Masterpieces - the numbers game

[Roalith]

I gotta say I laughed when I saw your post Arindel

Hmmm... my dog was trying to hump my arm when I made that MP breastplate...

 

[Roalith]

Sorry, I had to. Note this is predicted chance: No matter what, the supposed 'real' chance of producing an MP with Mythic's RNG is 2%, or 1 in 50.

The median (most frequent) occurance of MP is 1-35. IE: MPs happen within the range 1-35 more often than not.
Check

The average (mean) occurance is 1 in 50. This is because every time that you do not produce an MP within the first 1-35 makes, your average (mean) occurance raises the chance of MP to 1-50. IE: streaks of 36-Infinity makes with no MP, increasing the average above 1-35.
Check

However, because the median is lower than the mean, there is a greater chance of MP happening within 35 attempts of a previous MP. Note: A greater chance. Still not a certainty, I'd say nowhere even remotely near a certainty. We see "streaky" (IE: Better-than-the-mean) results from the RNG more often than we don't see streaky results, because of this.
Check

Therefore, using the hinge method, relying on "streaky" results, has a higher-than-mean (average) chance of producing an MP.
?

 

[Roalith]

I'll start by saying I made this graph myself, using paint

However, this does look more or less right to me. The probability rises faster within the first 35 remakes. It rises higher, but slower, within the 35-50 range. It rises to certainty at the end of the infinity side of the remake axis, but it rises very, very slowly.

This diagram is based on proven data that mythic's RNG is biased into producing a median of 1-35, a mean of 1-50, and that it could (theoretically) take an infinite number of attempts to produce a masterpiece.

Hell, even Chretien's data shows an average of 1-35 for a smaller sample of results. I'm willing to place odds that the more he makes, the higher his average becomes, because of the erroneous 'dry run' results.

Any way to test this theory with your proggy, Jenkz? Would need to show, for a 10,000 MP sample:

# of remakes
# of MPs where 1 was made within 35 remakes of another
# of MPs where 1 was made in the 35-50 range
# of MPs where 1 was made in the 51+ range
% of MPs produced in the 1-35 range
% of MPs produced in the 36-50 range
% of MPs produced in the 51+ range

We could then break down the data into % produced in < 50 tries, and % produced in > 50 tries. May well come out as a 50-50 split between the two. Would be interesting to see if it doesn't, though.

 

[Jenkz]

there is a greater chance of MP happening within 35 attempts of a previous MP

Chance of a masterpiece in 1 make = 2%

Chance of a masterpiece in 2 makes = 3.96%

Chance of a masterpiece in 10 makes = 18.29%

Chance of masterpiece in 35 makes = 50.69%

Chance of masterpiece in 50 makes = 63.58%

Chance of masterpiece in 100 makes = 86.78%

the chance of obtaining a masterpiece does not tail off after 35 makes. if anything, you make hinges and get a masterpiece, woot, you've made a masterpiece hinge instead of the masterpiece item you want.

as i said before, if you take really small sample sizes which you are doing atm, you will get lucky, you will find errenous results.

the maths though is pretty simple:

Chance of MP = 1 - (0.98^numberremakes)
graph that for 1-35 and 36-oo

i think all you are playing on here is the 50% chance of a masterpiece in 35 remakes - 1 in 2 times you'll get one in less than or equal to 35 remakes.

making hinges doesnt alter the maths at all, you may as well go make a cup of coffee or do what whoever said above for 10minutes and come back, or just make another 35 attempts. if you make 35 attempts and hinge till MP, the next item you make will still be the 36th attempt of the item itself, not the 1st.....

if this method seems to be working for you atm, which it obviously is, then who am i or anyone else to tell you not to do it, just the mathematics behind whta you are saying will (if mythic are correct in saying its a flat 0.02 chance of getting a MP) oneday catch up with you, and you'll still have to remake an item over 100 times to get an MP.

 

[Roalith]

Originally posted by Jenkz

Chance of a masterpiece in 1 make = 2%

Chance of a masterpiece in 2 makes = 3.96%

Chance of a masterpiece in 10 makes = 18.29%

Chance of masterpiece in 35 makes = 50.69%

Chance of masterpiece in 50 makes = 63.58%

Chance of masterpiece in 100 makes = 86.78%

Increase in chance from 0 to 15 makes = 26%, or thereabouts, right?

So, the increase in chance from 35-50 makes is only 13%, or so, right?

So, representing the percentage chance of the increase in making an MP in 1-50 makes:

40% of the increase in the chance of MP from 1-50 remakes occurs in 1-15.
40% of the increase in the chance of MP from 1-50 remakes occurs in 16-35.

80% of the increase in the chance of MP from 1-50 remakes occurs in the 1-35 band.
20% of the increase in the chance from 1-50 occurs at 36-50.

35 out of 50 attempts is 70% of the total number of attempts.
The last 15 attempts, 36 to 50, then, makes up the last 30%.

70% (1-35) of the attempts produce 80% of the increase in the chance of success in 1-50 odds.
30% (36-50) of the attempts produce 20% of the increase in the chance of success in 1-50 odds.

That's a disparity of 20% of what the figures should be. If the results don't tail off, 70% of the attempts should produce 70% of the increase. The last 30% of the attempts should produce their proportion of the increase.

Which means the probability does tail off at 36-50. That sound right?

 

[Roalith]

Originally posted by Jenkz

if this method seems to be working for you atm, which it obviously is, then who am i or anyone else to tell you not to do it, just the mathematics behind whta you are saying will (if mythic are correct in saying its a flat 0.02 chance of getting a MP) oneday catch up with you, and you'll still have to remake an item over 100 times to get an MP.

This is where the hinging helps. Say I have a bad run of luck, and the RNG throws up my MP on the 350th remake. I will have only made 35 actual items, and 315 hinges, before the probability is reset - the MP is made. Not the actual RNG being "reset", admittedly.

To actually make 350 items, this will need to have happened 10 times in a row (Hinge until MP, items to 35 makes and no MP, hinge until next MP).

Chance of masterpiece in 35 makes = 50.69%

Chance of flipping a coin face up or down = 50%.
Odds of flipping that coin face down (No MP) 9 times in a row (getting MP on the 10th): 1 in 512.

These odds, compared to 1 MP in 350 straight remakes, are a bit more favourable - and this is an extreme example, using 350 remakes as the basis - at least, as noone seems to have required more to make an MP thus far.

Scaling this up, 7 in 3500 for the hinge method, 10 in 3500 for the straight remake method.
70 in 35,000 for the hinge method, 100 in 35,000 for the straight remake method. The more you use the hinge method, the better the odds swing in your favour.

 

[Roalith]

Originally posted by Jenkz


Chance of a masterpiece in 1 make = 2%

Chance of a masterpiece in 2 makes = 3.96%

Chance of a masterpiece in 10 makes = 18.29%

Chance of masterpiece in 35 makes = 50.69%

Chance of masterpiece in 50 makes = 63.58%

Chance of masterpiece in 100 makes = 86.78%

Nerf late night insomnia. You say the chance doesn't tail off after 35 makes...

Chance of masterpiece in 35 makes = 50.69%

Chance of masterpiece in 100 makes = 86.78%

If the chance doesn't tail off, admittedly in an oblique curve from 0 to infinity rather than the straight lines my paint picture shows, then surely at 69 makes or so the probability should be 100%?

 

[Caerdhros]

Originally posted by Roalith


This is where the hinging helps. Say I have a bad run of luck, and the RNG throws up my MP on the 350th remake. I will have only made 35 actual items, and 315 hinges, before the probability is reset - the MP is made. Not the actual RNG being "reset", admittedly.

Roalith, what Jenkz is describing is a system with a perfect random number generator, i.e. every time you make an item, there is a 2% chance it is a masterpiece. In this system, hinging cannot help you. The next result is always totally unrelated to all previous results. The formula he quotes is correct (I think - I certainly came up with the same formula as I was thinking about it last night).

There are a few points that I think need to be made (please note, I assume a perfect system in all my points here):

What we are actually quoting here is the chance of making 1 OR MORE masterpieces. The percentages quoted are actually (100%) - (the chance of NOT making a masterpiece), so for 15 tries, there is a very small (0.02^15 = 0.0000000000000000000000032%) chance that you make 15 masterpieces in a row. There is also a higher chance (but I don't know the formula of the top of my head - getting into permutations and combinations here) that you make 2 masterpieces somewhere in there. The probability quoted is (the probability of making 1) + (the probability of making 2) + (the probability of making 3) + ..... + (the probability of making 15)

The 'starting point' we have picked is 'making a masterpiece'. We can pick any 'starting point' possible. So the chance of getting no masterpieces in 5 tries is 0.98^5 = 90.4%. In our next 5 tries, the chance of getting no masterpieces is exactly the same. And the next 5. The chance of getting no masterpieces in 40 tries is 44.6%. But you can pick any consecutive 5 in those 40, and the chance will be 90.4%. I think what you mean by 'tailing off' in your other post is that this you see that the chance for 5 is approximately 90% (=100-10), so you would expect the chance in 40 (which is 8 times bigger than 5) to be (100-(8*10)) = 20%. So you would expect a masterpiece with (100-20) = 80% probability, as opposed to (100-45) = 55% probability.

