Since now you are prohibited from advancing in enchantment ranks from rank 6 without buying so far expensive stuff from AH, I decided to calculate how well preservation wards fare against coalescent wards. Inb4: where you get this from, what are the formulas.
Well I don't know a thing about probablity theory, it's just small program using rnd with 100000 iterations (shame, really), it may be complete BS, especially consecutive chances, etc. So here are the results:
R6:
Success chance: 40%
Wards lost on average for successful fusion: 1.5
Chance for more than 5 consecutive failures: 4.7%
R7:
Success chance: 30%
Wards lost on average for successful fusion: 2.34
Chance for more than 8 consecutive failures: 4%
R8:
Success chance: 25%
Wards lost on average for successful fusion: 3
Chance for more than 10 consecutive failures: 4.3%
R9:
Success chance: 20%
Wards lost on average for successful fusion: 4
Chance for more than 13 consecutive failures: 4.4%
R10:
Success chance: 10%
Wards lost on average for successful fusion: 9
Chance for more than 30 consecutive failures: 4%
The results on average are true for very big number of attempts. If you are doing say R8 enchant, the table means if you buy 10 preservation wards you have 96% chance to make R8 enchant with them before running out of wards
*************************************
My conclusion: don't use coalescent wards on anything but weapon and armor enhancements. Worst case price for preservation wards is 5k AD, and you need only 10 on average even for R10 enchantments. You only have 5% chance of wasting more than coalescent's worth on making R10, and even that will be true not for long because wondrous chests content is BOP now and coals price gonna skyrocket.
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khimera906Member, NW M9 PlaytestPosts: 898Arc User
edited December 2013
I was using Coalescent Wards on Weapon/Armor Enchantments only anyway, but your experiment is very useful. With the free Coalescent wards gone, the prices are going to skyrocket indeed. There's no point is wasting them.
Thanks for that.
I hate dancing with Lady Luck. She always steps on my toes.
not really. coal wards from the coffer of augmentation are still here. they're just BoA now. let's not get people upset over incorrect information. thanks.
not really. coal wards from the coffer of augmentation are still here. they're just BoA now. let's not get people upset over incorrect information. thanks.
True. However, one tester opened a large number of coffers on the test server and showed that it was very likely the rate of coal ward drops was much lower now. It will be interesting to see how that plays out on the live server.
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khimera906Member, NW M9 PlaytestPosts: 898Arc User
not really. coal wards from the coffer of augmentation are still here. they're just BoA now. let's not get people upset over incorrect information. thanks.
Sorry for the mistake. What I meant is that they are gone from the market. I know we are still gonna get them in the Coffers.:p:o
I hate dancing with Lady Luck. She always steps on my toes.
Please explain the math behind your average ward losing numbers.
Upgrading probabilities are modeled by the binomial distribution, since
we're dealing with a simple yes/no experiment where the success
for each single "draw" is the same.
What I'm missing is the confidence level. What does "on average" mean?
That means if you are doing 100000 R8 enchants, you need to buy 100000 * 3 wards for failed attempts + 1 ward to begin with.
As for math, I don't do any, it's just a data from random generator working with very big number of iterations. It's actually a modification of an old program I used to calculate how many units I had to send to reliably capture enemy cities in Civ III. I wouldn't recommend launching any Mars missions based on the data from it, but as for games it works for me
The math behind all this isn't hard, but it does get messy at spots. But as the OP remarked, you don't need to use any of it to get good, useful approximate answers.
In a few of these, the OP has gotten the exact answer. For example, the number of wards used per successful fusion is a fairly result. Given probability of success P, on each attempt there is the expectation (I use the statistical definition of the word, not common English; e.g., https://en.wikipedia.org/wiki/Expected_value) of P upgraded enchantments being produced, and the expectation of 1-P wards being consumed. The number of wards expected to be lost per upgrade produce is simple division: (1-P)/P. For 40%, 30%, 25%, 20%, and 10%, the results are 60/40, 70/30, 75/25, 80/20, and 90/10; or 1.5, ~2.33, 3.0, 4.0, and 9.0. Apart from rounding 70/30 to 2.34 instead of 2.33, the OP's Monte-Carlo simulation had it spot on. There's no confidence intervals on these expected values, because they're exact.
