Probability And You

• Paradise wrote on 2013-08-02 06:38
  OK i was curious and took a look at my college notes
  
  On semiconductors we had some situations like this one on valence bands, wont go deep on explanation but this is how it was done
  
  We have 5 different situations, where using an intergral we get as a result that we can use an average success, an we use that for every case (including the 100% one)
  
  100+50+50+45+45=290 -> 290/5=58%
  
  Each time we fail, we go down a valence band, the rate for this is 58% each time, and this goes per valence band.
  so every time we fail, it adds 58% to the success line
  
  0.58exp(times we fail+times we need to success as min)
  
  so to calculate the probs of having success with X failures, just use the formula, remember its average.
  
  now, we may have an average failure rate, this goes again this way:
  (100-58)% =rounded 42%
  success rate with no failures: 6.5%
  Stones needed as average (not counting fail feedback):rounded 77
  Failure average (no feedback) = rounded 32.
  Average needed no feedback= 99.
  
  Now we apply the feedback
  
  0.58exp(2+5) (ik it sounds crazy but believe me) = 2% rounded of success as average with feedback .
  
  Now, we need some more numbers to get some average stone quantities, but without those numbers, we could say we need 5/0.02 stones (250)
  This number is a reference, and you might need way less than that. There are more operators to apply, and 2 ways to finish this, but i can't continue for now, sorry. Remember that, each failure makes the result even harder, thanks to the lvl loss per failure.
  
  Now for real life results, ive used 5 stacks on my old volcano, not r4 yet...
• Zekkii wrote on 2013-08-02 06:55
  It is better to presume that you would lose 0.2 points on average when repairing 10 points at 98% than it is to presume that you have a 18.29% chance of not failing. The problem being that the number represents two things: your chance to succeed on every point, and your chance of failure with any given number of points; it does not represent your chance of failing one point, two points, or et cetera. Neither statement is wrong of course, but I find the one I have given to be of more use. To explain further, I will walk you through how I choose to repair items.
  
  First step being the durability. If an item has 20 max durability and I would trash the item when it gets to 5 durability, it is safe to assume it has a useful life of 15 durability. The first thing we should calculate is the useful life per repair;
  
  Repairing at 98% (99.1% in actuality), 15 points of durability will give 15 divided by 0.009 or 1667 durability (rounded)
  Repairing at 97% (98.8% in actuality), 15 points of durability will give 15 divided by 0.012 or 1250 durability
  Repairing at 96% (98.4% in actuality), 15 points of durability will give 15 divided by 0.016 or 937.5 durability
  ..and so on.
  
  The next step is determine the cost of an item, this is the difficult part. Generally this is how much you value your item. Let's say you are talking about a reforge-less r5 Secret Penetrating Knight Lance, and you value the entire thing at 6m. Keep in mind this is your personal value, so if you really love your item you should value it very high. However you also value the Secret ES and Penetrating ES at 500k each as well, which can be burned off at 81% chance when you are done with the lance. The lance should be treated as if it costs 6m - (500k + 500k) * 0.81, or 5.19m.
  
  Then we should see how much we have to expense per repair:
  
  At 98% we will have to expense 5.19m / 1667 or 3113g per point repaired
  At 97% we will have to expense 5.19m / 1250 or 4512g per point repaired
  At 96% we will have to expense 5.19m / 937.5 or 5536g per point repaired
  
  Next, we should add the repair costs.
  
  98% = 5,990 G
  97% = 4,704 G
  96% = 3,416 G
  
  Finally, we add the two together and choose whichever is lowest.
  
  98% = 5990 + 3113 or 9103g per point
  97% = 4704 + 4512 or 9216g per point
  96% = 3416 + 5536 or 8952g per point
  
  So of the ones calculated, it seems that 96% is actually the ideal choice. Generally speaking, the cheaper the weapon the lower the repair % you will want to pay. This means that since most weapons are heavily reforged, upgraded, special upgraded, and enchanted, 98% is generally advised.
• wildk wrote on 2013-08-02 07:06
  Allow me to repost my solution since I edited it after you guys posted new messages:
  
  
  
  

  Quote from wildk;1130599:

  Let %N be the chance of success at step N;
  xN be the expected number of stones required to reach step N;
  
  xN = xN-1 + %N + (1-%N) * (xN - xN-2)
  
  
  Given initial condition
  x0 = 0
  x1 = 1
  
  x2 = x1 + 50% + 50% * (x2 - x0)
  x2 = 1 + 0.5 + 0.5 * x2
  x2 = 3
  
  x3 = x2 + 50% + 50% * (x3 - x1)
  x3 = 3 + 0.5 + 0.5 * x3 - 0.5
  x3 = 6
  
  x4 = x3 + 45% + 55% * (x4 - x2)
  x4 = 6 + 0.45 + 0.55 * x4 - 1.65
  x4 = 32/3 ~= 11
  
  x5 = x4 + 45% + 55% * (x5 - x3)
  x5 = 32/3 + 0.45 + 0.55 * x5 - 3.3
  x5 = 469/27 ~= 18
  
  x6 = x5 + 1 = 496/27 ~= 19
  
  In summary
  Step 0: 0
  Step 1: 1
  Step 2: 3
  Step 3: 6
  Step 4: 11
  Step 5: 18
  Step 6: 19
  
  Don't think I made any mistakes here but please check and also rep because I hate maths.
  
