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  • refracted0dawnrefracted0dawn Member, NW M9 Playtest Posts: 894 Arc User
    edited November 2014
    Actually, the probability of succeeding, on any attempt, ignoring the results of any previous attempts will always be 1/4. However, if you want to know the probability of succeeding BY try N, including try N, it is in fact different. Assuming to succeed you only need to succeed once and assuming you have a 1/4 chance of succeeding, the mathematics is as follows:
    N
    1/4+sigma((3^I-1)/(4^I))
    I=1
    Unfortunately I don't actually have an available sigma function to stick in here in order to make that more understandable

    Cheers! I am going to out that into Excel and try it out!



    :D
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  • thefabricantthefabricant Member, NW M9 Playtest Posts: 5,248 Arc User
    edited November 2014
    Cheers! I am going to out that into Excel and try it out!



    :D

    I made a silly mistake in that post, which I have now corrected. The probability is actually:
    N
    sigma((3^I-1)/(4^I))
    I

    Hope that helps :) I forgot that as I was running from 1 it auto includes the 1/4 :p (been a while since I worked with probability) :)
  • frishterfrishter Member Posts: 3,522 Arc User
    edited November 2014
    I do not need to read that, thank you very much. I am already perfectly aware that a 25% chance of success is a 1/4 chance of success, so if I make four attempts and it is a fair test, I fully expect to succeed once; on average.

    :rolleyes:

    If you roll a 6 sided die 6 times, there will likely be at least 1 side that didn't land.
    Flip a coin 4 times and there's a very real chance of not getting 2 heads and 2 tails. Have 1000 people flip a coin 4 times, and some of them will probably not get a single head or a single tail despite it still being 50% chance to land.

    It's also a gamblers weakness. "I've lost so many times, it's about time my luck changed" despite having the same chance to win.
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  • thefabricantthefabricant Member, NW M9 Playtest Posts: 5,248 Arc User
    edited November 2014
    macjae wrote: »
    Except in this case, the rolls aren't exactly independent, since you only roll until you succeed, and the question is which roll in a series will succeed. It's also a matter of what perspective you adopt and what question you put forward. If you pose the question "at what roll will I be most likely to finally succeed?" then the first roll is the correct answer, since that has the greatest chance of negating subsequent rolls. So if you are 25% likely to succeed at rolling a 1 at each given roll, then you are also 25% likely to negate the necessity of additional rolls with each roll, reducing the likelihood of subsequent rolls being the one that will actually succeed (even if each roll independently always has a 25% chance of success, that's not what he was calculating).

    Just try and imagine it in gambling terms: Someone is rolling a four-sided polyhedron, and you are to bet on which particular roll in a series will come up a 1. Once the die comes up a 1, there will be no more rolls. The first roll has a 25% chance of being a 1. Each subsequent roll has the same chance of being a 1, but each subsequent roll is also less likely to occur because it's increasingly likely that a 1 has already come up. Thus, the chance of the first successful roll being the third roll is less than the chance of the first successful roll being the first one.

    Those are the numbers he came up with; they add up to the cumulative chance of rolling a 1 with that many rolls, it's just how the chance is distributed between each roll being the roll to succeed.

    The first roll is 25% likely to be the one to succeed.
    The second roll is also 25% likely to succeed, but it's also only 75% likely to exist, if the first roll succeeded. That makes it 18.75% likely to be the successful roll.
    The third roll is also 25% likely to succeed, but it's also only 56.25% (.75 × .75) likely to exist, since either the first or second roll could have succeeded already. That makes it 14.0625% likely to be the successful roll.

