1. This site uses cookies. By continuing to use this site, you are agreeing to our use of cookies. Learn More.
  2. Welcome to Pokemon Perfect, Guest!

    Our motto is Pokémon Practice makes Pokémon Perfect. We are a competitive-battling community that encourages the development of players and their ideas, and fosters positive and respectful attitudes. We love Collaboration (working together), Competition (getting stronger), and Communication (being informed).

    You are free to post everywhere, unless the thread explicitly states otherwise (usually in the case of a vote), and there are no private forums whatsoever. We just require you to not make multiple accounts. Let us greet you by posting a thread in the Introduce Yourself! forum.

  3. Tiers

    View Introduction to Tiers if you don't know what tiers are. Pokémon Perfect tiers are named differently to those on Smogon. A numeral followed by the letter U, e.g. 1U, 2U, 3U, represents a main tier on Pokémon Perfect – the '1' of '1U' representing the tier level. For a tier to be a main tier, it must be balanced (nothing is too powerful and game-breaking) and diverse enough (include a variety of Pokémon and strategies). A numeral followed by the letter P, e.g. 1P, 2P, 3P contain all Pokémon that are deemed overpowered in the respective 1U, 2U, 3U tiers. The 1st tier level allows Pokémon that are banned in the 2nd level, and this process continues down. Read the tier list, and in-depth explanations of the tiers naming system and tiering system. Also check out our analyses for all tiers.

  4. Tournaments

    RBY 1U Seasons and its master tournaments are responsible for starting up the community, and tournaments continue to play a big role in maintaining interest in the forums. Signups Open gives you a list of tournaments you can join, and Ongoing lists tournaments that you might want to follow. Additionally, you can tap to find out approximate Schedules for tournaments.

    For historical threads, check out Signups Closed, Finished tournaments and Results. We also have Nominations, Voting and Event threads for exhibitions – past and present.

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 Member

    Joined:
    May 4, 2014
    Messages:
    5,336
    Likes Received:
    2,174
    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

    Joined:
    Apr 28, 2018
    Messages:
    2
    Likes Received:
    8
    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.
  3. magic9mushroom

    magic9mushroom BEST END. Member

    Joined:
    May 1, 2013
    Messages:
    552
    Likes Received:
    354
    These add to 107%. I am positive you made a mistake somewhere.
     
  4. Disaster Area

    Disaster Area Little Ball of Fur and Power Member

    Joined:
    May 4, 2014
    Messages:
    5,336
    Likes Received:
    2,174
    Yeah that ain't right... if you find the mistake tell me I guess, I mean honestly I'm not sure if anyone ever actually uses these numbers, lol.
     

Share This Page