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Keyrun Probabilities

Discussion in 'Diablo 3 General Discussion' started by phaedrus, Apr 11, 2013. | Replies: 3 | Views: 6357

  1. phaedrus

    phaedrus IncGamers Site Pal

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    Has anyone done any analysis on whether the actual drop rate of keys matches Blizzard's published rates (for MP levels less than 10)?

    I am asking because I do keyruns at MP5, and I have not been getting anything even close to a 50% drop rate. I am averaging about one drop every 5 runs.

    In addition, I have had multiple losing streaks of 13 and 14 runs in a row without a key. Now, I realize that a random 50% drop cycle can yield long losing streaks, but still - the probability of a 14 run losing streak in a series with a 50% chance is quite low. Having that occur multiple times seems to strain the probabilities.

    Also, while you might expect long losing streaks, in a truly random cycle you would also expect the counter-balancing long winning streaks - say, getting 10 keys in 15 runs.

    So, has anyone looked at this? Or do people only do keyruns at MP10, where the probabilities don't enter into it?

    Thanks for any input.
  2. spolja

    spolja IncGamers Member

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    It's all about RNG.

    I've tested it recently:
    ACT I key: MP3 - 20 runs - 3 keys (with a dry streak of 15 runs)
    ACT II key: MP3 - 10 runs - 8 keys
    Also, few weeks before:
    ACT II key: MP2 - 50 runs - 10 keys (perfect score)
  3. phaedrus

    phaedrus IncGamers Site Pal

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    Thanks for your response.

    Yes, I understand it's all about RNG, which is my point, really.

    In a large enough sample size, true RNG should smooth out the random perturbations and approach the theoretical drop rate.

    In your case, your MP3 drops yielded 11 keys for 30 runs - actually slightly better than the predicted drop rate of 9 keys.

    I've farmed a total of 61 keys at MP5. Let's say that translates into 300 runs (that's a guesstimate on my part, given my more recent track record of one drop every five runs - I didn't start keeping records until I noticed my drops weren't tracking Blizzard's published stats).

    With a sample size of 300 independent events, and a 50% win rate, the probability of a 14 run losing streak is 0.875%. The probability of a 13 run losing streak is 1.750%. The probability of BOTH a 13 and 14 run losing streak in 300 runs is multiplicative, or 0.015%.

    Now, I suppose it's possible I am just particularly unlucky, and am that one in 6,600 person that rolls those sort of losing streaks.

    However, if we were talking coin tosses, and you did 300 tosses and got 240 heads and 60 tails, I suspect you would start to look askance at the coin.
  4. sirwhere

    sirwhere IncGamers Member

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    phaedrus, long losing steaks are extremely common. That is especially true with distributions with a high variability, like the one at stake in keydrops. (Incidently, it is also why chances are you'll go bankrupt if you keep trying "double or nothing" at the casino rollette...)

    People have a tendency to recall the losing streaks, but not the winning ones. It's just that. Keep on playing you'll eventually go back into the odds.

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