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RBY 255s

Discussion in 'Analysis and Research' started by Disaster Area, Jul 25, 2015.

  1. Disaster Area

    Disaster Area Little Ball of Fur and Power Leader

    May 4, 2014
    Likes Received:
    All to 3dp. P(n= some number) indicates the number of turns.

    Probability of not getting a 255.
    P(n=10)= 96.162% (about 24 in 25)
    P(n=16)= 93.930% [Ice Beam's PP, Psychic's PP, Body Slam's PP]
    P(n=20)= 92.471%
    P(n=24)= 91.034% (about 10 in 11) [Thunderbolt's PP, Surf's PP]
    P(n=32)= 88.228% [Seismic Toss's PP]
    P(n=40)= 85.508% [Thunderbolt and Ice Beam's combined PP]
    P(n=50)= 82.226% (about 4 in 5)
    P(n=64) = 77.842% [2 user's Stoss PP, 2 IB+Psychic PP]
    P(n=72) = 75.442% (about 3 in 4) [Stoss+IB+TB PP]
    P(n=80) = 73.117% [2 user's IB+TB PP]

    Probability of getting a single 255 over a given number of hits.
    P(n=1)= 0.4% (1 in 256)
    P(n=5)= 1.923% (about 1 in 50)
    P(n=10)= 3.771% (about 1 in 26)
    P(n=16)= 5.894% (about 1 in 17) [Ice Beam's PP, Psychic's PP, Body Slam's PP]
    P(n=20)= 7.253% (about 1 in 13)
    P(n=24)= 8.568% (about 1 in 12) [Thunderbolt's PP, Surf's PP]
    P(n=32)= 11.072% (about 1 in 9) [Seismic Toss's PP]
    P(n=40)= 13.413% (about 2 in 15) [Thunderbolt and Ice Beam's combined PP]
    P(n=50)= 16.123% (about 4 in 25)
    P(n=64) = 19.539% (about 1 in 5) [2 user's Stoss PP, 2 IB+Psychic PP]
    P(n=72) = 21.301% [Stoss+IB+TB PP]
    P(n=80) = 30.405% (about 1 in 3) [2 user's IB+TB PP]

    Probability of getting two 255s.
    P(n=20)= 0.270% (about 1 in 400)
    P(n=24)= 0.386% (about 1 in 250) [Thunderbolt's PP, Surf's PP]
    P(n=32)= 0.668% (about 1 in 150) [Seismic Toss's PP]
    P(n=40)= 1.026% (about 1 in 100) [Thunderbolt and Ice Beam's combined PP]
    P(n=50)= 1.438%
    P(n=64) = 2.413% [2 user's Stoss PP, 2 IB+Psychic PP]
    P(n=72) = 2.965% (about 1 in 33) [Stoss+IB+TB PP]
    P(n=80) = 3.553% (about 1 in 28) [2 user's IB+TB PP]

    P(n=y)= 100 * (255/256)y-x * (1/256)x * yCx, where yCx = y!/(x!(y-x)!).
    Last edited: May 14, 2018
  2. DegenerateDitto

    DegenerateDitto Member

    Apr 28, 2018
    Likes Received:
    Nice analysis. I like how you annotated the probabilities. There's a small typo in P(n - 1). It should be 0.4% or 0.004, not 0.004%.

    A good rule of thumb for small probabilities is that they can be added directly. The probability of a 255 is 1/256, so the probability of getting it the first or second turn is 2 * 1/256, and for n turns (where n is small) it is n * 1/256.

    This works cause the true odds

    1 - (1 - 1/256)^n

    is approximately

    1 - (1 - n * (1/256)) = n * 1/256 (binomial approximation)

    So just remember that 1/256 = 4/1024 ≈ 4/1000 = 0.004. And if for some reason you want a better approximation just use (1 - 1/256)^n ≈ 1 - n * (1/256) + n * (n-1)/2 (1/256)^2.

    This trick will work for other small odds. Like the odds of a full para over two turns is about .25 * 2 = .5 (it's actually .44). Or freeze due to ice beam over 3 turns ≈30%. Or para'd Tauros getting full parad or missing hyper-beam is .10 + .25 ≈ .35.
    Last edited: May 14, 2018
    Disaster Area and Linkin Karp like this.

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