    The problem you are making is based off the way you making your calculations. You are arguing 2 specific things which end up contradicting each other. The first thing you are doing is you are saying that if you succeed, you aren't going to keep trying and so all further attempts down that path no longer exist. However, you are then basing your calculations, the 1/4*3/4*3/4*3/4... on the fact that they do. Why do I say that? Simple, every time you divide by 4, you are multiplying the number of probabilities by 4. In doing so, you are accounting for the existence of every single branch you have said to ignore. The reason this causes problems and causes your probability to incorrectly diminish is because you are dividing the number of successful outcomes on whichever attempt assuming you have failed up till then by the actual total number of outcomes along all branches including the successful ones which you have claimed we ignoring. What you are doing, for example, is this:

    number of successful chances first time=1
    number of possible outcomes on first time=4
    number of successful chances on second time on failed branch=3
    number of possible outcomes on second time=16
    Rather then:
    number of successful chances first time=1
    number of possible outcomes on first time=4
    number of successful chances on second time on failed branch=3
    number of possible outcomes on second time on failed branch=12

    If you want to count the outcomes from the successful branch, then you also have to count the fact that as that branch succeeded, every SINGLE one of those probabilities also has to be counted as a success. Just because you are infinitesimally unlikely to have not succeeded by the 1000th try, doesn't change the fact that on the 1000th try you still just as likely to succeed. Go back and read my post on probability which shows how to calculate the chance of succeeding by the nth try and stop arguing that independent events are dependent using flawed logic. Remember with independent events P(AB)=P(A)*P(B) which is what we are seeing in this case.
  • thefabricantthefabricant Member, NW M9 Playtest Posts: 5,248 Arc User
    edited November 2014
    frishter wrote: »
    If you roll a 6 sided die 6 times, there will likely be at least 1 side that didn't land.
    Flip a coin 4 times and there's a very real chance of not getting 2 heads and 2 tails. Have 1000 people flip a coin 4 times, and some of them will probably not get a single head or a single tail despite it still being 50% chance to land.

    It's also a gamblers weakness. "I've lost so many times, it's about time my luck changed" despite having the same chance to win.

    Agreed, and just because you have a 1/4 chance of succeeding, doesn't mean that you should on average succeed once every 4 times. What it means is that you have a 68.359% chance of succeeding at least once out of those 4 attempts:p Also, for anyone interested, here is how you calculate the probability of succeeding K number of times given N attempts:
    http://www.askamathematician.com/2010/07/q-whats-the-chance-of-getting-a-run-of-k-successes-in-n-bernoulli-trials-why-use-approximations-when-the-exact-answer-is-known/
  • gerbilhurdlergerbilhurdler Member, Neverwinter Beta Users Posts: 418 Bounty Hunter
    edited November 2014
    Agreed, and just because you have a 1/4 chance of succeeding, doesn't mean that you should on average succeed once every 4 times. What it means is that you have a 68.359% chance of succeeding at least once every 4 times :p Also, for anyone interested, here is how you calculate the probability of succeeding K number of times given N attempts:
    http://www.askamathematician.com/2010/07/q-whats-the-chance-of-getting-a-run-of-k-successes-in-n-bernoulli-trials-why-use-approximations-when-the-exact-answer-is-known/

    I hated this stuff in school.
    But yeah a 25% chance doesn't ever mean you will win 1 out of 4, after all you have a 75% chance on every roll not to succeed.

    Although, I wouldn't mind if the drop rates took this into account and raised the drop% after every unsuccessful attempt.
    So that at the 4th unsuccessful attempt the chance was 68% to drop instead of 25% still for that roll.
    A progressive drop rate would definitely help out in IWD *hint hint devs hint*.
  • tickdofftickdoff Member Posts: 0 Arc User
    edited November 2014
    b3llist0r wrote: »
    +1 for the TS. I agree in every point.

    My Neverwinter gaming:
    - Log in. Kill 5 dragons. Log out.
    - Log through all toons (invoke, leadership).
    - Exit Neverwinter.

    That´s it. All old dungeons including CN dont´t drop anything I could sell. New Dungeon and Skirmish bore me to death cause I ran them a hundred times and the AD gain per time, the BoP drops ... dont work. PvE players dont need the new equipment but everybody wants it. If a casual player wants legendary level equip... he or she has only a few options. $, illegal stuff or toon-farm. No one needs the game... only for a every-module-short-visit, dailies, ugly pvp and equipment posing.

