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    Probability for Beginners

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    B@T

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    Probability for Beginners

    Post by B@T on Wed Apr 22, 2015 6:08 pm


    Table of Contents
    1.Intro to Probability
    2. How Does it Work?
    3. Odds of Drawing a Certain Card
    4. Coin Toss
    5. Odds of Number 7: Lucky Straight Effect
    6. Odds of Getting all 5 Pieces of Exodia First Turn

    1.Intro to Probability:


    Probability is simply "How likely something is to happen" and using this, we can find the likelihood or percentage of that something happening.Concepts of probability have been around for thousands of years, but probability theory did not arise as a branch of mathematics until the mid-seventeenth century. You can use probability to find the odds of a coin toss being a certain result or finding the odds of a certain sum being rolled or even finding the odds of having a certain monster in your hand which i am going to explain today.


    2.How does it work?:


    Probability is simply the formula:

    we can use this formula to find the probability of something happening for anything from dice to cards to spinning a wheel.

    Probability application to YU-Gi-OH:
    You can use probability in yugioh to find the odds for the following:

    • Odds of drawing a certain card
    • Odds of rolling a dice
    • Odds of getting a certain coin toss permutations which is the odds of something happen in any order.



    3. Odds of Drawing a Certain Card:

    cards in deckodds of drawing a card
    1/402.5%
    1/412.43%
    1/422.38%
    1/432.33%
    1/442.27%
    1/452.22%
    1/462.17%
    1/472.13%
    1/482.08%
    1/492.04%
    1/502%
    1/511.96%
    1/521.92%
    1/531.87%
    1/541.85%
    1/551.82%
    1/561.79%
    1/571.75%
    1/581.72%
    1/591.69%
    1/60
    1.67%

    Here is a Graph for the Data:


    Does it matter how many cards i have in the deck?
    Even though the percent difference is small, your odds aren't great to begin with hence why people think "the less cards in your deck, the better the odds" because your are decreasing the total number of cards in the deck and increase the odds of a better card.

    Coin Toss:
    As stated before, you can use probability to find the odds of a coin toss. I will doing the following example
    Code:
    Toss a coin 3 times. If all 3 results are Heads, destroy all monsters on your opponent's side of the field. If all 3 results are Tails, destroy all monsters on your side of the field. You can only activate this effect once per turn, during your Main Phase.

    Suppose you use Sand Gambler's effect to destroy 5 of your opponent's monsters which you will need 3 coin toss that will result in all 3 being heads. I am going to show you using as probability tree.


    Probability Tree is basically a diagram used to find the odds of something by showing a map of the results. Ever branch is a probability of something happening thus we have 3 sections of branches for tossing a coin three times.
    Using the formula stated previously,
    (1/2) *(1/2)*(1/2)=( 1/8 ) which is 12.5% odds of getting result of all 3 being heads.

    Now lets do something a little more harder(don't worry its easier than it looks!)
    Suppose i use Barrel Dragon instead to destroy an opponent's monster

    Code:
    Once per turn: You can target 1 monster your opponent controls; toss a coin 3 times and destroy it if at least 2 of the results are Heads.

    Now using the probability tree for visual concept to find the odds of getting a result with at least 2 heads which will be using the same tree form before.



    now taking all the results of being at least 2 heads in the result and adding them

    (HHH)+(HHT)+(HTH)+(THH)=total probability of having 2 heads or more on a coin toss
    .125+.125+.125+.125=.5 or 50% of the result of having 2 heads or more for using barrel dragon's effect.

    5. Odds of Number 7: Lucky Straight Effect:
    Suppose i wanted to use Lucky Straight's effect to roll a dice two times and get a total result of exactly 7.


    Code:
    You can detach 1 Xyz Material from this card; roll a six-sided die twice and this card's ATK becomes the larger number rolled × 700 until your opponent's next End Phase, then if the total roll was exactly 7, apply 1 of these effects.
    ● Send all other cards on the field to the Graveyard.
    ● Special Summon 1 monster from your hand or from either Graveyard.
    ● Draw 3 cards, then discard 2 cards

    I can set up a table of the odds of rolling a total sum of 7.
    123456
    1234567
    2335678
    3456789
    45678910
    567891011
    6789101112
    I now take the total of times i can get a result of 7 and divivded over the number of possible rolls.

    123456
    1234567
    2335678
    3456789
    45678910
    567891011
    6789101112
    total number of rolling being sum of 7/total number of events=6/36=.1666667 or 16.7% of getting a sum of 7 from Lucky Straight's effect.

    6. Odds of Getting all 5 Pieces of Exodia First Turn:
    Believe or not, this is much simple than it seems. Suppose i had a 40 card deck with all monsters(different builds can change it and there is more than 1 type of Exodia builds so i am showing it just a practical results.). Suppose that Player 1 and Player 2 both used the same exact deck with all monsters and it's Player 1's Opening Turn.




