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Thread: For those who are wondering how many tries u need to obtain a Legendary General.

  1. #1

    Default For those who are wondering how many tries u need to obtain a Legendary General.

    To calculate the probability of getting at least one legendary general in n tries.

    Let X be the discrete random variable the number of legendary general obtained.
    Clearly X follows a binomial distribution with X~B(n,p)

    P(X=0)=(nC0)(p^0)(1−p)^n=(1−p)^n

    So the probability we are looking for is:

    P(X≥1)=1−P(X=0)=1−(1−p)^n

    where p is the probability of getting a legendary general in this case is 1% so 0.01
    n is the number of trials

    so we are looking at P(X≥1)=1−P(X=0)=1−(1−0.01)^n= 1- (0.99)^n
    In this case we want to find the n large enough to achieve a probability that one is satisfied.
    And this n is the number of chest rolls we are going to do.

    Good luck all, and happy rolling.

  2. #2

    Default

    n P(X>=1)==1-(0.99)^n

    50 0.394993933
    100 0.633967659
    150 0.778548213
    200 0.866020325
    250 0.918941484
    300 0.950959106
    350 0.970329962
    400 0.982049447
    450 0.989139806
    500 0.993429517
    550 0.996024818
    600 0.997594991
    650 0.998544955
    700 0.999119689
    750 0.999467406
    800 0.999677778
    850 0.999805054
    900 0.999882056
    950 0.999928643

  3. #3

    Default

    Quote Originally Posted by baoyutaohuagong View Post
    To calculate the probability of getting at least one legendary general in n tries.

    Let X be the discrete random variable the number of legendary general obtained.
    Clearly X follows a binomial distribution with X~B(n,p)

    P(X=0)=(nC0)(p^0)(1−p)^n=(1−p)^n

    So the probability we are looking for is:

    P(X≥1)=1−P(X=0)=1−(1−p)^n

    where p is the probability of getting a legendary general in this case is 1% so 0.01
    n is the number of trials

    so we are looking at P(X≥1)=1−P(X=0)=1−(1−0.01)^n= 1- (0.99)^n
    In this case we want to find the n large enough to achieve a probability that one is satisfied.
    And this n is the number of chest rolls we are going to do.

    Good luck all, and happy rolling.
    Remember, you need a sufficient sample size to test for it.

    I have a patent in Video Poker and generally the top payoff is a Royal Flush (4 per standard deck of playing cards).

    The cycle for a Royal Flush is about once in 40,000 hands using computer perfect strategy.

    The industry standard to test a slot machine or video poker machine is 10,000,000 “pulls” (aka bets) or 250 Royal Flush cycles.

    The gaming company I worked with told me that by 1,000,000 pulls or 25 royal cycles, they had a good idea of the return.

    This was all simulated hands (results) because the software to test the correct strategy wasn’t developed yet and cycling through each hand (which was used as a check figure) took a while. The company had a program that cycled through each 2.5+ million hands. That 2.5+ million hands was in a data file. Today, the cpu in an iPhone 11 is many times more powerful than Intel 286’s in desktops that people used back then.

    As for my personal experience, I estimated I went through 200,000 hands (5 royal cycles) over a 2-year stretch and did not hit a royal flush.

    A dealt royal flush occurs once in about 650,000 hands. I’ve only been dealt 3 royals in my lifetime and all 3 occurred in the same month with two in the same casino. Go figure. I would love to see baoyutaohuagong do the math for a dealt royal.

    Video poker is a high variance game and games of chance offering high variance is a beetch.

    The odds for Layla or Hera is assumed to be 0.5% each. The odds of a royal flush is about 0.0025%.

    It was quite painful to go through about 200,000 hands without a royal flush. As a result, I am very reluctant to go down the road that chest spins are broken because I understand variance a lot better than most people.

  4. #4
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    Default

    for the meantime add me 5E51FD and this
    Pls do not hurt me... coz i know someone who knows someone that knows someone who can hurt you.

  5. #5
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    Default

    Quote Originally Posted by Batw View Post
    Remember, you need a sufficient sample size to test for it.

    I have a patent in Video Poker and generally the top payoff is a Royal Flush (4 per standard deck of playing cards).

    The cycle for a Royal Flush is about once in 40,000 hands using computer perfect strategy.

    The industry standard to test a slot machine or video poker machine is 10,000,000 ďpullsĒ (aka bets) or 250 Royal Flush cycles.

    The gaming company I worked with told me that by 1,000,000 pulls or 25 royal cycles, they had a good idea of the return.

    This was all simulated hands (results) because the software to test the correct strategy wasnít developed yet and cycling through each hand (which was used as a check figure) took a while. The company had a program that cycled through each 2.5+ million hands. That 2.5+ million hands was in a data file. Today, the cpu in an iPhone 11 is many times more powerful than Intel 286ís in desktops that people used back then.