    Enough.

    //Bellistor

    Sounds like you should move to another game that will hold your interest better.
  • thefabricantthefabricant Member, NW M9 Playtest Posts: 5,248 Arc User
    edited November 2014
    Interestingly enough assuming that the chances of a belt drop in SoT are all independent and assuming you had 0.01% chance of seeing a belt drop, you would have, by the 100th try roughly a 10% chance of having a single belt drop... Then remember, there being 5 people in the party, you then need to multiply the chances of a belt dropping by the chances of you winning it which is 1/5. So in SoT with a realistic belt drop chance, you have roughly a 2% chance of winning a belt in 100 attempts. If you were to make 500 attempts, you would be approaching a 48% chance of seeing a belt drop and a 48/5% chance of winning one... Unfortunately my computer doesn't handle big enough fractions for me to be able to tell you when the probability of seeing a belt drop with this realistic drop chance is greater then 50%, but I would estimate it to be between 500 and 600 tries.
  • pmabrahampmabraham Member, NW M9 Playtest Posts: 145 Arc User
    edited November 2014
    Good day, Chem:

    There are times I wish this forum would allow us to vote on how well a given post was written (good or bad). I agree with all of your points; and it is those points along with problems in matchmaking with PVP (not class performance in general, but more so with matchmaking) that I don't continue to invest money in this game (they received $20 from me). I've only been playing since late August / early September of this year (I didn't write the start date down), and it is starting to weigh on me for how grindy it is to get anywhere once you get to 60.

    By the way, I do appreciate your guides and input; between you and Kalec, I think a lot of ground is covered.

    Thank you.
  • refracted0dawnrefracted0dawn Member, NW M9 Playtest Posts: 894 Arc User
    edited November 2014
    I made a silly mistake in that post, which I have now corrected. The probability is actually:
    N
    sigma((3^I-1)/(4^I))
    I

    Hope that helps :) I forgot that as I was running from 1 it auto includes the 1/4 :p (been a while since I worked with probability) :)

    Thanks for that!

    I am not much of a Maths buff, but I do enjoy learning new things with Excel.

    I have a table of all the Refining Points needed for Artifacts, their RP value for a matching and non-matching Artifact and what level you get by putting a certain Rank into a Rank 1.

    [B][COLOR="#000000"]
      A      B        C          D           E             F            G
    Rank  Tot RP   To Next  To Rank 100  RP No Match   RP Matched  Added Ranks
      1      0        20     3,847,635     1,500           7,500       17
      2     20        90     3,847,615     1,510           7,550       18
    [/COLOR][/B]
    


    Column G has:

    =INDEX($A$2:$A$101,MATCH(F2,$B$2:$B$101))


    This is VERY useful for calculating what I will get if I have two Bloodcrystals, make 1 level 59 and put it into the first, then put that into my Rank 89 etc and whether it is worth it or not.

    If I just put one Rank 1 into another Rank 1, I'll get a Rank 17 (assuming no Critical "hit" for refining).


    I'll have to make one for Artifact Gear as well!


    :)
  • refracted0dawnrefracted0dawn Member, NW M9 Playtest Posts: 894 Arc User
    edited November 2014

    But yeah a 25% chance doesn't ever mean you will win 1 out of 4.

    No one said it did.

    But if I make four attempts and it is a fair test, I fully expect to succeed once; on average.

    "On Average" means with a statistically valid number of trials. So if you roll 4,000,000 times, you'd expect to succeed 1,000,000 times. The deviation from a precise 1/4 success rate will not be statistically significant if it is a fair and unbiased test with no artificial constraints, such as taking into account the number of previous successes or failures, hypothesising that you stop when you succeed, or taking into account any attempts that will not be made etc.

    ~
  • thecorpserthecorpser Member, NW M9 Playtest Posts: 45 Arc User
    edited November 2014
    Interestingly enough assuming that the chances of a belt drop in SoT are all independent and assuming you had 0.01% chance of seeing a belt drop, you would have, by the 100th try roughly a 10% chance of having a single belt drop...

    .01% x 100 = 1%. But that doesn't matter. It doesn't make a difference if you run once or 1 million times, the chances of a drop remain the same as they are not cumulative. If the belt drops at a rate of .01% chance and assuming everyone chooses need, you'll have a .002% chance of winning it.
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  • tinead51tinead51 Member Posts: 305 Arc User
    edited November 2014
    b3llist0r wrote: »
    +1 for the TS. I agree in every point.

    My Neverwinter gaming:
    - Log in. Kill 5 dragons. Log out.
    - Log through all toons (invoke, leadership).
    - Exit Neverwinter.

    That´s it. All old dungeons including CN dont´t drop anything I could sell. New Dungeon and Skirmish bore me to death cause I ran them a hundred times and the AD gain per time, the BoP drops ... dont work. PvE players dont need the new equipment but everybody wants it. If a casual player wants legendary level equip... he or she has only a few options. $, illegal stuff or toon-farm. No one needs the game... only for a every-module-short-visit, dailies, ugly pvp and equipment posing.

    Enough.

    //Bellistor

    SNAP
    /10char
  • thefabricantthefabricant Member, NW M9 Playtest Posts: 5,248 Arc User
    edited November 2014
    thecorpser wrote: »
    .01% x 100 = 1%. But that doesn't matter. It doesn't make a difference if you run once or 1 million times, the chances of a drop remain the same as they are not cumulative. If the belt drops at a rate of .01% chance and assuming everyone chooses need, you'll have a .002% chance of winning it.

    I know they are not cumulative, otherwise my answer would have been 1% chance and not 10%, no, what I did was I stuck the numbers into the formula I posted above to calculate the chance of succeeding by the 100th try and I got out the numbers, surprisingly, if you were aiming to get just 1 belt, that is your chance of getting it, in a 100 tries. Go back a few posts if you want to see the explanation.
  • thefabricantthefabricant Member, NW M9 Playtest Posts: 5,248 Arc User
    edited November 2014
    macjae wrote: »
    I did read your post. Your numbers are the same, you're just expressing them in a different way. From your post:



    1/4 = 25%
    3/16 = 18.75% (= .25 × .75)
    9/64 = 14.0625% (= .25 × .75 × .75)
    27/256 = 10.546875% (= .25 × .75 × .75 × .75)
    Sum = 68.359375%

    The sum is the chance of succeeding within four rolls. The percentage for each roll is the chance of that roll being the successful one.

    In the case of rolling four-sided dice, the percentage number is the chance of that step being the one where we finally roll a 1. It gets smaller for each subsequent branch because there's an increasing chance of discounting those branches.



    No. Because in the case that you roll a 1, subsequent rolls don't exist. The first roll has a 100% chance of existing and a 25% chance of success; 25%. The second roll has a 75% chance of existing and a 25% chance of success. Each additional step eats another multiplicative 25% from the next step. This does not impact the numbers from the previous steps; the first roll will always have a 25% chance of being the successful one in an unknown number of rolls. The chance of the second roll being successful is reduced by removing all those branches in which the first roll was successful (25% of all branches); the chance of the third roll being successful is reduced by another 25%, and so on.

    Imagine this being a casino-style game: You get a table similar to roulette, with say, seven fields on it. The first six fields corresponds to six rolls, the seventh corresponds to "does not succeed within six rolls." The game is to roll a four-sided die until it comes up a 1. What is the likelihood of winning if you place your bet on the third field? (That is also the number he initially stated as being the chance of succeeding ON a given roll.)

    I understand what you getting at, yes, the probability of that branch being the likely one does decrease each time, but that is simply because it becomes more and more likely that you will have succeeded before. The fact that that particular branch is less likely to be the successful one the the prior branch doesn't in any way actually effect the fact that the probability of succeeding is still 1/4 on that branch though. In that particular branch, the number of possible outcomes will always be 4 times larger then the number of successful outcomes, as for example in my previous post with the example of the 3/16, the probability of it succeeding on that failed branch is 3/12 not 3/16, as there are only 12 possible outcomes on that branch.
  • edited November 2014
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  • thefabricantthefabricant Member, NW M9 Playtest Posts: 5,248 Arc User
    edited November 2014
    Now someone just needs to explain how to calculate the probability of succeeding k number of times after n number of tries in a way such that I actually understand it :p That's one thing in statistics I have never understood well at all.


    *edit, is it possible for a mod to move all of this probability stuff into its own thread in the correct section of the forums? I feel it has gone off topic (sorry chem :)) but i feel the content discussed still has merit for a discussion of its own separately :)
  • chemboy613chemboy613 Member, NW M9 Playtest Posts: 1,521 Arc User
    edited November 2014
    pmabraham wrote: »
    Good day, Chem:

    There are times I wish this forum would allow us to vote on how well a given post was written (good or bad). I agree with all of your points; and it is those points along with problems in matchmaking with PVP (not class performance in general, but more so with matchmaking) that I don't continue to invest money in this game (they received $20 from me). I've only been playing since late August / early September of this year (I didn't write the start date down), and it is starting to weigh on me for how grindy it is to get anywhere once you get to 60.

    By the way, I do appreciate your guides and input; between you and Kalec, I think a lot of ground is covered.

    Thank you.

    Thanks very much man!

    Many forums have some sort of reputation meter, where you can vote people positive or negative based upon our posts. I wish we had that here so we could

    a) Listen to the people who are actually helpful

    and

    b) Ignore the trolls.

    About guides - i just published my new mod 5 guide, check it out! I think i made a lot of improvements that will make it more useful to you.

    About PvP - I think a good matchmaking system would solve a ton of problems. How about you have a rating, they match teams and players of similar rating, and your rating is adjusted based upon ONLY wins and losses. Seems simple, right?

    When they put out tenacity, I thought, great... a very complicated solution to a very complicated solution to a very simple problem. They overthought it IMO

    That's off topic for this thread, but thank you. I appreciate it.
  • frishterfrishter Member Posts: 3,522 Arc User
    edited November 2014
    chemboy613 wrote: »
    Thanks very much man!

    Many forums have some sort of reputation meter, where you can vote people positive or negative based upon our posts. I wish we had that here so we could

    a) Listen to the people who are actually helpful

    and

    b) Ignore the trolls.

    About guides - i just published my new mod 5 guide, check it out! I think i made a lot of improvements that will make it more useful to you.

    About PvP - I think a good matchmaking system would solve a ton of problems. How about you have a rating, they match teams and players of similar rating, and your rating is adjusted based upon ONLY wins and losses. Seems simple, right?

    When they put out tenacity, I thought, great... a very complicated solution to a very complicated solution to a very simple problem. They overthought it IMO

    That's off topic for this thread, but thank you. I appreciate it.

    In some ways I like upvoted comments to see what is most agreed upon, however I also think the system can suck because generally people can really suck. It turns into a popularity content. If people disagree with you, even if your post is constructive or for the best for the game.

    Two examples:
    1) "Perma stealth is OP because...", that would instantly get downvoted by the TRs just because they don't like what they here even if some of the perma stealth changed should and are being changed.
    2) "cockatrice needs to be fixed". If it genuinely is broken or isn't working as intended then people will downvote you just because they won't want it nerfed. For the cockatrice it may not matter as much since the ones that don't own it are more than the ones that do. If it's something that the majority have and is too strong, you'll get downvoted for it.