It is appropriate to offer confidence intervals most of the time when one produces estimates via simulation, and one common and fairly easy way to do it is with the bootstrap method. For example, the OP might take his 100,000 simulations and divide them into 100 groups of 1000, and compute the results separately for each sub-group. Now there are 100 estimates of the result, and they have some spread. Let's call that group x_i for i ranging from 1 to 100. One computes the mean and variance of that group, m=sum(x_i)/100, and then v=sum((x_i-m)^2)/100. Take the variance m, and knowing that the effect of the law of large numbers on the variance is that it reduces proportionately with the sample size, we can estimate the variance of the full sample of 100,000 by knowing what the variance was computed to be for samples of 1000. Let's call the variance of the big sample V. So, V=v/100. Now, for a confidence interval, the usual rule of thumb is to produce a 95% confidence interval, and one uses the standard deviation times 1.96 (this is a point taken from the cumulative error function) to enclose 47.5% of the distribution on each side. So, the original result from the 100,000 simulation plus/minus 1.96 times square-root(V) will be a decent approximation of the confidence interval.
When can this fail? Not very often, when your sample size is large. One generally wants to pick enough samples so that the full 95% confidence interval estimate doesn't include any impossible values. For instance, if we are estimating the number of wards lost, and the confidence interval includes negative numbers on the low side, clearly we need more samples. As a rule of thumb, I would increase my samples until the confidence interval's bounds were a few times closer to my estimate than to any nearby out-of-bounds values. For instance, if I'm trying to put confidence intervals on an estimate like the probability of 30 or more failures in a row being 4%, I'd want to increase my samples until my confidence interval was from 3.6% to 4.4%, or narrower, to keep it away from zero. (Of course, as one increases the number of samples, the estimated mean value will drift around a bit too) The reason to keep the confidence interval relatively small is that most of these distributions behave normally when they have tight variances for their expectations, but once the variance becomes on the order of the size of the expectation, they can be asymmetric, and the normal approximation begins to fail.
Monte-Carlo simulation is a very powerful area of applied statistics, and is very well accepted for producing estimates of otherwise intractable statistical problems. Done well, with attention to sample sizes and confidence interval estimation, you can get very useful answers to complex problems without a lot of fuss. Make sure you've tested your code and know that it works well even in the odd circumstances, know the citation for the random number generator you're using (you can find this in your programming language's documentation, or often with a little searching on the internet), and never, ever, code your own random number generator.
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syka08Member, Neverwinter Beta UsersPosts: 0Arc User
edited December 2013
To save space I'm not going to quote you haelra. But wow, some great information there. I suppose, given a large enough sample size and control, the fact that OP is using (what I am going to assume is) a different RNG from the one Neverwinter has wouldn't produce results too varied from one another? Obviously there's most likely no legal way to obtain Neverwinter's RNG coding to test it, but keeping things as pure as possible is a concern in my mind.
That being said, and as many can attest to, "average" doesn't seem to apply very well over the population from anecdotes told. It probably does over the wide spread of things, but the constant stories of people that have run things like the Pit Fight CTA over 200 times without seeing the mount drop once for them or opening 100+ lockboxes without seeing a single purple drop, well, it really does discourage people away from playing the odds.
The latest story being the abysmal Mark of Power/Stability/Union drop rate. But! I don't want to hijack this thread with gripes on that.
Interesting numbers and good information. Thanks for sharing .
So long as the OP was using a good RNG, there's no real drawback to using a different one than NW uses, provided they're using a good one too. Basically, an RNG has to pass a set of very strict statistical tests which ensure that it has the properties one expects from truly random numbers. And I'll add, it's not easy at all to produce truly random numbers within a specified distribution. Most "pseudo" random number generators do pretty well, and can pass most statistical tests handily. I'll offer a good non-mathematical page to describe one such true random number generator, and which shows a corresponding plot from a not very good pseudo-random number generator -- http://www.random.org/analysis/. This link is a very good discussion, better than I could offer here, and even offers a pdf paper for those who want to go a little deeper http://www.random.org/analysis/Analysis2005.pdf. Recommended.
