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Old 07-08-2009, 01:01 AM   #1
Sonny Weblin
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Probability of being dealt gin

Hi,

I was playing gin with my girlfriend the other day and she dealt me gin (without using the down card). We currently have a prop bet as to the odds of this happening but aren't sure how to compute it. Does anybody know this?

Thanks,
Sonny
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Old 07-18-2009, 03:33 PM   #2
Sonny Weblin
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Re: Probability of being dealt gin

Hello,

Well, I guess nobody here knew the answer to this, so me and the girl wrote a simple program to compute this. It simply ran through all possible gin rummy hands, figured out which were gin, and counted them. Now since there are about 16 billion possible gin rummy hands, this took several hours, but we got an answer, which we believe to be correct. In case anybody here is curious, it is about 118k to 1. Our bet was over/under on 38k to 1 with her on the over and me on the under for $20 doubling each day it took before we resolved the bet, so I lost .
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Old 07-21-2009, 03:53 AM   #3
Sir Osbert Fairfax
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Re: Probability of being dealt gin

Osbert Here.
I say I say I am quite interested in this statistic, as I played gin as a lad in Birmingham. How can it be derived matematically?

Regards,
Osbert
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Old 07-21-2009, 07:40 PM   #4
Kittens
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Re: Probability of being dealt gin

Quote:
Originally Posted by Sir Osbert Fairfax View Post
Osbert Here.
I say I say I am quite interested in this statistic, as I played gin as a lad in Birmingham. How can it be derived matematically?
You would have to count them all! I started on this but got sidetracked. The approach I am using is to divide all possible gins up into structure categories (e.g. 4-of-kind + 3-run + 3-run), make sure each hand belongs to exactly one category, and count each category using normal combinatoric techniques.

Also, I have never played the game but am going off the description as given by Wikipedia.

Will post again if I get around to finishing!
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Old 07-22-2009, 08:14 PM   #5
Sonny Weblin
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Re: Probability of being dealt gin

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Originally Posted by Kittens View Post
You would have to count them all! I started on this but got sidetracked. The approach I am using is to divide all possible gins up into structure categories (e.g. 4-of-kind + 3-run + 3-run), make sure each hand belongs to exactly one category, and count each category using normal combinatoric techniques.
This is quite easy for some hand types, but it gets pretty sticky for the (4,3,3) types. We tried this at first, but got frustrated and gave up.

Sonny
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Old 07-23-2009, 05:51 AM   #6
Sir Osbert Fairfax
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Re: Probability of being dealt gin

I suppose an enumeration would be needlessly complicated, but surely a simple program making use of brute force algorithms could settle this matter.

Osbert
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Old 07-23-2009, 03:12 PM   #7
Sonny Weblin
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Re: Probability of being dealt gin

Quote:
Originally Posted by Sonny Weblin View Post
Hello,

Well, I guess nobody here knew the answer to this, so me and the girl wrote a simple program to compute this. It simply ran through all possible gin rummy hands, figured out which were gin, and counted them. Now since there are about 16 billion possible gin rummy hands, this took several hours, but we got an answer, which we believe to be correct. In case anybody here is curious, it is about 118k to 1. Our bet was over/under on 38k to 1 with her on the over and me on the under for $20 doubling each day it took before we resolved the bet, so I lost .
^^
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Old 09-28-2020, 02:17 PM   #8
rulemonger
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Re: Probability of being dealt gin

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Originally Posted by Kittens View Post
You would have to count them all! I started on this but got sidetracked. The approach I am using is to divide all possible gins up into structure categories (e.g. 4-of-kind + 3-run + 3-run), make sure each hand belongs to exactly one category, and count each category using normal combinatoric techniques.

Also, I have never played the game but am going off the description as given by Wikipedia.

Will post again if I get around to finishing!
Here's such a list and computation: https://entropyclay.wordpress.com/2020/09/28/gin/
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