The 'starting point' applies just as much to making masterpieces as to not making masterpieces, i.e. the chance of making 1 or more masterpieces in 5 tries is 9.6% (100-90.4). Your next 5 tries have exactly the same probability. And the next 5. Over those 15 tries, your probability is 26.14%, which is NOT the same as (9.6*3) = 28.8%. I know this seems counter-intuitive, but it is true.

I don't know whether the actual DAoC system is 'perfect' or not, but if you can, over a reasonably large sample size (note: the samples provided so far are not a large enough sample), prove that the chance of getting a masterpiece in 10 tries (following any 'starting point' you care to choose) is greater than 18.3%, you will have proved that it is NOT perfect, and can then be exploited.

Apologies for the long and rambling post, I hope it makes sense to someone. Please feel free to correct my maths if I've made a mistake.

Caerdhros.

 

[old.Wagn]

There's nothing wrong with any of the numbers here. They're more or less all correct.

Why isn't it working then? It's just the basic way of thinking that's wrong. It's most likely you will get an MP within the first 35-36 tries, true. But within the first 35 tries after what? The answer is: Anything, including the last MP made, but also including the last 96% qua hinge you've made, but most importantly, any non MP made.
So, what's the conclusion? How should you think when trying to craft as effectivly as possible?
Instead of thinking:
"Oh, no MP for 35 tries, I'll give up and trinket for a while.
Ah, an MP hinge. Back to crafting the real stuff!
Damn, no MP. But I still have 34 more tries.
Damn, no MP. But I still have 33 more tries.
Damn, no MP. But I still have 32 more tries.
etc."
Make it like this:
"lalalala... I'm crafting the real stuff whatever that is.
Damn, no MP for a bunch of tries, but just like the random number generator I've forgotten how many tries I've failed. But according to logic I should get one within the next 35 tries.
Damn, no MP. But I still have 34 more tries. Oh, but wait. The random number generator just forgot how long ago I made an MP, then so can I.
Damn, no MP. But I still have 34 more tries. Oh, but wait. The random number generator just forgot how long ago I made an MP, then so can I.
Damn, no MP. But I still have 34 more tries. Oh, but wait. The random number generator just forgot how long ago I made an MP, then so can I.
etc."

So, quick review:
No matter if the last try was 94%, 98% or 100%, the statistics show that you should get an MP within the next 35 tries, but you won't always get it, and there's nothing any methods can do about it.

[edit]Blah, someone already explained it[/edit]

 

[old.Jessica]

*rolls eyes*

What you advocates of the theory that trinketing does help don't realise, is the amount of TIME saved by making non masterpiece trinkets.

Regardless of how random the ramdom generator is, the chance of you getting an MP every time you hit the button is astronomical. Yet each time you make a non masterpiece, you've wasted a lot of time.

Making 50 hinges and seeing them all non-MP, you get the feeling that sooner than before you'll get your MP, and as tons of crafters that use this method will declare, it works, and it works well.

From my own worst case example, making a pair of chain boots, my poor customer paid for 136 attempts before he ran out of money, still no MP. This was followed by me chain making sleeves with a further 80 attempts before I finally got a masterpiece. Took around 8 hours to make 1 MP.

Around that time I discoved the hinging technique and have been using it ever since. Now I spend about an hour crafting and produce at least 2 100% items, 6-7 99% items and a large pile of cash from the hinges.

All in all, it's time better spent for the crafter - they get the cash they need, while at the same time, produce MPs.

Computer based random number generators are utterly broken and will continue to be for years to come. They produce a semi random effect and no amount of pure maths will make any difference to the problem, due to the fact the assumptions of the maths are all wrong. It's not 2% chance at all, it's actiallly "will the random number generator which is set to give me a number between 1 and 100 give me a number below 3.