    Player 1's odds of getting Exodia in his first 5 cards from opening hand:

    remember its :total number of success/total number of cards to find probability.
    (5 pieces of exodia left in deck/40 cards left)*(4 pieces of exodia left in deck/39 cards left)*(3 pieces of exodia left in deck/38 cards left)*(2 pieces of exodia left in deck/37 cards left)*(1 pieces of Exodia left in deck/36 cards left)=1:658008 chance of getting exodia for Player 1


    Player 2's odds of getting Exodia in his first 5 cards from opening hand and 1 card from draw phase for a total of 6 cards:

    Remember its :Total Number of Success/Total Number of Cards to find Probability.
    (5 pieces of exodia left in deck/40 cards left)*(4 pieces of exodia left in deck/39 cards left)*(3 pieces of exodia left in deck/38 cards left)*(2 pieces of exodia left in deck/37 cards left)*(35 card left in deck/36 cards left)*(1 piece of exodia left/35 cards left in deck)*6 different ways you can not draw exodia piece=1:09668 chance of getting exodia for Player 2.


    Since Player 2 drew a card from his draw phase, his odds are better than Player 1's odds which i just proved.

    Hope you enjoy reading this article!
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    RinTakasu

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    Re: Probability for Beginners

    Post by RinTakasu on Sun Apr 26, 2015 2:15 pm

    To enrich this post information, I'll try to explain some drawing mechanics with math:

    The first time you are drawing cards (5 ~ 6 cards first to go or second to go) most of the time someone desires to pull out a specific card.

    In math there's a funny thing called Hypergeometric Distribution and Binomial Distribution:
    http://en.wikipedia.org/wiki/Hypergeometric_distribution
    http://en.wikipedia.org/wiki/Binomial_distribution

    You can read further information if you wish to corroborate on this post, however I'll try to give a little TL;DR.

    Hypergeometric = Multiple attempts without replacement

    Which means that if we have ball pit with 28 red balls and 2 black balls, everytime we pull out a ball we won't throw our balls back to the pit

    Binomial =  Multiple attempts with replacement

    Which means that if we have a ball pit with 28 red balls and 2 black balls, everytime we pull out a ball we will throw our balls back to the pit

    [Calculators]
    http://stattrek.com/online-calculator/hypergeometric.aspx
    http://stattrek.com/online-calculator/binomial.aspx
    We'll use these to aid us on our problems

    Now taking this information
    1) Are the cards shuffled back to the deck? (Are we replacing our chances?)
    2) How many of that cards are on the deck? (Which are the number of successes?)
    3) Which are the number of attempts? (Which are the number of trials?)
    4) How many cards do we have on our deck? (Which is our population?)
    5) How many of THAT card do we want in our hand?

    In a Card game the situation that happens most of the time is:
    1) No
    2) 3
    3) 5 ~ 6
    4) 40
    5) 1

    1) Gives us which kind of distribution it is, in this case is Hypergeometric

    So we'll use the Hypergeometric calculator:
    First to go:


    30.11%

    Second to go:


    34.06%

    Afterwards the math is simple:
    You already pulled out 5 ~ 6 of your cards and didn't draw any of them?
    Then the chances are

    First to go:
    (3/35)*100 = 8.57%
    Second to go:
    (3/34)*100 = 8.82%

    *Note: THIS EXAMPLE IS BASED ON HAVING 3 CARDS OF THAT NAME IN DECK, IF YOU WISH TO CHANGE IT TO 2 OR 1 THEN CHANGE THE NUMBER OF SUCCESSES IN POPULATION BY THAT NUMBER AND IF YOU WISH TO HAVE MORE OF THAT CARD IN HAND THEN CHANGE THE NUMBER OF SUCCESSES IN SAMPLE BY THE NUMBER OF THAT CARD THAT YOU WANT IN HAND.


    Last edited by RinTakasu on Sun Apr 26, 2015 2:16 pm; edited 1 time in total (Reason for editing : ball* not bal, hue.)

    B@T

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    Re: Probability for Beginners

    Post by B@T on Sun Apr 26, 2015 5:01 pm

    Spoiler:

    RinTakasu wrote:To enrich this post information, I'll try to explain some drawing mechanics with math:

    The first time you are drawing cards (5 ~ 6 cards first to go or second to go) most of the time someone desires to pull out a specific card.

    In math there's a funny thing called Hypergeometric Distribution and Binomial Distribution:
    http://en.wikipedia.org/wiki/Hypergeometric_distribution
    http://en.wikipedia.org/wiki/Binomial_distribution

    You can read further information if you wish to corroborate on this post, however I'll try to give a little TL;DR.

