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Delreich

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Odds of drawing a card based on number in deck https://elementscommunity.org/forum/index.php?topic=588.msg5511#msg5511
« on: December 15, 2009, 10:09:56 pm »

http://stattrek.com/Tables/Hypergeometric.aspx

Pop. size = deck size, sample size = cards drawn, the others should be fairly easy to figure out.

Evil Hamster

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Odds of drawing a card based on number in deck https://elementscommunity.org/forum/index.php?topic=588.msg5512#msg5512
« Reply #1 on: December 15, 2009, 10:09:56 pm »

I was looking for something on the flashkit forum and found this very useful picture:

probabilities to get k copies in a 8-first-hand in a deck of 30 with 1,2,3,4,5 or 6 copies of a certain card:



(thanks to -Samura- on flashkit)

Evil Hamster

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Odds of drawing a card based on number in deck https://elementscommunity.org/forum/index.php?topic=588.msg5513#msg5513
« Reply #2 on: December 15, 2009, 10:09:56 pm »

It would be neat if there was a formula that could determine odds of getting at least one by turn X.

Though I suppose you could substitute a bigger hand size to simulate that.


Scdr

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Odds of drawing a card based on number in deck https://elementscommunity.org/forum/index.php?topic=588.msg5514#msg5514
« Reply #3 on: December 15, 2009, 10:09:56 pm »

If anyone is interested in a more flexible version: Paste the code below into an Excel document. As most of you are probably not using a german Version of Excel, you will have to substitute "FAKULTÄT" with a translation. Probably this would be "FACTORIAL", but since i don't have any english / american excel version I am not sure about that.


=1 - (FAKULTÄT(B1 - D1) / FAKULTÄT(B1 - (D1 + C1))) / ((FAKULTÄT(B1) / FAKULTÄT(B1 - C1)))


Afterwards you can enter your parameters and watch the percentage chance change in the field you pasted above code into.
Parameters are:

B1 - Size of you deck
C1 - Number of copies of the card in question in your deck
D1 - The number of cards you draw

Assuming you pasted the formula into the field A1:
In a deck of B1 cards, a C1-times appearing card is drawn with a propability of A1 within the first D1 cards.

Sometimes Excel confuses Minus signs (is this the correct translation?) and dashes in pasted formulas. So if it doesn't work, you might want to delete the minus signs and rewrite them manually.


Edit: I just reread the opening post and noticed, that there is an important difference between the two versions. The table Evil Hamster quoted does show you the chances of getting more than one card, too, while I just went for the chance of getting at least one. On the other hand, you can still check your chances with bigger decks or more cards drawn. May be useful to ensure you get that really central card which your decks requires to work within the first 2 or 3 rounds - when you actually have the quanta to play it. So it's at least not completely useless...

Scdr

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Odds of drawing a card based on number in deck https://elementscommunity.org/forum/index.php?topic=588.msg5515#msg5515
« Reply #4 on: December 15, 2009, 10:09:56 pm »

That's the main reason why i made the number of drawn cards a variable. You have 7 or 8 cards in your starting hand and then can add as many additional cards, as you want. A 10 in the field D1 for example would mean your starting deck + 3 (or 2 if you didn't start the battle) cards from drawing. So usually turn 2 or 3.

Only "problem" whith this are sundials and hourglasses, as they are not included. But including them would make this calculation horibly complicated: Not only would one have to include the probability of drawing the dials / glasses, but the odds of drawing sufficient towers to supply them, too. In case of Quantum towers, one would need to add the chances of them to produce Time / Light Quantum. The players mark would interfere, too. Additionally one would have to distinguish between towers and pillars.
After finally solving all these problems, the player decides to bless his Oytugh instead of drawing an additional card with his sundial and the entire calculation is screwed up.

Therefore your best bet to get a reliable result is ignoring multi card drawing, and working with the number of cards drawn. In a deck that extremely relies on drawing several cards each turn, even in the early turns, you still could guess how many cards you draw per turn. Honestly, an educated guess would probably more exact than any calculation, as you could include the priority of your multidrawing cards.

(The other reason for making it editable, is the possibility of using it mid-game. In a tight game one might want to know whether you should use your quantum for that boneyard (i.e.) in your hand, or wait for a Bone Wall to be drawn.)

elfreth

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Re: Odds of drawing a card based on number in deck https://elementscommunity.org/forum/index.php?topic=588.msg29423#msg29423
« Reply #5 on: February 25, 2010, 06:22:25 pm »
http://stattrek.com/Tables/Hypergeometric.aspx

Pop. size = deck size, sample size = cards drawn, the others should be fairly easy to figure out.
Nice link, thanks.

So, if I'm interpreting this correctly.  I only have 3.5% chance of drawing 3 qt in my first 19 cards in a deck comprised of 41 cards and 13 qt, is that correct?

If so, I seem to fall into that "upper" 3.5% a lot!  :D

But seriously...am I correct in my interpretation?

Tea is good

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Re: Odds of drawing a card based on number in deck https://elementscommunity.org/forum/index.php?topic=588.msg29442#msg29442
« Reply #6 on: February 25, 2010, 07:40:06 pm »
That looks quite useful. I will be using this.

Delreich

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Re: Odds of drawing a card based on number in deck https://elementscommunity.org/forum/index.php?topic=588.msg29464#msg29464
« Reply #7 on: February 25, 2010, 08:31:53 pm »
So, if I'm interpreting this correctly.  I only have 3.5% chance of drawing 3 qt in my first 19 cards in a deck comprised of 41 cards and 13 qt, is that correct?
Kinda, but kinda not. You have a 3.5% chance of getting exactly 3 qt, but a 99.2% chance of getting 3 or more qt.

 

blarg: