Understand probability better; drop rate statistics

  • #41
    Um, and I kept on wondering why Blizzard actually increased the drop rates. These threads just keep on coming. :c
    HARDCORE T4 rift farm with a crusader, top 1 STR in the world, 6 Akkhan pieces! :o
  • #42
    I think one simply needs to cite the Infinite Monkey Theorem. In layman terms, it states that if a monkey were to randomly push keys on a type writer for an infinite period of time, the probability that it would type the English translated version of the bible is 1. What does this say for ROS? It means that if you play ROS for an infinite period of time, the probability that you will have found every legendary is 1. Get farming boys!
  • #43
    Quote from Shurgosa

    thats an interesting story....is gamblers fallacy strictly the idea that a certain thing is due?

    The Gambler's fallacy boils down to seeing black 10 times in a row on a roulette wheel and your thought process becomes "I should bet red because it's due" or "I should bet red because there's no way it hits black 11 times in a row."

    After you've already hit black 10 times in a row, there is a 50/50 chance that you hit black that 11th time. There is no natural balancing mechanism that demands a lengthy black streak is balanced out by a lengthy red streak. Although over time it's reasonable to believe such things will happen, it's completely unreasonable to believe that will happen immediately. When we talk about "over time" we're talking about thousands of spins. We're talking about timeframes that are too long for a single gambler to witness.

    The thing about gambling, and even D3 drops, is that ANYTHING can happen in the short term. You can have several horrible dry streaks where you're only getting 1 item every 3 hours for 2 weeks straight. You can also get 10 items in 2 hours. You can turn $400 into $10,000 at a blackjack table. You can also lose $2,000 in $400 increments. When you're looking at a small segment of the total ANY streak is possible. For example, at a blackjack table this past week I had three players. All three of them hit blackjack in the same hand. The odds of that are pretty low. But it happens. The casino didn't shut down the table because of "bad RNG." No one from the casino came over and threw a tantrum claiming that on the very next hand everyone was "due to lose" because, aside from being terrible customer service, that's just not how it works. Just because the casino has an advantage (albeit small) on blackjack does not mean that in the short term everything gets balanced out.
    p427 :: 89.1k EK :: 2.47m TK
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  • #44
    Quote from shaggy »

    After you've already hit black 10 times in a row, there is a 50/50 chance that you hit black that 11th time. There is no natural balancing mechanism that demands a lengthy black streak is balanced out by a lengthy red streak. Although over time it's reasonable to believe such things will happen, it's completely unreasonable to believe that will happen immediately. When we talk about "over time" we're talking about thousands of spins. We're talking about timeframes that are too long for a single gambler to witness.

    More importantly, "balanced out" is in terms of the ratio of red and black, not the difference. The expected absolute difference grows in terms of the square root of the number of flips, if I recall correctly.

  • #45
    Quote from BigEd781
    Quote from Kilo55555
    • Time for a Diablo3 example: if you go one hour without a single leg drop, you should not expect to find one the next hour just because of this. What you can say is “after 100 hours I should expect X legs” based on previous calculations.

    Actually, you should. Blizz has a timer in there to account for cold streaks.



    This is so fake... I've played for 9-12 hrs for 3 days and I did not get a single drop. Either the damn timer is broken or it's another line of crap from blizzard.
  • #46
    Quote from Tijhor

    This is so fake... I've played for 9-12 hrs for 3 days and I did not get a single drop. Either the damn timer is broken or it's another line of crap from blizzard.

    When people say this I can't help but wonder what they've been doing for those 9-12 hours. Josh stated pretty unequivocally during the beta that a dry spell of even 6 hours was more than what they wanted us to experience. He also hinted that the "failsafe" does not take into account idle time.

    So, given that most people aren't having issues with going 12 hours of gameplay without a drop, I cannot help but wonder how accurate that 9-12 hour estimate is in terms of actually killing monsters.






    Correct. When you only have 100 coin flips a "difference" of 20 seems massive. As you progress to 1,000, 10,000, 100,000, etc. that difference becomes less and less significant.

    When you're at a roulette wheel and you only have enough cash to witness a dozen spins, sure that streak of eight black in a row seems absurd. You're only looking at twelve spins! If you observe that wheel over a week, though, you'll probably come to see that it comes out pretty close to 50/50.

    In the short term ANYTHING can happen. I've drawn four straight Aces on a 13 which caused a massive uproar at the table. The odds of that aren't very good (roughly .00035%) but that is actually the same as the odds of drawing ANY specific four-card sequence. A-A-A-A is no rarer than A-7-2-Q or 2-3-4-5.

    For anyone who doesn't "get it" I would seriously suggest going to your local casino with an open mind. Observe some games and, in particular, the players. See how frequently you find people complaining that "the dealer never busts" at blackjack and observe exactly how frequently the dealer DOES bust. I've been a tables where a player has claimed to have lost 35 consecutive hands. I know, for a fact, he didn't. I know, for a fact, that two hands prior to him making that statement, he won a hand. I know, for a fact, that he didn't cash in for the amount he said he did either. I've been at tables where players have claimed I've pulled 21 for seven or eight straight hands even though the very last hand I broke.

    What's my point in mentioning that? Well when you're on the wrong end of lady luck people have a tendency to exaggerate. So maybe those five rifts you ran becomes 10 when you're retelling the story because you're pissed off about going five rifts with no orange lightshaft. Just like the gambler who is pissed off because he's down $500 saying that the he lost 35 hands in a row, even though everyone at the table knows that is completely untrue.
    Last edited by shaggy: 4/18/2014 1:25:17 PM
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  • #47
    @Shaggy - I want to hire you to come stand next to me when I roll up at the tables and slap me in the back of the head every time I start to make a bad move. I'll give you 50% of my profits.

    But on the 6th hand, I'll only give you 10% if the cards are red and not black. Unless you have a coin that you can flip.

    So I used Casinos to explain a RNG theory about Diablo in another thread. And I understand much of what is said here and the analogies made to Casino card games, games of truly random chance (flipping cards, rolling dice) but would you care to pass along information about the way slot machines work?

    For me right now they are the true comparison to this game and the RNG system. I'd like to learn more if you all have information to pass along.

    PS - I love this thread.

    Edit: I would also assume that those (both in Diablo and BlackJack) who claim they haven't gotten anything in hours or won a hand in hours are ignoring plans, crafting materials and Pushes.
    Last edited by Polrayne: 4/18/2014 4:55:24 PM
  • #48
    Most slot machines are computerized at this point.

    Typically they generate hundreds to thousands of pseudorandom numbers every second and when the user presses the button or pulls the dummy lever or whatever, they use the most recent number to determine the results. Results are weighted such that after a lot of "spins" (let's just call that 1 million) the user would get a certain percentage of their money back (this is VERY similar to the "house edge" concept on all table games). In the short term, just like a table game, anything is possible. You could have 300 spins where you win a lot. You could have 300 spins where you lose a lot.

    Ultimately, a slot machine really doesn't operate that differently from a roulette wheel, or the shuffled order of cards in a blackjack shoe, or the dice in a game of craps, or the tiles in a pai gow game.
    Last edited by shaggy: 4/19/2014 12:10:29 PM
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  • #49
    Quote from Polrayne

    PS - I love this thread.

    Edit: I would also assume that those (both in Diablo and BlackJack) who claim they haven't gotten anything in hours or won a hand in hours are ignoring plans, crafting materials and Pushes.

    :)

    Also there is a BIG difference between "I haven't gotten a leg in hours" and "I haven't gotten an UPGRADE in hours" which I think most actually mean.
  • #50
    Quote from shaggy

    In the short term ANYTHING can happen. I've drawn four straight Aces on a 13 which caused a massive uproar at the table. The odds of that aren't very good (roughly .00035%) but that is actually the same as the odds of drawing ANY specific four-card sequence. A-A-A-A is no rarer than A-7-2-Q or 2-3-4-5.

    Well, actually it is. :)

    4 Aces = 4/52 x 3/51 x 2/50 x 1/49 = approximately 270,000 to 1.

    A-7-2-Q or 2-3-4-5 = 4/52 x 4/51 x 4/50 x 4/49 = 25,380 to 1.

    But of course your point still stands. In the short term, anything can happen!

    Edit: I missed that you were talking about blackjack dealing .. and you do that with more than one full deck, right? That would mostly cancel out my maths. :)
    Last edited by st0rmie: 4/19/2014 5:36:28 PM
  • #51
    This calculation (NOT MY OWN) states that from T4 rifts you will probably find 0,86 legs/person/rift - with 10 min rift time - roughly 5 legs/hour.

    Person 1: 95 legs, 100 rifts, 0,95 legs/rift

    Person 2: 77 legs, 91 rifts, 0,84 legs/rift

    Person 3: 74 legs, 81 rifts, 0,91 legs/rift

    Person 4: 71 legs, 95 rifts, 0,74 legs/rift

    Person 5: 12 legs, 9 rifts, 1,33 legs/rift

    Person 6: 9 legs, 19 rifts, 0,47 legs/rift

    Person 7: 4 legs, 4 rifts, 1 leg/rift

    Person 8: 0 legs, 1 rift, 0 legs/rift

    The total drops were 342 in 100 rifts which means that the average per person was 0,86 legs/rift.

    Plans and kadela is not included. Rifts were only cleared to guardian.
    Last edited by Kilo55555: 4/21/2014 8:49:41 AM
  • #52
    Quote from st0rmie
    Edit: I missed that you were talking about blackjack dealing .. and you do that with more than one full deck, right? That would mostly cancel out my maths. :)

    Yes. You're right, but the effect is almost negligible in an 8-deck shoe. The odds of A-A-A-A are roughly .0029% while the odds of A-K-Q-J are roughly .0036%. You are more likely to see a non-repeating sequence, but ANY four-card sequence is rare enough that it's pretty remarkable. Yet no one is like "Wow, 2-5-7-10, the odds of that are so low!" because there is nothing memorable about it. But you pull A-A-A-A and people crap their pants.

    Some guy hit three straight twos of diamonds last night. There are crazy (both good and bad) streaks out there at every turn. It's just a matter of how big your sample size is so that you can see them. Nothing more, nothing less. I've, quite literally, seen more hands of blackjack than the average person will see in their lifetime. I've seen more hands of blackjack than the average PLAYER will see. So none of these "streaks" shock me at all. None of the good/bad RNG in D3 shocks me. To me it's just a way of life. It happens. Yet, no matter what, there are people who just cannot mentally process it.
    Last edited by shaggy: 4/21/2014 1:21:34 PM
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  • #53
    Whatever you say, here is another fact. Last game I played gave me 5 leg drops for 10 minutes. 6 legs per rift total. What was that? Streak of luck? Feel free to discuss. P.S. All drops were of average quality and didn't give me any upgrades.
  • #54
    Blizzard told us MF no longer affects chest drops, but I've seen different so far.

    I was doing chest runs, opened about 1000 chests, 500 with 0% mf, 500 with 127%. (Both sets took about 4 hours to do.)

    I did the first 500 with 0% MF and came out with, 10 legendaries so 2.5 LPH.

    With 127 MF, came out with 14 legendaries, 3.5 LPH.

    Now, this is just MY information and I want to do another 1000 (With and without MF) I should have been recording yellows as well, which I will do this time.

    I was doing Act V, 6.2, Teleporting to Abandoned siege camp, averages out to about 3 chests a run, 5 possible locations.
  • #55
    Quote from Valiantshiro

    Whatever you say, here is another fact. Last game I played gave me 5 leg drops for 10 minutes. 6 legs per rift total. What was that? Streak of luck? Feel free to discuss. P.S. All drops were of average quality and didn't give me any upgrades.

    As you stated, a streak of luck.

    PS. I'm collecting some data on drop rates in bounties. for anyone that's interested, will be up in a few days.
  • #56
    Quote from Kilo55555 »
    This calculation (NOT MY OWN) states that from T4 rifts you will probably find 0,86 legs/person/rift - with 10 min rift time - roughly 5 legs/hour.
    Person 1: 95 legs, 100 rifts, 0,95 legs/rift
    Person 2: 77 legs, 91 rifts, 0,84 legs/rift
    Person 3: 74 legs, 81 rifts, 0,91 legs/rift
    Person 4: 71 legs, 95 rifts, 0,74 legs/rift
    Person 5: 12 legs, 9 rifts, 1,33 legs/rift
    Person 6: 9 legs, 19 rifts, 0,47 legs/rift
    Person 7: 4 legs, 4 rifts, 1 leg/rift
    Person 8: 0 legs, 1 rift, 0 legs/rift
    The total drops were 342 in 100 rifts which means that the average per person was 0,86 legs/rift.
    Plans and kadela is not included. Rifts were only cleared to guardian.

    You know...... This is more consistent than I expected. I kind of expected it to converge to the average a little slower than this. So by the time you do about 100 rifts, there aren't going to be too much variations.

  • #57
    This imo shows that you should just keep grinding and focus on having fun doing it, eventually you'll get what you want. Hopefully sooner than later.
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