    I personally find downvoting quite rude that should be reserved for those that are toxic, spamming etc rather than a difference in opinion.

    As for pvp balancing I think there's too many variables now. We have extremely strong glyphs, an extremely massive gs gap, a big difference in skill effectiveness, pots that imo should be usable in pvp. Personally I think it's turned into a balancing nightmare.
  • chemboy613chemboy613 Member, NW M9 Playtest Posts: 1,521 Arc User
    edited November 2014
    frishter wrote: »
    In some ways I like upvoted comments to see what is most agreed upon, however I also think the system can suck because generally people can really suck. It turns into a popularity content. If people disagree with you, even if your post is constructive or for the best for the game.

    Two examples:
    1) "Perma stealth is OP because...", that would instantly get downvoted by the TRs just because they don't like what they here even if some of the perma stealth changed should and are being changed.
    2) "cockatrice needs to be fixed". If it genuinely is broken or isn't working as intended then people will downvote you just because they won't want it nerfed. For the cockatrice it may not matter as much since the ones that don't own it are more than the ones that do. If it's something that the majority have and is too strong, you'll get downvoted for it.

    I personally find downvoting quite rude that should be reserved for those that are toxic, spamming etc rather than a difference in opinion.

    As for pvp balancing I think there's too many variables now. We have extremely strong glyphs, an extremely massive gs gap, a big difference in skill effectiveness, pots that imo should be usable in pvp. Personally I think it's turned into a balancing nightmare.

    This is a good criticism as well. I would like to have a warning sign "THIS PERSON IS A TROLL" and "THIS PERSON IS KNOWLEDGEABLE AND HELPFUL" would be nice.

    I'm not sure what the best system for that is, but i would like one :)

    PvP balance is a nightmare for sure. That's why i say just match up on something like a ranking. you get points for win and loss. If the sample size is large enough it "should" match people of similar strength.
  • canija777canija777 Member Posts: 27 Arc User
    edited November 2014
    I have just been to preview and refinment stones are still bound on account. So I guess they will stick to their decisions.
  • wixxgs1chtwixxgs1cht Member Posts: 430 Arc User
    edited November 2014
    canija777 wrote: »
    I have just been to preview and refinment stones are still bound on account. So I guess they will stick to their decisions.

    Of course they do. Also I wouldn't expect any generosity such as reduced RP requirements, increased RP drop rates and the likes. Short/Mid Term Profit > Player Happyness (= Long Term Profit).
  • iambecks1iambecks1 Member Posts: 4,044 Arc User
    edited November 2014
    Yeah guess panderus decided not to fight the players corner afterall , so much for the " I'll talk to them on Monday" nonsense.
    YourSecretsAreOurSecrets.gif
  • wixxgs1chtwixxgs1cht Member Posts: 430 Arc User
    edited November 2014
    iambecks1 wrote: »
    Yeah guess panderus decided not to fight the players corner afterall , so much for the " I'll talk to them on Monday" nonsense.

    Maybe he meant today... :rolleyes:
  • k3ll0k3ll0 Member Posts: 373 Arc User
    edited November 2014
    iambecks1 wrote: »
    Yeah guess panderus decided not to fight the players corner afterall , so much for the " I'll talk to them on Monday" nonsense.

    Curious leap of logic you have there.
  • iambecks1iambecks1 Member Posts: 4,044 Arc User
    edited November 2014
    k3ll0 wrote: »
    Curious leap of logic you have there.

    Why is that? he posted on Friday the 7th of November that he would talk to the developers on Monday , how is that a curious leap of logic? he didn't say " oh I'll talk to the developers a week next Monday" at this point we have been waiting a week for him to get back to us with the results of that followup.
    YourSecretsAreOurSecrets.gif
  • chemboy613chemboy613 Member, NW M9 Playtest Posts: 1,521 Arc User
    edited November 2014
    We have no idea, honestly. Find out tomorrow.
This discussion has been closed.