Probability of drawing 5 of one kind from two sets of 10 - Gambling and Probability

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Probability of drawing 5 of one kind from two sets of 10

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03-18-2018 , 12:04 AM

Aytumious

Carpal \'Tunnel

Join Date: Jan 2005 Posts: 7,516

I should know how to do this, but I didn't ever study statistics and google is surprisingly being unhelpful. I think the issue is that I'm not exactly sure what to search for.

The problem is as stated in the topic. How does one calculate the chance of drawing 5 of one kind from two sets of 10?

I'm guessing there is a very basic equation that is eluding me since the problem is not that complex. In times like this, I regret not having studied statistics.

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03-18-2018 , 12:45 AM

whosnext

Carpal \'Tunnel

Join Date: Mar 2009 Posts: 6,730

It is not immediately obvious to me what you are asking.

Could you clarify or give an example?

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03-18-2018 , 01:24 AM

Aytumious

Carpal \'Tunnel

Join Date: Jan 2005 Posts: 7,516

Quote:

Originally Posted by whosnext

It is not immediately obvious to me what you are asking.

Could you clarify or give an example?

Sure.

This applies to Slay the Spire on Steam.

At the most basic level you have cards that are defends and cards that are attacks. Let's assume you've balanced your deck so that there is an equal balance of 10 defends and 10 attacks. On your turn, you draw 5 cards from that pool.

My question is, how do you calculate what the odds are that you draw a certain set of cards out of that group of 10 defends and 10 attacks. In other words, what are the odds you draw 5 attacks, for example, from the pool of 10 attacks and 10 defends.

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03-18-2018 , 01:30 AM

David Sklansky

Administrator

Join Date: Aug 2002 Posts: 17,073

9/19 x 8/18 x 7/17 x 6/16

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03-18-2018 , 01:37 AM

whosnext

Carpal \'Tunnel

Join Date: Mar 2009 Posts: 6,730

Look up the Hypergeometric Distribution.

It gives the probability of drawing k "successes" out of n draws (without replacement) from a population of N items of which K are "successes".

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03-18-2018 , 01:44 AM

Aytumious

Carpal \'Tunnel

Join Date: Jan 2005 Posts: 7,516

Quote:

Originally Posted by whosnext

Look up the Hypergeometric Distribution.

It gives the probability of drawing k "successes" out of n draws (without replacement) from a population of N items of which K are "successes".

Thank you.

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