The problem with true random number generators is they're usually based on an ongoing "physics experiment", such as random atmospheric noise, which must be measured by an instrument before being translated into numerical values, which itself can be imperfect in many ways. Generally speaking, once one gets into the realm of the current well-regarded pseudo-random number generators (such as the RNG in Matlab, most high quality programming language libraries, the GNU Scientific Library (GSL) and so on, the advantages of one method over another tend to be trivial. I'd stay away from the RNG's in lightweight languages, like php, basic, javascript, and so on, unless they cite their RNG algorithm in the documentation. For example, 'Octave' a publically available Matlab clone commonly used for scientific computation has this description for its random number generator:
To compute the pseudo-random sequence, rand uses the Mersenne Twister with a period of 2^19937-1 (See M. Matsumoto and T. Nishimura, Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator, ACM Trans. on Modeling and Computer Simulation Vol. 8, No. 1, pp. 3-30, January 1998, http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html). Do not use for cryptography without securely hashing several returned values together, otherwise the generator state can be learned after reading 624 consecutive values.
For comparison, many naiive RNG's are written using simple LCG (Linear Congruential Generator) of the form X_n+1 = (A X_n + C) mod M. The constants A, C, and M are chosen from a few alternatives and the initial value, X_0 is called the 'seed'. These tend to have lots of problems, and fail most of the trict tests; for example, much less that 623-dimensional equidistributional property of Octave's rand, many of these will fail a two-dimensional test, showing lots of patterns and line artifacts, and once you have a few X_n values recorded, you can usually figure out which A, C, and M are being used, and then predict the series forever. (So much for it being "random", lol.) Their short series of X_n do look random at a first glance though, and will pass the simpler tests. But seriously, don't try to publish a paper using one of these.
The probabilities are exact in this case since we're dealing with simple discrete geometric variables.
So, let p = probability of success and q = 1 - p, the analytical solutions to your statements are:
- X = wards lost on average for successful fusion: (1/p) - 1
- Y = chance for more than m consecutive failures: q^(m+1)
R5->R6: p = 0.4, q = 0.6, m = 5
=> X = 2.5 - 1 = 1.5, Y = 0.6^(5+1) = 4.7%
R6->R7: p = 0.3, q = 0.7, m = 8
=> X = 3.3 - 1 = 2.3, Y = 0.7^(8+1) = 4.0%
R7->R8: p = 0.25, q = 0.75, m = 10
=> X = 4 - 1 = 3, Y = 0.75^(10+1) = 4.2%
R8->R9: p = 0.20, q = 0.8, m = 13
=> X = 5 - 1 = 4, Y = 0.8^(13+1) = 4.4%
R9->R10: p = 0.10, q = 0.9, m = 30
=> X = 10 - 1 = 9, Y = 0.9^(30+1) = 3.8%
I justed wanted to know how the numbers were derived. It's too easy to write them down
without the reader being able to retrace them.
When talking about a "confidence level" I was referring to the following: How many tries
does it take to be successful at least once with a given probabilty. This can be calculated
by solving the equation
1-(1-p)^n >= c,
where p is the probability to be successful (the enchantment is upgraded).
n is the number of tries and c the probability of getting (at least) one hit
in the n tries. Let's say you want to be 99,99% sure that you get a hit in
n tries. In that case c would be 0,9999.
Using the above equation it is easy to derive the cost of upgrading using preservation
wards and to compare it to the costs without using any wards or a coalescent wards.
My conclusions were as follows:
1) Don't care to use any wards for upgrading up to rank 5.
2) Use preservation wards for upgrading up to rank 9.
These conclusions depend on the prices of reagents and wards. Looking at
the current AH enchantment prices it seems to be best to by enchantments
up to rank 7 - assuming you have to buy reagents and wards.
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ironzerg79Member, Neverwinter Moderator, NW M9 PlaytestPosts: 4,942Arc User
True. However, one tester opened a large number of coffers on the test server and showed that it was very likely the rate of coal ward drops was much lower now. It will be interesting to see how that plays out on the live server.
Just to keep accurate information out there, when the coffers were first changed on the test server to BoA, the drop rate on C-Wards was reduced to about 5%. Prior to the patch going live, the rate was returned to the normal 15%. If you look in the feedback thread on the change in the Test Forums, you'll find the post.
No coal wards since patch on my 8 characters capable of getting them. Admittedly 2 of those didn't exist at time of patch, only a week or so ago and have only started 'earning' in the last week. Am watching with interest to see when I get my first since Module 2 went live.
