  Probability Article for Beginners.  
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B@TMAN
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 Subject: Probability Article for Beginners. Mon Aug 03, 2015 11:37 pm#1  

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 midseventeenth 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.

3. Odds of Drawing a Certain Card:cards in deck  odds of drawing a card  1/40  2.5%  1/41  2.43%  1/42  2.38%  1/43  2.33%  1/44  2.27%  1/45  2.22%  1/46  2.17%  1/47  2.13%  1/48  2.08%  1/49  2.04%  1/50  2%  1/51  1.96%  1/52  1.92%  1/53  1.87%  1/54  1.85%  1/55  1.82%  1/56  1.79%  1/57  1.75%  1/58  1.72%  1/59  1.69%  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 sixsided 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.
 1  2  3  4  5  6  1  2  3  4  5  6  7  2  3  3  5  6  7  8  3  4  5  6  7  8  9  4  5  6  7  8  9  10  5  6  7  8  9  10  11  6  7  8  9  10  11  12  I now take the total of times i can get a result of 7 and divivded over the number of possible rolls.
 1  2  3  4  5  6  1  2  3  4  5  6  7  2  3  3  5  6  7  8  3  4  5  6  7  8  9  4  5  6  7  8  9  10  5  6  7  8  9  10  11  6  7  8  9  10  11  12  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! 

Last edited by B@TMAN on Tue Aug 04, 2015 7:43 pm; edited 2 times in total 
   Master Marcus
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 Subject: Re: Probability Article for Beginners. Tue Aug 04, 2015 1:56 pm#2  
 numbers are very important in deck building
nice article _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 
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 Subject: Re: Probability Article for Beginners. Tue Aug 04, 2015 1:59 pm#3  
 just have faith on heart of da cards in the end its just "RNG"EEEEEEEEEEEEEEZUZ no matter haw many % is dat RNGEEEZUZ is always RNGEEEEEEEEEEEEEEZUZ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Wicked Blade's Let's Dance All Night Rising Special Ultra Miracle Super Mario Brothers Second Edition Luigi's Revenge Director's Cut 
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 Subject: Re: Probability Article for Beginners. Tue Aug 04, 2015 4:38 pm#4  
 i would appropriate it if someone didnt remove my banner i made. 
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 Subject: Re: Probability Article for Beginners. Tue Aug 04, 2015 6:20 pm#5  
 Nice article @B@tman and it sheds light into an important factor in YuGiOh that a lot of people, ignorently attribute to luck. Although your calculation are correct, they don't show the complete truth. When calculated the odds of drawing a certain card you assumed 1 copy of that card in the deck, and drawing 1 card from the deck. Which is not what happens in a YGO duel. When taking copies of the cards, and drawing 5 cards from the deck into consideration, the table would look something like this **: #  x3draw5  x3draw6  x2draw5  x2draw6  x1draw5  x1draw6  40  33.7%  39.4%  23.7%  28%  12.5%  15%  42  32.3%  37.8%  22.6%  26.8%  11.9%  14.2%  48  28.6%  33.6%  19.9%  23.7%  10.4%  12.5%  60  23.3%  27.5%  16.1%  19.15%  8.33%  10%  37*  36.16%  42.14*  25.5%  30.18%  13.5%  16.2%  *3upstart goblins**see Hypergeometric distribution for info on how the odds are calculated.Interesting things to note here is how different the odds are when running x2 and x3. And how much better odds running 3 Upstarts gives you. This goes to show that luck is not the only culpurt when blaming bad draws. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 
   B@TMAN
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 Subject: Re: Probability Article for Beginners. Tue Aug 04, 2015 7:39 pm#6  
  @LoudFist wrote:
 Nice article @B@tman and it sheds light into an important factor in YuGiOh that a lot of people, ignorently attribute to luck.
Although your calculation are correct, they don't show the complete truth. When calculated the odds of drawing a certain card you assumed 1 copy of that card in the deck, and drawing 1 card from the deck. Which is not what happens in a YGO duel. When taking copies of the cards, and drawing 5 cards from the deck into consideration, the table would look something like this**:
#  x3draw5  x3draw6  x2draw5  x2draw6  x1draw5  x1draw6  40  33.7%  39.4%  23.7%  28%  12.5%  15%  42  32.3%  37.8%  22.6%  26.8%  11.9%  14.2%  48  28.6%  33.6%  19.9%  23.7%  10.4%  12.5%  60  23.3%  27.5%  16.1%  19.15%  8.33%  10%  37*  36.16%  42.14*  25.5%  30.18%  13.5%  16.2%  *3upstart goblins **see Hypergeometric distribution for info on how the odds are calculated.
Interesting things to note here is how different the odds are when running x2 and x3. And how much better odds running 3 Upstarts gives you.
This goes to show that luck is not the only culpurt when blaming bad draws.
i should of explained why the 1/401/60 chart. its there to explained how 1 card makes a difference in a deck. this was for top decking cases where limited card. this article is for beginners so i might making an higher up article which i have thought about for awhile. 
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 Subject: Re: Probability Article for Beginners. Wed Aug 05, 2015 11:27 am#7  
 RNGEEEEZUS IS RNGEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEZUS
daz maek luck is just expression of probabilities/chance/RNGEEEEEEEEEEEEEEEEEEEEEEEZEUS
Stopped W.O.P.i.E from breaking the forum again. ~Thanako _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Wicked Blade's Let's Dance All Night Rising Special Ultra Miracle Super Mario Brothers Second Edition Luigi's Revenge Director's Cut 
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 Subject: Re: Probability Article for Beginners. Wed Aug 05, 2015 6:53 pm#8  
 Oh, I like this banner a lot more than the other one you were using, and the general layout! A lot of improvements put into an already amazing guide for beginners. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ La La La La La La La La La La...「私は愛した」
La La La La La La La La La La...「私は生きてた」 
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 Subject: Re: Probability Article for Beginners. Wed Aug 05, 2015 7:35 pm#9  
  @Thanako wrote:
 Oh, I like this banner a lot more than the other one you were using, and the general layout! A lot of improvements put into an already amazing guide for beginners.
Your welcome ^.^
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 
  
 Subject: Re: Probability Article for Beginners. #10  
 
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