# Let's talk probability

## Let's talk probability

Lets take a moment and talk about probability (since i rbought this up in the originality topic, I'll go more in depth about it here). Every formula will be given to you so you can hopefully understand it better, and i will attempt to explain to the best of my capacity. so without further adue here we go.

Factorials: Represented by an "!" after a given number. For example, 5! is equivalent to 5x4x3x2x1, which equals 120. Factorial is very important for calculating the number of combinations and permutations of a given event.

Probability Formula: (Number of successes/Number of possible outcomes). If there are 3 cans of coke, 3 cans of pepsi, and 2 cans of moutain dew in a box, the probability of me grabbing a can of coke out of the box is 3/8. Pretty simple

Combination Formula: A combination is a selection in which order is not important. The number of combinations of 'n' objects taken 'r' at a time is described as nCr, which is the same as n!/(r!(n-r)!). Because the order in which we draw the Exodia pieces does not matter, we will be using this formula.

Calculating the Probability: So the first thing we need to do is calculate the number of ways we can draw the 5 pieces of Exodia in our opening hand, i.e., the Number of successes used in the probability formula. Because there are 5 pieces of Exodia in a deck and we have 5 cards in our opening hand, we will plug in the number 5 as both 'r', and 'n' in the combination formula, which will look like 5C5 (pronounced as "5 choose 5"), or 5!/(5!(5-5)!). 5-5 is 0, so we can simplify it to be 5!/(5!0!). "Ress man come on, you can't divide by 0." I hear your cries, but 0! factorial is actually equivalent to 1. I can explain this if enough people want me to. Because multiplying a number by 1 doesn't change the value of the number, we are left with 5!/5!. Any number divided by itself is equal to 1, therefore we have calculated that the Number of successes of drawing the 5 pieces of Exodia, is 1.

Now that we have the Number of successes for the numerator of the probability formula, we need to calculate the Number of possible outcomes for the denominator. This means that with the Combination Formula, we need to calculate the number of possible 5 card hands in a 40 card deck. Because we have 40 cards in a deck, and we are choosing 5 of them, we will have 'n' be substituted with 40 in all instances, and we will have 'r' be substituted with 5 in all instances. This gives us 40C5 (pronounced 40 choose 5), or 40!/(5!(40-5)!). 40-5 equals 35, so we are left with 40!/(5!35!). Remember how 5!= 5x4x3x2x1? Well 35! and 40! follow the same pattern, except they start at 35 and 40 respectively instead of 5. This means that 40!/(5!35!) can be simplified to (40x39x38x37x36)/5!. 40x39x38x37x36= 78,960,960, and 5! is equal to 120, so now we are left with 78,960,960/120. Punching this operation into a calculator gives us the number 658,008, which means that in a 40 card deck, there are 658,008 possible 5 card hands, which means that our Number of possible outcomes is 658,008.

Now that we have both parts of our Probability Formula, we can finally calculate it! Remember the Probability Formula is (Number of successes)/(Number of possible outcomes), so we are left with the operation 1/658,008. Punching this operation into a calculator gives it to us in Scientific Notation and is 1.519738362x10-6, or 0.000001519738362. In terms of percentages, this number is equal to 0.0001519738362%.

Meaning that with a 40 card deck, you have a

Factorials: Represented by an "!" after a given number. For example, 5! is equivalent to 5x4x3x2x1, which equals 120. Factorial is very important for calculating the number of combinations and permutations of a given event.

Probability Formula: (Number of successes/Number of possible outcomes). If there are 3 cans of coke, 3 cans of pepsi, and 2 cans of moutain dew in a box, the probability of me grabbing a can of coke out of the box is 3/8. Pretty simple

Combination Formula: A combination is a selection in which order is not important. The number of combinations of 'n' objects taken 'r' at a time is described as nCr, which is the same as n!/(r!(n-r)!). Because the order in which we draw the Exodia pieces does not matter, we will be using this formula.

Calculating the Probability: So the first thing we need to do is calculate the number of ways we can draw the 5 pieces of Exodia in our opening hand, i.e., the Number of successes used in the probability formula. Because there are 5 pieces of Exodia in a deck and we have 5 cards in our opening hand, we will plug in the number 5 as both 'r', and 'n' in the combination formula, which will look like 5C5 (pronounced as "5 choose 5"), or 5!/(5!(5-5)!). 5-5 is 0, so we can simplify it to be 5!/(5!0!). "Ress man come on, you can't divide by 0." I hear your cries, but 0! factorial is actually equivalent to 1. I can explain this if enough people want me to. Because multiplying a number by 1 doesn't change the value of the number, we are left with 5!/5!. Any number divided by itself is equal to 1, therefore we have calculated that the Number of successes of drawing the 5 pieces of Exodia, is 1.

Now that we have the Number of successes for the numerator of the probability formula, we need to calculate the Number of possible outcomes for the denominator. This means that with the Combination Formula, we need to calculate the number of possible 5 card hands in a 40 card deck. Because we have 40 cards in a deck, and we are choosing 5 of them, we will have 'n' be substituted with 40 in all instances, and we will have 'r' be substituted with 5 in all instances. This gives us 40C5 (pronounced 40 choose 5), or 40!/(5!(40-5)!). 40-5 equals 35, so we are left with 40!/(5!35!). Remember how 5!= 5x4x3x2x1? Well 35! and 40! follow the same pattern, except they start at 35 and 40 respectively instead of 5. This means that 40!/(5!35!) can be simplified to (40x39x38x37x36)/5!. 40x39x38x37x36= 78,960,960, and 5! is equal to 120, so now we are left with 78,960,960/120. Punching this operation into a calculator gives us the number 658,008, which means that in a 40 card deck, there are 658,008 possible 5 card hands, which means that our Number of possible outcomes is 658,008.

Now that we have both parts of our Probability Formula, we can finally calculate it! Remember the Probability Formula is (Number of successes)/(Number of possible outcomes), so we are left with the operation 1/658,008. Punching this operation into a calculator gives it to us in Scientific Notation and is 1.519738362x10-6, or 0.000001519738362. In terms of percentages, this number is equal to 0.0001519738362%.

Meaning that with a 40 card deck, you have a

**0.0001519738362%**chance of drawing all 5 pieces of Exodia in your opening 5 card hand. Holy shit, thats a big number! So if you have ever drawn the 5 pieces of Exodia in your opening hand, consider yourself very very very god damn lucky.Last edited by Reessiel on Thu Sep 17, 2015 7:47 pm; edited 1 time in total

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## Re: Let's talk probability

good one bro

~Dark Angel~

[21:14:35] yugideckfan : is angel on another "brb" ?

[22:05:20] hazmah : I am dark's clone

[22:05:34] hazmah : U got a problem with that?

[09:07:44] God742 : its angel!

[09:08:32] God742 has logged off the chat on Mon 6 Oct 2014 - 9:08

^ live in fear

[19:07:53] @ Drace101 : if i can't trust random ppl on the internet who can i trust?

**Angel**- Administrator
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## Re: Let's talk probability

Let's just bowl for a second to this guy...GG

:wha:

:wha:

**On your knees before the GOD OF GODS****Pepchoninga**- Member
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## Re: Let's talk probability

Nice numbers Reess (yet why don't just hope that we can pull this draw xD)

**Lux**- Administrator
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## Re: Let's talk probability

Reessiel wrote:

Omg, I remember that card! When I was scrub, it was like the strongest monster in my deck and tbh it's still pretty awesome =)

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**Dat Magician**- Member
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## Re: Let's talk probability

@Lux wrote:Omg, I remember that card! When I was scrub, it was like the strongest monster in my deck and tbh it's still pretty awesome =)

I think i should totally use that pic as my signature and make my avatar mathematician xD

Holy shit that's something

It certainly is something my friend haha, thats what makes searching cards so great because it takes that 0.0001519738362% and dramatically increases the probability of getting what you want.

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## Re: Let's talk probability

one guy drew once all 5 pieces of exodia in 1st turn...

sooo yeah.... it is possible

sooo yeah.... it is possible

~Dark Angel~

[21:14:35] yugideckfan : is angel on another "brb" ?

[22:05:20] hazmah : I am dark's clone

[22:05:34] hazmah : U got a problem with that?

[09:07:44] God742 : its angel!

[09:08:32] God742 has logged off the chat on Mon 6 Oct 2014 - 9:08

^ live in fear

[19:07:53] @ Drace101 : if i can't trust random ppl on the internet who can i trust?

**Angel**- Administrator
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## Re: Let's talk probability

Thats why you never play 5 peaces of exodia without any card to help you deck them xD My opponent onece got 2 chicken game a pseudo space and 2 upstart and 1 into the void and drew all peaces...they were all on top of his deck.

**On your knees before the GOD OF GODS****Pepchoninga**- Member
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## Re: Let's talk probability

Thats why you never play 5 peaces of exodia without any card to help you deck them xD

Of course you don't, you can't have a 5 card deck XD

Joking, well, true.

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## Re: Let's talk probability

https://www.youtube.com/watch?v=9rIy0xY99a0 figured this video is good for the topic. Given, it is talking about "random" in general, but since this is a topic about probability, in theory, it's all good

**riot1man**- Member
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