Roo. Cleric. Mad as a bag of badgers, will heal for beer.
Just to keep accurate information out there, when the coffers were first changed on the test server to BoA, the drop rate on C-Wards was reduced to about 5%. Prior to the patch going live, the rate was returned to the normal 15%. If you look in the feedback thread on the change in the Test Forums, you'll find the post.
Wrong. Nothing is known about the drop rate of the Coffers on Live, other than anecdotal evidence.
All that happened on Preview prior to Shadowmantle going live, is that devs eventually confirmed that pre-Shadowmantle Coffers and Coalescent Wards (indeed everything) would be wholly unaffected by the changes to the contents of the new Shadowmantle Coffers.
What is known is that prior to the removal of the glitch (or bug) that let us see the content of the new Coffers, because they took over the identity of all the old Coffers, is that additional Rare quality items (Coalescent Wards are also Rare) and other items were added to the Coffer and the drop rate for Coalescents went down to 5%.
The content of the new (Bind to Account) Coffers have remained the same on Live as on Preview. So, without further statistical evidence, i.e. several weeks worth and many alts with the new Coffers copied to Preview, people have unsurprisingly assumed the drop rate has remained the same as on Preview, i.e. 5%, until shown evidence otherwise.
yogokouMember, Neverwinter Beta UsersPosts: 0Arc User
edited December 2013
Actually it was closer to 3% (3,9% exactly), but people have been rounding it up to 5% for ease for reference I guess.
Regarding the OP, I'm lost a bit. Wasn't it common knowledge to never use Coals for anything over 5% chance to fuse? Thanks for the extra math crunchin, though.
Since the last expansion, among my 7 characters, I've received ZERO preservation wards and ZERO coalescent. I used to get at least get a preservation ward. So, unless we want to pay money, I guess getting any enchantment past level 6 is a no go.
All of these posts about percentages and RNG are forgetting one thing, NO-ONE outside of Cryptic/PWE knows how the system was implemented, for all we know there is a second RNG that is player based, i.e coffers themselves have 5% chance, but you only have a 5% chance of actually being a 5% chance player ...
AFAIK, Cryptic (or more likely PWE) have greatly reduced the drop rate on all of the (high value) items, like the coal wards, and blue marks of potency. They have also changed the RNG for upgrade success as well. I burnt through 27 pres wards going from lvl 1 to 5 on a dark enchantment last night, now tell me THAT isn't simply fleecing players!
cbrowne0329Member, NW M9 PlaytestPosts: 293Arc User
edited December 2013
I was buying about 4 boxes a day between my toons and average 3 to 7 coal wards a week.
and then the free 6 I was getting... so out of 34 boxes I had a week, I was getting 3 in a bad week, 7 in a good week. So say 4 average a week out of 34... so a little over 10%. Since the patch... nada!
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beckylunaticMember, NW M9 PlaytestPosts: 14,231Arc User
I burnt through 27 pres wards going from lvl 1 to 5 on a dark enchantment last night, now tell me THAT isn't simply fleecing players!
That'll happen, but I used fewer preservation wards than that upgrading a couple of radiants from rank 6 to 7 on Saturday (success in one or two tries). I don't think I'd use any preservation wards going up to rank 5 though. Much as burning the green marks would annoy me, each failure still has less cost to it than the relative value of a pres ward.
It's not that the percentages lie, just that you can hit such frustrating streaks of failure, and people get mad and insist it's because Cryptic is out to get them.
It's 5%, I tested it with a sample of 1111 coffers on the preview a few weeks ago.
your testing on the preview server is null and void as anything on there is subject to change prior to it going live. and since you haven't done this test on the live shard, it cannot be proven. plus, wasn't this done via a bug where existing (old) coffers were showing up as new coffers?
also your probability % is faulty based on the fact that every time you open a coffer, the chance resets. had multiple people opened 1111 coffers, each of their results would have been different. just like other people can come here and report that they've opened 7 coffers with 0 coal wards dropping, i've opened about 5 coffers and have had 2 coal wards drop. what is the probability that i'll never get another coal ward in the next 20-30 coffers i open? according to you, it's probable. while you could take this accumulated data of coffer drops and create a statistical table based on your findings, it would not be absolute.
statistically speaking you have limited anecdotal data from the preview shard and nothing more.