    As for my personal experience, I estimated I went through 200,000 hands (5 royal cycles) over a 2-year stretch and did not hit a royal flush.

    A dealt royal flush occurs once in about 650,000 hands. Iíve only been dealt 3 royals in my lifetime and all 3 occurred in the same month with two in the same casino. Go figure. I would love to see baoyutaohuagong do the math for a dealt royal.

    Video poker is a high variance game and games of chance offering high variance is a beetch.

    The odds for Layla or Hera is assumed to be 0.5% each. The odds of a royal flush is about 0.0025%.

    It was quite painful to go through about 200,000 hands without a royal flush. As a result, I am very reluctant to go down the road that chest spins are broken because I understand variance a lot better than most people.

    Royal flush
    Distinct hands 1
    Frequency 4
    Probability 0.000154%
    Cumulative probability 0.000154%
    Odds 649,740 : 1

    I'm no expert in computer poker; however... in actual poker you already laid out why...
    Last edited by shadoxfoxspirit; 09-19-2019 at 04:24 AM.
    "Nothing is true, everything is permitted"
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  6. #6

    Default

    Dealt Royal from standard 52 card deck.

    C( 52, 5 ) = 2,598,960 possible distinct hands.

    Only 4 of those are Royal Flushes.

    The maths:

    Permutations, nPr = 52!/(52 - 5)! = 311,875,200


    Combinations, nCr = 52!/ (5! ◊ (52 - 5)!) = 2,598,960


    [Remember, you didn't ask (and you shouldn't, since the order doesn't matter) for the permutations of Royal Flushes.]

    4/2,598,960 = 1/649,740 = 0.00015% chance of being dealt a royal flush.
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  7. #7

    Default

    Quote Originally Posted by Batw View Post
    Remember, you need a sufficient sample size to test for it.

    I have a patent in Video Poker and generally the top payoff is a Royal Flush (4 per standard deck of playing cards).

    The cycle for a Royal Flush is about once in 40,000 hands using computer perfect strategy.

    The industry standard to test a slot machine or video poker machine is 10,000,000 “pulls” (aka bets) or 250 Royal Flush cycles.

    The gaming company I worked with told me that by 1,000,000 pulls or 25 royal cycles, they had a good idea of the return.

    This was all simulated hands (results) because the software to test the correct strategy wasn’t developed yet and cycling through each hand (which was used as a check figure) took a while. The company had a program that cycled through each 2.5+ million hands. That 2.5+ million hands was in a data file. Today, the cpu in an iPhone 11 is many times more powerful than Intel 286’s in desktops that people used back then.

    As for my personal experience, I estimated I went through 200,000 hands (5 royal cycles) over a 2-year stretch and did not hit a royal flush.

    A dealt royal flush occurs once in about 650,000 hands. I’ve only been dealt 3 royals in my lifetime and all 3 occurred in the same month with two in the same casino. Go figure. I would love to see baoyutaohuagong do the math for a dealt royal.

    Video poker is a high variance game and games of chance offering high variance is a beetch.

    The odds for Layla or Hera is assumed to be 0.5% each. The odds of a royal flush is about 0.0025%.

    It was quite painful to go through about 200,000 hands without a royal flush. As a result, I am very reluctant to go down the road that chest spins are broken because I understand variance a lot better than most people.
    I found a par sheet (a piece of paper that discloses the slot machine’s return) and towards the bottom, they list 90% confidence intervals for 1,000 “pulls” to 10,000,000 “pulls”, respectively.

    You can see the huge swings at 1,000 pulls but by 10,000,000 pulls, the casino should make it’s expected value of 14.5% house edge.

    My point is you can see huge swings in small data sets and be lulled in the belief that the game is not random. After 1,000 spins, you were supposed to lose 14.5% of your money but could lose at a rate of 45%+ (because game returns 54%+) or win at a rate of 16.88%. By looking at any 1,000 pulls is not sufficient data size to determine the game returns 85.5% (same as house edge of 14.5%) DESPITE THE FACT each spin has a house edge of 14.5%!

    https://easy.vegas/games/slots/par_s...neric-1987.gif

    A casino slot machine return is based on 10,000,000 observations. It is really important to understand binomial results within the correct data set.

  8. #8

    Default

    Quote Originally Posted by shadoxfoxspirit View Post
    Royal flush
    Distinct hands 1
    Frequency 4
    Probability 0.000154%
    Cumulative probability 0.000154%
    Odds 649,740 : 1

    I'm no expert in computer poker; however... in actual poker you already laid out why...
    And the math for 3 dealt Royal Flushes in one month? I would love to see the math using binomial distribution.

  9. Default

    2 x universe = tube

  10. #10
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    Default

    Quote Originally Posted by dani2000 View Post
    ^^ +1

    and 10 chars

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