Gachapon Mechanics

• Rydian wrote on 2015-06-22 19:32
  So since the news about KR promising gacha probabilities is out, I think it's a good time to talk about the mechanics behind gachas (since I've been asked a few times).
  
  So let's see how gachapon scripts work, using the Exploration Gachapon 2010 (91025).
  (It works just like older dungeon rewards, for those of you that saw those already.)
  
  
  1 - Set a counter to 0.
  
  2 - Roll a random number up to 2077 (the max depends on the gacha). Let's say we get 25.
  
  3 - Start a loop that cycles through rewards until breaking past the random number.
  [SPOILER="Step 3"]3a - Grace Shawl Dress has a value of 4, so select it and add 4 to the counter.
  Random number (25) is not less than the counter (4), so go to the next check.
  
  3b - Mandolin (Enchanted) has a value of 4, so select it and add 4 to the counter.
  Random number (25) is not less than the counter (8), so go to the next check.
  
  3c - Crossbow (Enchanted) has a value of 4, so select it and add 4 to the counter.
  Random number (25) is not less than the counter (12), so go to the next check.
  
  3d - Leather Long Bow has a value of 4, so select it and add 4 to the counter.
  Random number (25) is not less than the counter (16), so go to the next check.
  
  3e - Crossbow has a value of 4, so select it and add 4 to the counter.
  Random number (25) is not less than the counter (20), so go to the next check.
  
  3f - Composite Bow has a value of 4, so select it and add 4 to the counter.
  Random number (25) is not less than the counter (24), so go to the next check.
  
  3g - Kite Shield has a value of 4, so select it and add 4 to the counter.
  Random number (25) IS less than the counter (28), so stop.[/SPOILER]
  4 - The last set item (Kite Shield) ends up being the reward.
  
  
  So you can think of it working like a roulette wheel or something of the sort. There's a list of prizes that it rolls through, stopping at a certain point depending on the random number that was picked. Different items have different ranges, an item that has a range of 5 is 5x as likely as an item with a range of 1.
  
  The important point is that there's only one thing that determines the output of all the gachapons I looked at. The result of a call to Random(). Without having the definition of the function itself (which would require the server/Mint source code) we can't tell for sure, but given that Random() is used in a variety of other cases we can assume that player ID, level, any character stats, anything like that is not taken into account.
• X wrote on 2015-06-22 19:41
  Random is most likely (95% certainty here) a call to a static Mersenne Twister's GenerateRandom method.
• Rydian wrote on 2015-06-22 19:44
  And assuming time (or time concatenated with something else) for the seed.
• X wrote on 2015-06-22 19:48
  If it's static, it's not re-seeded.
  
  The twister is prolly seeded with the time the first time it's created. After that, every script uses the same instance of the twister, so re-seeding it would actually hurt randomness. This means if you got a bad gacha roll, you can blame it on everyone else in your channel for influencing the RNG. Heck, even Fergus uses it for calculating repairs!
  
  Yes, your bad gacha roll is Fergus's fault. You can go kill him now.
• Rydian wrote on 2015-06-22 19:52
  The server restarts at times too though, so it's gotta' re-seed then with the start time?
• Kingofrunes wrote on 2015-06-22 20:00
  So this disproves Teto's theory that the items are in pools then. It's all one big giant blob of items with different probability ranges to increase it's chance of getting picked. Thus using these number ranges you can derive a % of probability of getting an item.
  
  Although that counter bit is very interesting.
  
  In the example though you didn't mention what exactly it does with the number range when adding to the counter. Does it take the upper or lower end of that range? or is the counter value it's own number that's fixed.
  
  That is unless in your example all of those items had a range of 4 and it's the item range that's increases it's chance of being picked so for example:
  
  Pet Dye is 10, and odd kitty head (M) is 1 so odd kitty head (M) would only add 1 to the counter while pet dye would add 10 to the counter.
  
  If that's the case, then this is the oddest implementation I've seen of a gachapon ever.
• Rydian wrote on 2015-06-22 20:13
  Each item's counter-adder-number is added directly, and also the range.
  
  An item with a counter value of 1 will only be rolled if you hit that exact number.
  An item with a counter value of 100 has 100 possible numbers that will roll that item.
  
  (It's a stupid case/switch in a while loop setup.)
• X wrote on 2015-06-22 20:26

  Quote from Rydian;1279602:

  The server restarts at times too though, so it's gotta' re-seed then with the start time?

  
  
  Yes. The Twister is initialized once, on server start, probably with the current time. After that, everything uses the same twister.
• Rydian wrote on 2015-06-22 20:37
  Well how it's seeded might still be interesting. Just time, or time with something else? Normal time (Unix timestamp) or microtime?
  
  Then again seeing how the server timestamps for items are so incredibly off-kilter, using a timestamp seed prediction (like happened on NAO for nethack) is probably not feasible anyways.
• X wrote on 2015-06-22 20:51
  It's not feasible. Even if you could guess the micro/milli/whatever second, all the shared state means you'd need to know every action that had happened on the server from when it was started to now to even predict the next number. If you can do that, you're so deep into the server already that you don't need to predict RNG calls, you can just invoke your target code directly xD.
  
  Incidentally this is why Uladh bosses do not have, and have never had, spawn schedules. You repairing your gathering knife changes the next spawn delay of the Goblin Bandits. It's actually really cool, when you think about it.
• Rydian wrote on 2015-06-22 20:56

  Quote from Xcelled194;1279616:

  all the shared state means you'd need to know every action that had happened on the server from when it was started to now to even predict the next number

  Unless you're on Tarlach!
  
  Oh hoh hoh hoh hoh~
• X wrote on 2015-06-22 21:02
  [Image: http://i0.kym-cdn.com/photos/images/newsfeed/000/757/858/8f5.jpg]