your testing on the preview server is null and void as anything on there is subject to change prior to it going live. and since you haven't done this test on the live shard, it cannot be proven. plus, wasn't this done via a bug where existing (old) coffers were showing up as new coffers?
also your probability % is faulty based on the fact that every time you open a coffer, the chance resets. had multiple people opened 1111 coffers, each of their results would have been different. just like other people can come here and report that they've opened 7 coffers with 0 coal wards dropping, i've opened about 5 coffers and have had 2 coal wards drop. what is the probability that i'll never get another coal ward in the next 20-30 coffers i open? according to you, it's probable. while you could take this accumulated data of coffer drops and create a statistical table based on your findings, it would not be absolute.
statistically speaking you have limited anecdotal data from the preview shard and nothing more.
As mod you should be still. The testing on PTS shard is the same on live. They run the same builds so it's the same result.
And a testdata of 1111 opened coffer show the droprate is only ~5% for the new coffer. The old one was ~15%. And that a data vary is nothing special. It's the difference in the vary that count. So please go out of discussions if you only try to troll people. Especially AS MOD. If you have a fact, then so it. Else you MUST have to bring something to proof your opinion.
Being an altoholic I have 16 characters on my account and have opened the 7 day reward on the coffers for them at least once each. Zero coal wards and just a couple of green ones......
As mod you should be still. The testing on PTS shard is the same on live. They run the same builds so it's the same result.
And a testdata of 1111 opened coffer show the droprate is only ~5% for the new coffer. The old one was ~15%. And that a data vary is nothing special. It's the difference in the vary that count. So please go out of discussions if you only try to troll people. Especially AS MOD. If you have a fact, then so it. Else you MUST have to bring something to proof your opinion.
just because i'm a mod doesn't exclude me from participating in discussions. i am a volunteer, not paid staff, and my opinions are my own.
that said, in order to validate the % of success, you need to have data that you do not have access to. let's look at the example of a dice roll. what is the probability that i will roll a 4 on a six-sided dice? well, i know that i have a one in six chance of rolling a 4, so my % chance is 16.67%. 1/6 = 0.1667 = 16.67%
the problem with RNG data is you are missing the initial information that you have on a dice roll. you know how many sides the dice has. you don't know how the coalescent ward drops are calculated. you have statistical data only. so you have 43/1111 = 0.0387 = 3.87%
if there were more players that had done this test with shared results, you still would have a drop rate based on statistical data only. this is not absolute and no one should put stock in these figures.
Comments
Well I don't know a thing about probablity theory, it's just small program using rnd with 100000 iterations (shame, really), it may be complete BS, especially consecutive chances, etc. So here are the results:
R6:
Success chance: 40%
Wards lost on average for successful fusion: 1.5
Chance for more than 5 consecutive failures: 4.7%
R7:
Success chance: 30%
Wards lost on average for successful fusion: 2.34
Chance for more than 8 consecutive failures: 4%
R8:
Success chance: 25%
Wards lost on average for successful fusion: 3
Chance for more than 10 consecutive failures: 4.3%
R9:
Success chance: 20%
Wards lost on average for successful fusion: 4
Chance for more than 13 consecutive failures: 4.4%
R10:
Success chance: 10%
Wards lost on average for successful fusion: 9
Chance for more than 30 consecutive failures: 4%
The results on average are true for very big number of attempts. If you are doing say R8 enchant, the table means if you buy 10 preservation wards you have 96% chance to make R8 enchant with them before running out of wards
*************************************
My conclusion: don't use coalescent wards on anything but weapon and armor enhancements. Worst case price for preservation wards is 5k AD, and you need only 10 on average even for R10 enchantments. You only have 5% chance of wasting more than coalescent's worth on making R10, and even that will be true not for long because wondrous chests content is BOP now and coals price gonna skyrocket.
Thanks for that.
not really. coal wards from the coffer of augmentation are still here. they're just BoA now. let's not get people upset over incorrect information. thanks.
True. However, one tester opened a large number of coffers on the test server and showed that it was very likely the rate of coal ward drops was much lower now. It will be interesting to see how that plays out on the live server.
Upgrading probabilities are modeled by the binomial distribution, since
we're dealing with a simple yes/no experiment where the success
for each single "draw" is the same.