So long as the crafter is happy, it's not a big deal.

Jesi

 

[chretien]

Jesi you're still making the same number of actual items though. If you sit and hinge for ten minutes, that's ten minutes you're not trying for an MP armour piece. You get an MP hinge, start again on the armour and your chances of getting another MP are still the same. What my data showed was that I got an average of one MP per 35 item makes and this tallied with Roaliths figures for the same stats using the hinging method. However you look at it you still have to make an average of 35 or so pieces to get each MP. You may be lucky and get one in ten remakes, you may be unlucky and sit hinging all day, over time the averages wil stay the same.

 

[Caerdhros]

Re: *rolls eyes*

Originally posted by old.Jessica
What you advocates of the theory that trinketing does help don't realise, is the amount of TIME saved by making non masterpiece trinkets.

Only if the generator is 'streaky', and predictably so.

Making 50 hinges and seeing them all non-MP, you get the feeling that sooner than before you'll get your MP

Yes, you'll certainly get that feeling. It won't necessarily be true, though.

and as tons of crafters that use this method will declare, it works, and it works well.

If you use the method, it will give you masterpieces, whether the generator is broken or not, so it 'works'. Will it give you masterpieces more often than not using the method? I've yet to see it proved.

Around that time I discoved the hinging technique and have been using it ever since. Now I spend about an hour crafting and produce at least 2 100% items, 6-7 99% items and a large pile of cash from the hinges.

2 MPs every hour? Really EVERY hour? I've certainly produced 2 masterpieces in 22 tries (not using any method) and more recently, only 3 masterpieces in over 200 tries.

I really don't know if the generator is broken or not - I haven't seen any proof of it, only anecdotes. I'm going to start logging my crafting results, and try the hinge method, and analyze the log file for results.

 

[Roalith]

Okay: The average is 1 in 50. The median is 1-35.


What it comes down to is: You can spend several hours remaking the same item to increase your statistical likelihood of producing an MP, or you can make hundreds of hinges with 35 remakes post-MP hinge to increase your statistical likelihood of producing an MP (in a shorter total space of time).

Say you make 200 items without an MP. That's 200 x 3 minutes wasted, let alone the remake cost of the item.

Now, say you make 150 hinges and 50 items without an MP. That's (150 x 0.25 minutes) + (50 x 3 minutes). You will also have saved yourself the cost of 150 remakes.

Both methods increase your statistical likelihood, I personally believe the hinge method increases it a greater amount (but that's another story). However, at the end of the day, your average chance of producing an MP is 1 in 50.

 

[old.Wagn]

Roalith, did you read Caerdhros' or my post? What part didn't you understand, so I can try to explain better?

 

[Roalith]

And, in terms of streakyness, using Chretien's results:

0 - 12 Interval = 12
12 - 66 Interval = 54
66 - 192 Interval = 126
192 - 233 Interval = 41
233 - 287 Interval = 54
337 - 354 Interval = 17
354 - 406 Interval = 52
406 - 409 Interval = 3
409 - 428 Interval = 19
428 - 455 Interval = 27
455 - 461 Interval = 6
461 - 493 Interval = 32
547 - 493 Interval = 54
547 - 548 Interval = 1
548 - 577 Interval = 29
577 - 589 Interval = 12

That's 73 makes for the first trinket-method MP, +336 hinges. As opposed to 12 straight item makes.
16 item makes for the second trinket-method MP, +36 hinges. As opposed to 54 straight item makes.
11 item makes for the third trinket-method MP, +76 hinges. As opposed to 126 straight item makes.

 

[Caerdhros]

Originally posted by Roalith

Both methods increase your statistical likelihood

IF the generator is working properly, then NOTHING you can do will increase the chance of making a masterpiece.

That's the big question here: is the generator working properly? If it is, then no method will help you.

 

[Roalith]

Please read my post before mounting your soapbox Wagn. I'm talking statistical likelihood, not actual chance. I'm fully aware of the average chances and median results; I'm the one that introduced the median result information into this thread.

Probability says we are more likely to get a result within the first 35 attempts since the last MP (Caerdhros, that's what the median result was based on).

Average says 1 in 50, because of the erroneous results over 35 attempts 'raising the bar', so to speak.

Hinge-method crafting attempts to avoid the erroneous results over 35 attempts. Doesn't always work. Seems to work more often than not, in practical, in-game terms, though.

