=13.3, rounded up to 14 cause I think its better to assume the worst and hope for the best.

The methods used by Wolfof Phyrexia and Hart are really sound, and I'd go with it. Expected value is easier to understand and in my opinion more useful than more detailed information such as "in 10 trials, you have 'x'% of 10 drops, 'y'% of 9 drops, 'z'% of 8 drops... etc." Correct me if I'm wrong, but I'm pretty sure that the number of drops obtained by calculating the expected value indicate the most likely scenario. Of course, I could be wrong; I've only got Grade 12 Data Management behind me.  

You really have two questions:  1.  What is the most efficient method?  2.  How many attempts would I typically expect this method to take to reach a goal value?

Here are the relevant points to question 1, best I can tell:

1.  When killing, you get 3 carving chances
2.  When capturing, you get 1 chance at higher odds

Once you have determined the more efficient method, you can then calculate the expected #attempts.  Things like total needed materials and the bonus cut are not relevant to the decision of the most efficient method.

What I need to clarify here are the *exact* odds of both methods.  If 3 carving chances = 3 attempts at 31% EACH, then you'd pick that for sure.  However, if by 31% you're saying that killing and 3 carving attempts = ~31% chance, then capturing looks better before considering other factors.

One last question is whether killing or capturing takes considerably more or less time than the other.  Hart's #'s, assuming that you have a ~31% chance of the item/kill, look fine (~19-20 expected kill attempts, ~13-14 capture).  However, if capturing is materially slower, it might still be efficient from a time standpoint  to kill.

TheMeInTeam wrote:What I need to clarify here are the *exact* odds of both methods.  If 3 carving chances = 3 attempts at 31% EACH, then you'd pick that for sure.  However, if by 31% you're saying that killing and 3 carving attempts = ~31% chance, then capturing looks better before considering other factors.

One last question is whether killing or capturing takes considerably more or less time than the other.  Hart's #'s, assuming that you have a ~31% chance of the item/kill, look fine (~19-20 expected kill attempts, ~13-14 capture).  However, if capturing is materially slower, it might still be efficient from a time standpoint  to kill.

With the carving, each carving attempt has a 31% chance individually. Given what's been said though, it sounds unlikely for more than one successful find to happen per fight.

Capturing is actually faster than killing, shortening each fight by ~3-5 minutes since it involves a Pokemon-esque mechanic of capturing it as it reaches critically low health and essentially allowing me to skip the final stages of the fight.  With the average fight length on a kill attempt being 15-20 minutes, it's hard to say if it's a significantly impactful length of time saved.  Though given enough attempts it certainly wouldn't be negligible.

Just some perspective, assuming that I got this right. If you have a 31% chance of getting the drop in one try and 3 tries per kill, then you have a ~67.15% of getting at least one drop per kill.

With the carving, each carving attempt has a 31% chance individually. Given what's been said though, it sounds unlikely for more than one successful find to happen per fight.

If you have 3 rolls at 31%, you have a 69% chance of failure on each roll, or a ~33% chance of failure on 3 rolls.

This puts your success rate of getting at least one item on 3 rolls around 2/3, which is much higher than ~45%.

Capturing is actually faster than killing, shortening each fight by ~3-5 minutes since it involves a Pokemon-esque mechanic of capturing it as it reaches critically low health and essentially allowing me to skip the final stages of the fight.

I'm not familiar with MH at all, but if capturing is FASTER than killing, it's definitely not good to compare it with pokemon, where capturing is consistently slower, and much so.

It's not a good idea to discount time/fight.  In determining which method will get you the items more quickly, it's a *crucial* variable and every bit as important as the success rate on any 1 attempt.

It sounds like kills are more efficient on a per fight basis, but how many fights/hour can you do with either approach?

TheMeInTeam wrote:I'm not familiar with MH at all, but if capturing is FASTER than killing, it's definitely not good to compare it with pokemon, where capturing is consistently slower, and much so.

It's not a good idea to discount time/fight.  In determining which method will get you the items more quickly, it's a *crucial* variable and every bit as important as the success rate on any 1 attempt.

It sounds like kills are more efficient on a per fight basis, but how many fights/hour can you do with either approach?

The Pokemon example was just to provide a perspective to help those unfamiliar with the mechanics of MH understand the process. I'm well aware that the analogy breaks down in every aspect except for the "capture while at low health" part. Rule of thumb for internet analogies; look for what works in the comparison before looking at what doesn't because what works is more likely the point they were trying to convey in the first place. Though maybe I could have emphasized that MH fights take 20 or so minutes as opposed to Pokemon's 45 second fights to better show that the extra effort is more beneficial in MH since that last 15% or so of the opponent's HP takes so much longer to get rid of.

Which actually segues very well into the next bit about fights/hour. As said a few times before, the average time of a fight going for a kill is approximately 15 to 20 minutes, meaning 3-4 fights per hour. Capturing reduces the time of a fight by approximately 2-4 minutes since it's that much less HP you have to chip away. My logic is telling me that this 2-4 minutes would not do me much good if I was only in it for a few fights, and it would take a few hours of fighting for the time-saving to be genuinely beneficial. Going with the worst-case scenario (saving only 2 minutes a fight and assuming all fights run long at 20 minutes instead of 15 minutes), it would take 10 fights before I've actually reduced the total number of fights I'd have to do (2 minutes saved every fight for 10 fights saves me 20 minutes, or one whole encounter). Anything less than 10 fights and I'll be having the same number of encounters as if I was going for kills.

So...yeah. Sounds like kills are going to be more efficient

Anything less than 10 fights and I'll be having the same number of encounters as if I was going for kills.

Fights end with capture though, don't they?  If so fight time is not static and you can't assume such easy break points.

2-4 minutes is 10-20% of 20 minutes, and in the 13-27%ish of 15 minutes.  Probably a complicated way to look at it compared to just doing this:  Let's take an *aggressive* look at capturing time savings, to see if it's even plausible that they can yield faster materials.  Let's therefore assume 4 minutes saved out of 15.  If even that can't make it win, we don't need to worry about the actual time much if the actual times are somewhere within your estimates on average.

Killing:  4 fights per hour
Capturing:  5.454545 fights per hour.

Expected rate from K:  4 * .67 = 2.68 expected items/hour
Expected rate from C:  5.454545 * .45 = 2.454545 expected items/hour

Assuming that this 31% and 45% are both the probability of getting the exact item you want per "carving" (3x 31% on kills, 1x 45% on captures), it's hard to picture capturing beating killing based on your estimates, because even at the very aggressively capture-favored ends of your estimate, the time saved doesn't appear to be enough.

Also note that by discounting the possibility of multiple items per kill, we have actually low-balled that estimate as well (it will happen at least some of the time and is reasonably likely to happen across a few hours).  Unless your time estimates are way off or the probability of desired item is inacurrate for one or both of these methods, killing looks like a clear favorite.