What I'm missing is the confidence level. What does "on average" mean?
As for math, I don't do any, it's just a data from random generator working with very big number of iterations. It's actually a modification of an old program I used to calculate how many units I had to send to reliably capture enemy cities in Civ III. I wouldn't recommend launching any Mars missions based on the data from it, but as for games it works for me
In a few of these, the OP has gotten the exact answer. For example, the number of wards used per successful fusion is a fairly result. Given probability of success P, on each attempt there is the expectation (I use the statistical definition of the word, not common English; e.g., https://en.wikipedia.org/wiki/Expected_value) of P upgraded enchantments being produced, and the expectation of 1-P wards being consumed. The number of wards expected to be lost per upgrade produce is simple division: (1-P)/P. For 40%, 30%, 25%, 20%, and 10%, the results are 60/40, 70/30, 75/25, 80/20, and 90/10; or 1.5, ~2.33, 3.0, 4.0, and 9.0. Apart from rounding 70/30 to 2.34 instead of 2.33, the OP's Monte-Carlo simulation had it spot on. There's no confidence intervals on these expected values, because they're exact.
It is appropriate to offer confidence intervals most of the time when one produces estimates via simulation, and one common and fairly easy way to do it is with the bootstrap method. For example, the OP might take his 100,000 simulations and divide them into 100 groups of 1000, and compute the results separately for each sub-group. Now there are 100 estimates of the result, and they have some spread. Let's call that group x_i for i ranging from 1 to 100. One computes the mean and variance of that group, m=sum(x_i)/100, and then v=sum((x_i-m)^2)/100. Take the variance m, and knowing that the effect of the law of large numbers on the variance is that it reduces proportionately with the sample size, we can estimate the variance of the full sample of 100,000 by knowing what the variance was computed to be for samples of 1000. Let's call the variance of the big sample V. So, V=v/100. Now, for a confidence interval, the usual rule of thumb is to produce a 95% confidence interval, and one uses the standard deviation times 1.96 (this is a point taken from the cumulative error function) to enclose 47.5% of the distribution on each side. So, the original result from the 100,000 simulation plus/minus 1.96 times square-root(V) will be a decent approximation of the confidence interval.
When can this fail? Not very often, when your sample size is large. One generally wants to pick enough samples so that the full 95% confidence interval estimate doesn't include any impossible values. For instance, if we are estimating the number of wards lost, and the confidence interval includes negative numbers on the low side, clearly we need more samples. As a rule of thumb, I would increase my samples until the confidence interval's bounds were a few times closer to my estimate than to any nearby out-of-bounds values. For instance, if I'm trying to put confidence intervals on an estimate like the probability of 30 or more failures in a row being 4%, I'd want to increase my samples until my confidence interval was from 3.6% to 4.4%, or narrower, to keep it away from zero. (Of course, as one increases the number of samples, the estimated mean value will drift around a bit too) The reason to keep the confidence interval relatively small is that most of these distributions behave normally when they have tight variances for their expectations, but once the variance becomes on the order of the size of the expectation, they can be asymmetric, and the normal approximation begins to fail.
Monte-Carlo simulation is a very powerful area of applied statistics, and is very well accepted for producing estimates of otherwise intractable statistical problems. Done well, with attention to sample sizes and confidence interval estimation, you can get very useful answers to complex problems without a lot of fuss. Make sure you've tested your code and know that it works well even in the odd circumstances, know the citation for the random number generator you're using (you can find this in your programming language's documentation, or often with a little searching on the internet), and never, ever, code your own random number generator.
That being said, and as many can attest to, "average" doesn't seem to apply very well over the population from anecdotes told. It probably does over the wide spread of things, but the constant stories of people that have run things like the Pit Fight CTA over 200 times without seeing the mount drop once for them or opening 100+ lockboxes without seeing a single purple drop, well, it really does discourage people away from playing the odds.
The latest story being the abysmal Mark of Power/Stability/Union drop rate. But! I don't want to hijack this thread with gripes on that.