  
  
  
  You can't do a simulation because it's an open loop. You'll never get a result, only maths will work here :<

• Gensokyou wrote on 2013-08-02 07:08
  No rep because DATS NOT HOW IT WORKS.
  
  +rep to the cat though for stating the obvious.
• wildk wrote on 2013-08-02 07:09

  Quote from Gensokyou;1130612:

  No rep because DATS NOT HOW IT WORKS.
  
  +rep to the cat though for stating the obvious.

  
  
  :< please tell me where I went wrong
  
  It's only an expected number fyi, you can have seriously bad luck and reach over a million stones
  
  I've failed dorrens request without a single cube success even at 70% synth success rates and managing to get enough materials for some 12 cubes.
  
  I was expected to get ~8 cubes but I got nil.
  
  The mean is only a reference not to mention mabi's RNG tends to go to the extreme
• drezzt wrote on 2013-08-02 07:32

  Quote from wildk;1130613:

  :< please tell me where I went wrong
  
  It's only an expected number fyi, you can have seriously bad luck and reach over a million stones
  
  I've failed dorrens request without a single cube success even at 70% synth success rates and managing to get enough materials for some 12 cubes.
  
  I was expected to get ~8 cubes but I got nil.
  
  The mean is only a reference not to mention mabi's RNG tends to go to the extreme

  
  
  Well I guess that's just it. The LUCK FACTOR makes it impossible to calculate 8D
• Zekkii wrote on 2013-08-02 07:35

  Quote from drezzt;1130625:

  Well I guess that's just it. The LUCK FACTOR makes it impossible to calculate 8D

  
  Luck has no place in averages.
• wildk wrote on 2013-08-02 07:38

  Quote from drezzt;1130625:

  Well I guess that's just it. The LUCK FACTOR makes it impossible to calculate 8D

  
  
  XD that's statistics for you, you can only estimate the expected amount, the probabilities of things happening and such, when it comes down to real life none of it matters so much anymore which was what lead to the economic crisis in 2007-08 since they thought the probability was way to small to happen.
• wildk wrote on 2013-08-02 07:47

  Quote from merrykitten;1130596:

  it's one of those tasks which you should just run simulation for
  
  10000 tries give 29, rarely 30 stones
  
  [code]
  av_stones, tries = 0, 10000
  tries.times do
  step, stones = 1, 1
  while 1
  stones += 1
  if step == 0
  step = 1
  elsif step == 1 or step == 2
  rand > 0.5 ? step -= 1 : step += 1
  elsif step == 3 or step == 4
  rand > 0.45 ? step -= 1 : step += 1
  end
  break if step == 5
  end
  av_stones += stones
  end
  p av_stones/tries
  [/code]

  
  
  Derp sorry, on closer inspection the theory of your program works just fine, my bad
  
  I trust computers more than myself, anyone care to show me where I went wrong? :<
• Rydian wrote on 2013-08-02 08:16
  Pretty nice math on the cost-per-success-average stuff, I was too lazy to do that!
  
  As far as upgrade stones... it's bad because you need to beat the odds. A success is +1 while a fail is -1, and with 50% success... this means that it'll try to be rank 0 or 1 (with the 100% success).
  
  So you might as well try flipping coins to simulate it, and you'll need to get more heads than tails on average (and no, more heads or tails won't work, as one is success and the other is just repeated fail, it has to skew towards the same pre-selected side each time).
  
  Assuming you have 15 stones to burn...
  http://www.random.org/coins/?num=15&cur=60-usd.0025c-pa
  Flip Again a few times and check your luck! Everybody's a [s]winner[/s] loser!
  
  

  Quote from Paradise;1130576:

  btw this works the other way around to check for failure rates

  Yeah I was originally going to extrapolate this and use more examples to apply to things that used the same math (like production skills), but then realized that the concept isn't as important there (as higher successes are done with higher ranks so there's no argument that higher is better), and for a lot of other things (drops, etc.) we don't have the proper numbers anyways.
  