    Hypergeometric = Multiple attempts without replacement

    Which means that if we have ball pit with 28 red balls and 2 black balls, everytime we pull out a ball we won't throw our balls back to the pit

    Binomial =  Multiple attempts with replacement

    Which means that if we have a ball pit with 28 red balls and 2 black balls, everytime we pull out a ball we will throw our balls back to the pit

    [Calculators]
    http://stattrek.com/online-calculator/hypergeometric.aspx
    http://stattrek.com/online-calculator/binomial.aspx
    We'll use these to aid us on our problems

    Now taking this information
    1) Are the cards shuffled back to the deck? (Are we replacing our chances?)
    2) How many of that cards are on the deck? (Which are the number of successes?)
    3) Which are the number of attempts? (Which are the number of trials?)
    4) How many cards do we have on our deck? (Which is our population?)
    5) How many of THAT card do we want in our hand?

    In a Card game the situation that happens most of the time is:
    1) No
    2) 3
    3) 5 ~ 6
    4) 40
    5) 1

    1) Gives us which kind of distribution it is, in this case is Hypergeometric

    So we'll use the Hypergeometric calculator:
    First to go:


    30.11%

    Second to go:


    34.06%

    Afterwards the math is simple:
    You already pulled out 5 ~ 6 of your cards and didn't draw any of them?
    Then the chances are

    First to go:
    (3/35)*100 = 8.57%
    Second to go:
    (3/34)*100 = 8.82%

    *Note: THIS EXAMPLE IS BASED ON HAVING 3 CARDS OF THAT NAME IN DECK, IF YOU WISH TO CHANGE IT TO 2 OR 1 THEN CHANGE THE NUMBER OF SUCCESSES IN POPULATION BY THAT NUMBER AND IF YOU WISH TO HAVE MORE OF THAT CARD IN HAND THEN CHANGE THE NUMBER OF SUCCESSES IN SAMPLE BY THE NUMBER OF THAT CARD THAT YOU WANT IN HAND.

    this is a good thing i was going to add in another time but not something similar to this because its for beginner players to understand how probability comes into play. what i am trying to say is " your scaring the children."
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    RinTakasu

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    Re: Probability for Beginners

    Post by RinTakasu on Sun Apr 26, 2015 5:12 pm

    B@TMAN wrote:

    this is  good thing i was going to add in another time but not something similar to this because its for beginner players to understand how probability comes into play. what i am trying to say is " your scaring the children."

    The main point of my explanation is that there's a huge difference between drawing a single card every turn, to your first 5~6 cards on your first turn and how important it is to have 3 of the same card if someone wants to see it much more often.

    Also that probabilities are not cumulative properties.

    Sorry if I made it sound to complex.
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    jef12345

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    Re: Probability for Beginners

    Post by jef12345 on Mon Apr 27, 2015 2:12 am

    batman it's a furom for duelists not a nursery. if they can't understand some simple mathematics probabilities then they gotta get outta here.
    YUGIOH IS NOT GAME FOR CHILDREN!!
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    Ptolemy

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    Re: Probability for Beginners

    Post by Ptolemy on Mon Apr 27, 2015 5:04 am

    Uh...wasn't Yugioh meant to be a children's card game from the start?

    B@T

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    Re: Probability for Beginners

    Post by B@T on Mon Apr 27, 2015 12:15 pm

    jef12345 wrote:batman it's a furom for duelists not a nursery. if they can't understand some simple mathematics probabilities then they gotta get outta here.
    YUGIOH IS NOT GAME FOR CHILDREN!!

    i hate to be that guy but......
    http://www.yugioh-card.com/en/about/parents_after-event.html
    "Like the game of Chess, the Yu-Gi-Oh! TRADING CARD GAME is a simple game with a lot of complex strategies. At the most basic level, the Yu-Gi-Oh! TRADING CARD GAME forces kids to use simple math and reading skills, while exercising the social skills necessary to play against other kids. "

    konami seems to think it is.....
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    AkatsukiClan:Sasori

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    Re: Probability for Beginners

    Post by AkatsukiClan:Sasori on Tue Apr 28, 2015 5:10 am

    preach it B@tman

    B@T

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    Re: Probability for Beginners

    Post by B@T on Thu Apr 30, 2015 8:23 pm

    AkatsukiClan:Sasori wrote:preach it B@tman

    if i was a preacher, i would be wearing my dueling glove and my yugi socks
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    duckymomo101

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    Re: Probability for Beginners

    Post by duckymomo101 on Fri May 01, 2015 11:24 am



    B@TMAN wrote:if i was a preacher, i would be wearing my dueling glove and my yugi socks

    How do we know that you aren't wearing them....hmmm x3

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    Re: Probability for Beginners

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