 

[Roalith]

Originally posted by Caerdhros
IF the generator is working properly, then NOTHING you can do will increase the chance of making a masterpiece.

That's the big question here: is the generator working properly? If it is, then no method will help you.

Argh! Statistical likelihood, NOT actual, physical, random-number-generated likelihood!

 

[old.Wagn]

I have read your posts, Roalith. I'm just trying to figure out what it is you don't understandm so i can help you to understand it. No need to get all defensive. But with your last post I think I've figured it out.

Probability says we are more likely to get a result within the first 35 attempts since the last MP

It's like I said in my last post:
Probability says we are more likely to get a result within the first 35 attempts since the last non MP aswell

 

[Caerdhros]

Originally posted by Roalith


Argh! Statistical likelihood, NOT actual, physical, random-number-generated likelihood!

I *think* that you mean that you are only going on Chretien's observed results here, in which case I'd say that there's not enough data to be conclusive. Oh, and you're missing the 287-337 interval from your data as well

 

[Caerdhros]

Originally posted by Roalith
Probability says we are more likely to get a result within the first 35 attempts since the last MP (Caerdhros, that's what the median result was based on).

Roalith, I think we're talking at cross-purposes here - are you talking about Chretien's results only, or the 'perfect' system I've been talking about?

Because if it's the perfect system, I'd disagree with the above.

 

[Roalith]

Wagn: I see what you're driving at. However, the sets of data used to produce the median founded those results on the last MP produced: For the simple reason that whenever you produce an MP, the cumulative probability resets. The cumulative probability does not reset each time you produce a non-MP. These cumulative odds are the odds of creating an MP within a given number of makes, after all: Not the cumulative odds of creating a non-MP.

This is why the probability is based on the last MP produced, and not the last non-MP produced.

Caerdhros: The median result was based on physical data collected from Mythic's RNG. Not Chretien's, someone else's. The 'perfect' system is another matter.

 

[Roalith]

Another way to test Jenkz' program:

Out of 10,000 MPs, show:

Total number of items crafted.
Total number of MPs where MP produced in 35 or less remakes from the last MP.
Total number of MPs where MP produced is greater than 35.
Percentage of MPs (out of the total items crafted) in 35 or less remakes from the last MP.
Percentage of MPs (out of the total items crafted) in more than 35 remakes from the last MP.

Daoc's RNG median results show that the higher percentage of MPs produced occur in the 1-35 range. Jenkz's program says...?

 

[Caerdhros]

Originally posted by Roalith
Wagn: I see what you're driving at. However, the sets of data used to produce the median founded those results on the last MP produced: For the simple reason that whenever you produce an MP, the cumulative probability resets. The cumulative probability does not reset each time you produce a non-MP. These cumulative odds are the odds of creating an MP within a given number of makes, after all: Not the cumulative odds of creating a non-MP.

That's one hell of an assumption based on looking at some data. I can't imagine GOA using anything other than a standard PRNG for this, which will just generate a number between 0 and 1, not something that resets everytime it generates certain results...

Caerdhros: The median result was based on physical data collected from Mythic's RNG. Not Chretien's, someone else's. The 'perfect' system is another matter.

Well, I'd love to see that data!

Caerdhros

 

[Caerdhros]

Right, this is going to be a long, techy and boring post, so You Have Been Warned.

I think I've got the formula for the probability of getting EXACTLY x masterpieces from n tries, if the generator is random:

probability of x MPs * probability of (n-x) non-MPs * possible combinations of x masterpieces in n tries

You can see a discussion of combinations here: http://mathforum.org/dr.math/faq/faq.comb.perm.html

The formula for the combinations of x from n is: n!/(x!*(n-x)!), so the full formula is:

0.02^x * 0.98^(n-x) * (n!/(x!*(n-x)!))

So, for Roalith's example, using the 10 retries method on Chretien's data, he gets 3 MPs from 100 tries (remember the missing data point from 287 to 337).

I won't put all the working in, just the results:

Probability of 0 MPs from 100 tries (0.98^100) = 13.26%
Probability of 1 MPs from 100 tries = 27.07%
Probability of 2 MPs from 100 tries = 27.34%

So the probability of getting 3 (or more) MPs from 100 tries is (100 - (13.26 + 27.07 + 27.34)) = 32.33% IF the generator is random.

I think this shows that the results from Chretien's data, even using the hinging method, are not unlikely, even if the generator is working. Bear in mind that if the generator is working, the hinging will make absolutely no difference.