Interesting numbers and good information. Thanks for sharing
The problem with true random number generators is they're usually based on an ongoing "physics experiment", such as random atmospheric noise, which must be measured by an instrument before being translated into numerical values, which itself can be imperfect in many ways. Generally speaking, once one gets into the realm of the current well-regarded pseudo-random number generators (such as the RNG in Matlab, most high quality programming language libraries, the GNU Scientific Library (GSL) and so on, the advantages of one method over another tend to be trivial. I'd stay away from the RNG's in lightweight languages, like php, basic, javascript, and so on, unless they cite their RNG algorithm in the documentation. For example, 'Octave' a publically available Matlab clone commonly used for scientific computation has this description for its random number generator:
For comparison, many naiive RNG's are written using simple LCG (Linear Congruential Generator) of the form X_n+1 = (A X_n + C) mod M. The constants A, C, and M are chosen from a few alternatives and the initial value, X_0 is called the 'seed'. These tend to have lots of problems, and fail most of the trict tests; for example, much less that 623-dimensional equidistributional property of Octave's rand, many of these will fail a two-dimensional test, showing lots of patterns and line artifacts, and once you have a few X_n values recorded, you can usually figure out which A, C, and M are being used, and then predict the series forever. (So much for it being "random", lol.) Their short series of X_n do look random at a first glance though, and will pass the simpler tests. But seriously, don't try to publish a paper using one of these.
So, let p = probability of success and q = 1 - p, the analytical solutions to your statements are:
- X = wards lost on average for successful fusion: (1/p) - 1
- Y = chance for more than m consecutive failures: q^(m+1)
R5->R6: p = 0.4, q = 0.6, m = 5
=> X = 2.5 - 1 = 1.5, Y = 0.6^(5+1) = 4.7%
R6->R7: p = 0.3, q = 0.7, m = 8
=> X = 3.3 - 1 = 2.3, Y = 0.7^(8+1) = 4.0%
R7->R8: p = 0.25, q = 0.75, m = 10
=> X = 4 - 1 = 3, Y = 0.75^(10+1) = 4.2%
R8->R9: p = 0.20, q = 0.8, m = 13
=> X = 5 - 1 = 4, Y = 0.8^(13+1) = 4.4%
R9->R10: p = 0.10, q = 0.9, m = 30
=> X = 10 - 1 = 9, Y = 0.9^(30+1) = 3.8%
Details about the math describing the probabilites can be found here: http://en.wikipedia.org/wiki/Binomial_distribution.
I justed wanted to know how the numbers were derived. It's too easy to write them down
without the reader being able to retrace them.
When talking about a "confidence level" I was referring to the following: How many tries
does it take to be successful at least once with a given probabilty. This can be calculated
by solving the equation
1-(1-p)^n >= c,
where p is the probability to be successful (the enchantment is upgraded).
n is the number of tries and c the probability of getting (at least) one hit
in the n tries. Let's say you want to be 99,99% sure that you get a hit in
n tries. In that case c would be 0,9999.
Using the above equation it is easy to derive the cost of upgrading using preservation
wards and to compare it to the costs without using any wards or a coalescent wards.
My conclusions were as follows:
1) Don't care to use any wards for upgrading up to rank 5.
2) Use preservation wards for upgrading up to rank 9.
These conclusions depend on the prices of reagents and wards. Looking at
the current AH enchantment prices it seems to be best to by enchantments
up to rank 7 - assuming you have to buy reagents and wards.
Just to keep accurate information out there, when the coffers were first changed on the test server to BoA, the drop rate on C-Wards was reduced to about 5%. Prior to the patch going live, the rate was returned to the normal 15%. If you look in the feedback thread on the change in the Test Forums, you'll find the post.
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Wrong. Nothing is known about the drop rate of the Coffers on Live, other than anecdotal evidence.
All that happened on Preview prior to Shadowmantle going live, is that devs eventually confirmed that pre-Shadowmantle Coffers and Coalescent Wards (indeed everything) would be wholly unaffected by the changes to the contents of the new Shadowmantle Coffers.
What is known is that prior to the removal of the glitch (or bug) that let us see the content of the new Coffers, because they took over the identity of all the old Coffers, is that additional Rare quality items (Coalescent Wards are also Rare) and other items were added to the Coffer and the drop rate for Coalescents went down to 5%.
The content of the new (Bind to Account) Coffers have remained the same on Live as on Preview. So, without further statistical evidence, i.e. several weeks worth and many alts with the new Coffers copied to Preview, people have unsurprisingly assumed the drop rate has remained the same as on Preview, i.e. 5%, until shown evidence otherwise.