  

  Quote from merrykitten;1130579:

  we successfully repaired 9 points of durability already and want to repair 10th, what chance of success do we have? no, it's not 77.6%, it's 97.5%

  Which would be listed in the table for one attempt at that rate, since you only intend to repair one point. :P
• merrykitten wrote on 2013-08-02 08:26

  Quote from wildk;1130635:

  Derp sorry, on closer inspection the theory of your program works just fine, my bad
  
  I trust computers more than myself, anyone care to show me where I went wrong? :<

  
  
  i think my program is correct but, well, who doesn't when code :3 i might make a subtle mistake but i doubt i did
  
  if you can try to write yours, you probably should get a similar result
• wildk wrote on 2013-08-02 08:51

  Quote from merrykitten;1130657:

  i think my program is correct but, well, who doesn't when code :3 i might make a subtle mistake but i doubt i did
  
  if you can try to write yours, you probably should get a similar result

  
  
  Yeah, I kept getting ~27.6 too :P
  
  GARG now I have a gigantic headache cause I can't figure out where my maths went wrong, but here the following is the table for expected stones / steps out of 1mil tries using
  
  [SPOILER="this program which is practically the same as merry's"][PRE]#define trials 1000000
  #define targetStep 5
  
  
  int main()
  {
  int step, stone, totalStone = 0, i, failRate;
  for(i = 0; i < trials; i++){
  for(step = stone = 1; step < targetStep; stone++){
  switch(step){
  case 0:
  failRate = 0;
  break;
  case 1:
  case 2:
  failRate = 50;
  break;
  case 3:
  case 4:
  case 5:
  failRate = 55;
  }
  if(rand() % 100 < failRate)
  step--;
  else
  step++;
  }
  totalStone += stone;
  }
  std::cout << (float)totalStone / trials;
  system("pause");
  return 0;
  }[/PRE][/SPOILER]
  
  Step 0: 0
  Step 1: 1
  Step 2: 4.00502
  Step 3: 9.01437
  Step 4: 17.3932
  Step 5: 29.8369
• Paradise wrote on 2013-08-02 13:31

  Quote from wildk;1130613:

  :< please tell me where I went wrong
  
  It's only an expected number fyi, you can have seriously bad luck and reach over a million stones
  
  I've failed dorrens request without a single cube success even at 70% synth success rates and managing to get enough materials for some 12 cubes.
  
  I was expected to get ~8 cubes but I got nil.
  
  The mean is only a reference not to mention mabi's RNG tends to go to the extreme

  
  
  
  if you give initial conditions to use a prob formula, its not a prob formula.
  Still, useful post
  
  
  

  Quote from wildk;1130670:

  Yeah, I kept getting ~27.6 too :P
  
  GARG now I have a gigantic headache cause I can't figure out where my maths went wrong, but here the following is the table for expected stones / steps out of 1mil tries using
  
  [SPOILER="this program which is practically the same as merry's"][PRE]#define trials 1000000
  #define targetStep 5
  
  
  int main()
  {
  int step, stone, totalStone = 0, i, failRate;
  for(i = 0; i < trials; i++){
  for(step = stone = 1; step < targetStep; stone++){
  switch(step){
  case 0:
  failRate = 0;
  break;
  case 1:
  case 2:
  failRate = 50;
  break;
  case 3:
  case 4:
  case 5:
  failRate = 55;
  }
  if(rand() % 100 < failRate)
  step--;
  else
  step++;
  }
  totalStone += stone;
  }
  std::cout << (float)totalStone / trials;
  system("pause");
  return 0;
  }[/PRE][/SPOILER]
  
  Step 0: 0
  Step 1: 1
  Step 2: 4.00502
  Step 3: 9.01437
  Step 4: 17.3932
  Step 5: 29.8369

  
  
  
  
  remember to put a random seed based on a random factor, if not, you will always get a set numbers, since -random()- function is not really random. Its not a good function to use on a program that requires real randomness, unless you put a seed there, and i mean a random seed (sometimes video RAM memory locations are good enough as seeds to get randomness, more if they are checksums).
  
  in other words
  
  [CODE]av_stones, tries = 0, 10000
  tries.times do
  step, stones = 1, 1
  while 1
  stones += 1
  if step == 0
  step = 1
  elsif step == 1 or step == 2
  rand > 0.5 ? step -= 1 : step += 1
  elsif step == 3 or step == 4
  rand > 0.45 ? step -= 1 : step += 1
  end
  break if step == 5
  end
  av_stones += stones
  end
  p av_stones/tries[/CODE]
  
  will pretty much repeat the same results, and remember that the generated number has a set max number, which is not setted on this example (maybe just to make the post shorter?)
  if im not wrong, not setting the random max, will take the default max range (wich is 10 if i remember well)
  
  in the case of Wildk, its setted to 100, but still, its the default random seed, so as i said, the results will pretty much be the same over time.
• merrykitten wrote on 2013-08-02 13:37
  well unless you write in c you shouldn't initiate the seed (usually it's done with the system time) explicitly. ruby which i used does it itself for instance
• Paradise wrote on 2013-08-02 13:52

  Quote from merrykitten;1130724:

  well unless you write in c you shouldn't initiate the seed (usually it's done with the system time) explicitly. ruby which i used does it itself for instance

  
  
  ooh ruby, i see
  
  

  Quote from Rydian;1130653:

  
  So you might as well try flipping coins to simulate it, and you'll need to get more heads than tails on average (and no, more heads or tails won't work, as one is success and the other is just repeated fail, it has to skew towards the same pre-selected side each time).

  
  
  this is the best way to get an idea on how many stones you will get without doing so much maths
  +rep