So I was wondering what was the specific likelihood of getting a very specific hand, so here's what I have
60 card deck
drawing opening hand
I need 3 of a card I have 4 of
I need 1 of a card I have 4 of (2 times)
I need 1 of a card I have 2 of
and I need 1 of a card I have 15 of (lands)
I know there are ways of finding out the probability of getting any one of these but I need to do it 5 times and the chances change for each one because as I draw my cards the chances for each specific one waver, like if I was to draw my land first that changes the chances of all the other cards I need to by */59 instead of */60 but what if I don't draw that first? all in all I know it's very low but would still like an exact number.
Hypergeometric Distribution is the method of determining the chance of getting A cards (called "successes") when drawing B cards (called "sample size") out of a C-card deck (called "Population") with D copies of the target success.
In example, the chances of getting your 3-card success in a 7-card sample size out of a 60-card population that has 4 possible successes is 0.0038 - About one third of one percent.
When you start adding in different successes with different success pools (ie: Your other cards after the first one), but are pulling out of the same sample size and population, you are then graduating to Multivariate Hypergeometric Distribution.
If you're wanting to go down a nice long rabbit hole of math, you can read up on calculating Multivariate Hypergeometric Distribution Here.
If this is a specific example you want, and don't want to do all that math, you're looking at somewhere around one in 50,000 times, give or take. That's a rough shot from the hips though.
60 card deck
drawing opening hand
I need 3 of a card I have 4 of
I need 1 of a card I have 4 of (2 times)
I need 1 of a card I have 2 of
and I need 1 of a card I have 15 of (lands)
I know there are ways of finding out the probability of getting any one of these but I need to do it 5 times and the chances change for each one because as I draw my cards the chances for each specific one waver, like if I was to draw my land first that changes the chances of all the other cards I need to by */59 instead of */60 but what if I don't draw that first? all in all I know it's very low but would still like an exact number.
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In example, the chances of getting your 3-card success in a 7-card sample size out of a 60-card population that has 4 possible successes is 0.0038 - About one third of one percent.
When you start adding in different successes with different success pools (ie: Your other cards after the first one), but are pulling out of the same sample size and population, you are then graduating to Multivariate Hypergeometric Distribution.
If you're wanting to go down a nice long rabbit hole of math, you can read up on calculating Multivariate Hypergeometric Distribution Here.
If this is a specific example you want, and don't want to do all that math, you're looking at somewhere around one in 50,000 times, give or take. That's a rough shot from the hips though.
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