Caerdhros.

EDIT: corrected 0.098 to 0.98 (typo)

 

[old.Jessica]

Still the problem comes back to not making more masterpieces, but how quickly you make them.

For every one hinge you make (in 6 seconds) that isn't a masterpiece saves you 84 seoconds of wasted time (and additional resource costs) that making a non MP item.

The chances of making ANY ITEM a MP is still 2%. At not point anywhere does it suggest you have 2% chance of making an MP hinge and a difference 2% chance of making an MP torso.

Hingeing is a time saving device, cutting down NOT the number of tries till you get a MP, but the time it takes you get an MP.

It takes less time to make 49 hinges and 1 torso than it does to make 50 torsos.

The method here work along the these lines;

Make 50 hinges in a row that are not MPs.
If you make an MP hinge, start counting from 0 again.
When you hit 50, start making the item you want. If after you make 5 items, still no MP, rinse, repeat.

For the time you spend doing this, you'll make more MPs, but lots of them will be hinges. In a shorter period of time, you'll have the MP you desired.

Gods, I must be bored to type more into this thread... yup, I'm bored.

 

[Caerdhros]

Originally posted by old.Jessica
Still the problem comes back to not making more masterpieces, but how quickly you make them.

For every one hinge you make (in 6 seconds) that isn't a masterpiece saves you 84 seoconds of wasted time (and additional resource costs) that making a non MP item.

The chances of making ANY ITEM a MP is still 2%. At not point anywhere does it suggest you have 2% chance of making an MP hinge and a difference 2% chance of making an MP torso.

Hingeing is a time saving device, cutting down NOT the number of tries till you get a MP, but the time it takes you get an MP.

It takes less time to make 49 hinges and 1 torso than it does to make 50 torsos.

The method here work along the these lines;

Make 50 hinges in a row that are not MPs.
If you make an MP hinge, start counting from 0 again.
When you hit 50, start making the item you want. If after you make 5 items, still no MP, rinse, repeat.

For the time you spend doing this, you'll make more MPs, but lots of them will be hinges. In a shorter period of time, you'll have the MP you desired.

Gods, I must be bored to type more into this thread... yup, I'm bored.

Jessica, I don't understand your method here. You say that there is a 2% chance every time of making a masterpiece. I assume this means that it doesn't matter what you've just made, there's still a 2% chance every time. This means that the time you spend making hinges is wasted, as when you finish making hinges, hey presto, the next time you make something, still only a 2% chance of making a masterpiece, exactly the same as when you started making hinges...

 

[chretien]

Jesi the system doesn't 'know' how many non mp hinges you've made. If you make ten items and don't get an mp make 50 hinges then go make ten more items, you have the same chance of any of those items being MPs as you would if you'd just sat down and made 20 items straight through. You will get more MPs because you're making more things but a lot of those Mps will be hinges. (if you make 50 hinges then ten items, rinse and repeat then 83% of your Mps will be hinges going on probabilities). There is no counter that says 'fifty pieces made since the last Mp time to wheel out another one'.

 

[Novamir]

from a non-mathematician, non-crafters viewpoint ( )it seems from everything that Roalith has typed that there's some form of continuous strand. the evidence is very compelling to suggest that after a MP hinge has been made, and roalith switches to normal items, he has a greater chance to get a MP sooner. the statistics suggest, however, that it should not make a blind bit of difference.

the question is, does this 'method' work for everyone? more tests needed . i think there's something dodgy with that RNG anyhow.

 

[Jenkz]

Originally posted by Roalith
If the chance doesn't tail off, admittedly in an oblique curve from 0 to infinity rather than the straight lines my paint picture shows, then surely at 69 makes or so the probability should be 100%?

Do the maths:

Chance of MP = 1 - (0.98^numberremakes)
69 remakes = 75.19% chance of obtaining a masterpiece

Originally posted by Novamir
from a non-mathematician, non-crafters viewpoint ( )it seems from everything that Roalith has typed that there's some form of continuous strand. the evidence is very compelling to suggest that after a MP hinge has been made, and roalith switches to normal items, he has a greater chance to get a MP sooner. the statistics suggest, however, that it should not make a blind bit of difference.

this is my point:

1. The hard statistics say that nothing makes any difference. hinging is just wasting your time. i have proven beyond any reasonable doubt that the STATISTICS of what roalith says is frankly bullshit, and Caerdhros has said exactly the same.