Carefully, re-read the last 3 to 5 pages of the Coffers thread, if you find believe any statement I have made is incorrect: http://nw-forum.perfectworld.com/showthread.php?532641-Cryptic-OFFICIAL-Feedback-Thread-The-Coffers-of-Wondrous-Augmentation/page28&highlight=coffer+wondrous
The last developer statement in that thread: http://nw-forum.perfectworld.com/showthread.php?532641-Cryptic-OFFICIAL-Feedback-Thread-The-Coffers-of-Wondrous-Augmentation&p=6580511&viewfull=1#post6580511
Also, this is an unfortunate thread derailment.
But on the subject of the original post, it was never worthwhile using coalescent wards on fusing ordinary runes/enchantments.
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Regarding the OP, I'm lost a bit. Wasn't it common knowledge to never use Coals for anything over 5% chance to fuse? Thanks for the extra math crunchin, though.
AFAIK, Cryptic (or more likely PWE) have greatly reduced the drop rate on all of the (high value) items, like the coal wards, and blue marks of potency. They have also changed the RNG for upgrade success as well. I burnt through 27 pres wards going from lvl 1 to 5 on a dark enchantment last night, now tell me THAT isn't simply fleecing players!
and then the free 6 I was getting... so out of 34 boxes I had a week, I was getting 3 in a bad week, 7 in a good week. So say 4 average a week out of 34... so a little over 10%. Since the patch... nada!
That'll happen, but I used fewer preservation wards than that upgrading a couple of radiants from rank 6 to 7 on Saturday (success in one or two tries). I don't think I'd use any preservation wards going up to rank 5 though. Much as burning the green marks would annoy me, each failure still has less cost to it than the relative value of a pres ward.
It's not that the percentages lie, just that you can hit such frustrating streaks of failure, and people get mad and insist it's because Cryptic is out to get them.
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your testing on the preview server is null and void as anything on there is subject to change prior to it going live. and since you haven't done this test on the live shard, it cannot be proven. plus, wasn't this done via a bug where existing (old) coffers were showing up as new coffers?
also your probability % is faulty based on the fact that every time you open a coffer, the chance resets. had multiple people opened 1111 coffers, each of their results would have been different. just like other people can come here and report that they've opened 7 coffers with 0 coal wards dropping, i've opened about 5 coffers and have had 2 coal wards drop. what is the probability that i'll never get another coal ward in the next 20-30 coffers i open? according to you, it's probable. while you could take this accumulated data of coffer drops and create a statistical table based on your findings, it would not be absolute.
statistically speaking you have limited anecdotal data from the preview shard and nothing more.
As mod you should be still. The testing on PTS shard is the same on live. They run the same builds so it's the same result.
And a testdata of 1111 opened coffer show the droprate is only ~5% for the new coffer. The old one was ~15%. And that a data vary is nothing special. It's the difference in the vary that count. So please go out of discussions if you only try to troll people. Especially AS MOD. If you have a fact, then so it. Else you MUST have to bring something to proof your opinion.
Wait, aren't the reagents for upgrading ranks 1-4 MUCH cheaper than a Preservation ward and if so why are you risking a Pres ward?
I just checked the AH: Lesser marks are 250 AD on the Ah while Preservation Wards are 3000.....
just because i'm a mod doesn't exclude me from participating in discussions. i am a volunteer, not paid staff, and my opinions are my own.
that said, in order to validate the % of success, you need to have data that you do not have access to. let's look at the example of a dice roll. what is the probability that i will roll a 4 on a six-sided dice? well, i know that i have a one in six chance of rolling a 4, so my % chance is 16.67%. 1/6 = 0.1667 = 16.67%
the problem with RNG data is you are missing the initial information that you have on a dice roll. you know how many sides the dice has. you don't know how the coalescent ward drops are calculated. you have statistical data only. so you have 43/1111 = 0.0387 = 3.87%
if there were more players that had done this test with shared results, you still would have a drop rate based on statistical data only. this is not absolute and no one should put stock in these figures.
He provided far more detail than "it might not have changed" or "1111 isnt enough". Sure is for me.
We believe what we choose.
I choose to believe 5%.
you are free to believe what you want, however the fact is his figures are not absolute. they are anecdotal at best.