2. The practicality is, however, that on SOME occasions, hinging makes a LOT of difference - whether this be lucky, psychological, or there is something "wrong" with the RNG. (and Jesi, RNGs, as i said, are a lot better than you think. look at my code, that is a computer generated random number, and it proves beyond all doubt the chance is 1 in 50 if you make hinges or not)

i would however suggest, that because many crafters are finding SOME KIND of benefit from doing this, if you are a crafter - try it out, but by all means do not take this as a definite - it's actually very likely you will ONE DAY run into the following sutiation:

- make hinges till MP
- make 20 items, without a MP
- make hinges till MP
- make 20 items, without a MP
- make hinges till MP
- make 20 items, without a MP
- make hinges till MP
- make 20 items, without a MP
- make hinges till MP
- make 5 items and get a MP.

that's 85 makes, and an awful lot of hinges. my point is, sure, sometimes you will get one within 35, but a large proportion of the time (50% of the time) it will be over 35 according to the maths.

i've modified my program to output the results you wanted to see roalith, and here's 3 runs from the non hinge method, and 3 runs from the hinge method:

-------------------------------------------------------------

oxygen:~$ python non-roalith.py
Total masterpieces: 10000
Total remakes: 500915
Worst Case: 472
Best Case: 1
Average: 50
Total number of MP in 35 or less remakes: 5048
Total number of MP in over 35 remakes: 4952

oxygen:~$ python non-roalith.py
Total masterpieces: 10000
Total remakes: 500497
Worst Case: 502
Best Case: 1
Average: 50
Total number of MP in 35 or less remakes: 5091
Total number of MP in over 35 remakes: 4909

oxygen:~$ python non-roalith.py
Total masterpieces: 10000
Total remakes: 494136
Worst Case: 546
Best Case: 1
Average: 49
Total number of MP in 35 or less remakes: 5130
Total number of MP in over 35 remakes: 4870

oxygen:~$ python roalith.py
Item masterpiecess: 10000
Item remakes: 495447
Hinge masterpieces: 29847
Total hinges crafted: 1500982
Total masterpieces (items and hinges): 39847
Total remakes (items and hinges): 1996429
Worst Case (item remakes): 416
Best Case (item remakes): 1
Average (remakes per item, not hinge): 49
Total number of MP in 35 or less remakes: 5125
Total number of MP in over 35 remakes: 4875

oxygen:~$ python roalith.py
Item masterpiecess: 10000
Item remakes: 496188
Hinge masterpieces: 29925
Total hinges crafted: 1496384
Total masterpieces (items and hinges): 39925
Total remakes (items and hinges): 1992572
Worst Case (item remakes): 462
Best Case (item remakes): 1
Average (remakes per item, not hinge): 49
Total number of MP in 35 or less remakes: 5119
Total number of MP in over 35 remakes: 4881

oxygen:~$ python roalith.py
Item masterpiecess: 10000
Item remakes: 504614
Hinge masterpieces: 30305
Total hinges crafted: 1511284
Total masterpieces (items and hinges): 40305
Total remakes (items and hinges): 2015898
Worst Case (item remakes): 512
Best Case (item remakes): 1
Average (remakes per item, not hinge): 50
Total number of MP in 35 or less remakes: 5062
Total number of MP in over 35 remakes: 4938

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The above conforms with the statistical mathematics of:

Chance of MP = 1 - (0.98^numberremakes)
Chance of MP in 35 remakes = 50.69%
That means, chance of a masterpiece in anything ABOVE 35 is around 49.3%

You may as well consider that as 1 in 2 chance of getting a MP in 35 remakes.

What really needs to be done here is some testing with bronze brackets. I'm in IRC on #daoc.prydwen all the time. If i can get 10 people to make (and LOG) 1,000 bronze brackets, i'll parse the data through a simple program and do some comparisons on the mythic RNG. If you feel like making 1,000 bronze brackets (pretty quick, i think) please log it, PM me in IRC and send me the log. I'll do the same on my crafter also....

Taking the math at face value, there is no increase in probability, no decrease in remakes, or anything else. the chance is 2% and you're as equally (give or take 0.69 of a percent) likely to get a MP in 35 makes as you are to get one in 36 or more.

Let's look at the mythic RNG eh? We may actually obtain some data we can argue with. It's clear to me that there is no mathematical workaround to help increase MP changes.