<p>Three Independent sources counted <em>about</em> 136,694 Gin hands, out of 15.8B possible 10-cards hands.</p>
<ol>
<li><p><strong><a href="https://forumserver.twoplustwo.com/25/probability/probability-being-dealt-gin-528078/" rel="nofollow noreferrer">2+2 forum post</a>:</strong> 1 in ~118,000.  Using brute force which checked for Gin each of the 15.8B hands.</p>
</li>
<li><p><strong><a href="https://entropyclay.wordpress.com/2020/09/28/gin/" rel="nofollow noreferrer">Rulemonger's analysis</a>:</strong> 136,694 in 15,820,024,220 or <strong>1 in ~115733</strong></p>
</li>
<li><p><strong>How to Win at Gin Rummy:</strong> 1 in ~117,000, according to the book <a href="https://books.google.co.il/books?id=eS4IswEACAAJ&amp;source=gbs_book_other_versions" rel="nofollow noreferrer">How to Win at Gin Rummy: Playing for Fun and Profit</a> which state that there are 136,694 Gin hands out of 15,820,024,220 hands.  See page 65:
<a href="https://i.sstatic.net/S6fvq.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/S6fvq.jpg" alt="gin hand - starting amount of deadwood" /></a></p>
</li>
</ol>

CC BY-SA 4.0
2020-09-28T15:33:57.583Z
I've made a combinatorics count as well, as further confirmation: https://entropyclay.wordpress.com/2020/09/28/gin/
L. Scott Johnson
CC BY-SA 4.0
2019-07-20T10:15:52.270Z
2021-06-03T17:57:12.587Z
2021-06-03T17:57:12.587Z
Cohensius
<p>EDIT: this count is flawed, it doesn't recognize sets of three that include a spade. The correct number is given in the accepted answer. When the code is corrected, it gives the 136,694 unique gin hands, matching the accepted answer.</p>
<p>Original:</p>
<p>1 in 308,984, according to <a href="https://canadianandrew.wordpress.com/2016/09/13/odds-of-dealing-gin/" rel="nofollow noreferrer">Andrew Inwood's analysis</a>, which includes <a href="https://bitbucket.org/ainwood87/gin/src/master/" rel="nofollow noreferrer">source code</a>.</p>

CC BY-SA 4.0
2019-07-15T12:07:58.613Z
Does that include being able to pick up a visible discard to make Gin on your first turn?  I'm inclined to think it doesn't, because I've done that twice, and I only play gin for an hour, once a week, for the past 4-5 years.
Zeiss Ikon
CC BY-SA 4.0
2019-07-15T12:14:02.920Z
it does not.  Just the first 10 cards.  Getting a gin in the first turn (out of the first 11 cards) is a better (much harder question
Cohensius
CC BY-SA 4.0
2020-09-22T16:55:07.477Z
This appears to count Aces as low-only, I assume this is why it disagrees with the other counts. See GinManager::SetUsableCards in https://bitbucket.org/ainwood87/gin/src/master/GinManager.cpp, which has nine types of length-five runs, when it should be 10.
DanTilkin
CC BY-SA 4.0
2020-09-22T17:12:32.780Z
Because Aces are low-only, in the standard rules of Gin (https://en.wikipedia.org/wiki/Gin_rummy#Objective)
L. Scott Johnson
CC BY-SA 4.0
2020-09-23T05:27:17.990Z
@DanTilkin, also the other counts use Ace as low-only.
Cohensius
CC BY-SA 4.0
2020-09-23T13:29:04.363Z
Found it: it doesn't recognize three-of-a-kinds that include a spade, so undercounts the number of gin hands accordingly.
L. Scott Johnson
CC BY-SA 4.0
2020-09-25T16:25:39.627Z
@L.ScottJohnson Interesting. Either my memory of playing is wrong, or we were using non-standard rules. I didn't even notice the missing spade check.
DanTilkin
CC BY-SA 4.0
2020-09-26T10:29:15.293Z
@DanTilkin, In the "official" rules aces are only low, however there are many variations where aces can be either high or low, for example TCC-Gin https://www.pagat.com/docs/TCCGinBook.pdf
Cohensius
CC BY-SA 4.0
2019-07-15T11:58:25.430Z
2021-04-11T20:52:49.060Z
2021-04-11T20:52:49.060Z
L. Scott Johnson
<p>In Gin-Rummy, in the start of a round players draw 10 cards.</p>

<p>What is the probability to draw 10 cards such that all the cards are part of some  meld?</p>

<statistics><gin-rummy>
In Gin-Rummy, what are the chances to start with a Gin?
Cohensius
# In Gin-Rummy, what are the chances to start with a Gin?

(Asked by: username_0 on 2019-07-15)

In Gin-Rummy, in the start of a round players draw 10 cards.

What is the probability to draw 10 cards such that all the cards are part of some meld?

**Tags:** statistics, gin-rummy


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## 2 answers

### Answer by username_0 on 2019-07-20. Score: 2 | Accepted answer

Three Independent sources counted *about* 136,694 Gin hands, out of 15.8B possible 10-cards hands.

1. **[2+2 forum post](https://forumserver.twoplustwo.com/25/probability/probability-being-dealt-gin-528078/):** 1 in ~118,000. Using brute force which checked for Gin each of the 15.8B hands.
2. **[Rulemonger's analysis](https://entropyclay.wordpress.com/2020/09/28/gin/):** 136,694 in 15,820,024,220 or **1 in ~115733**
3. **How to Win at Gin Rummy:** 1 in ~117,000, according to the book [How to Win at Gin Rummy: Playing for Fun and Profit](https://books.google.co.il/books?id=eS4IswEACAAJ&source=gbs_book_other_versions) which state that there are 136,694 Gin hands out of 15,820,024,220 hands. See page 65:
   [![gin hand - starting amount of deadwood](https://i.sstatic.net/S6fvq.jpg)](https://i.sstatic.net/S6fvq.jpg)

> **Comments:**
> **username_1**: I've made a combinatorics count as well, as further confirmation: https://entropyclay.wordpress.com/2020/09/28/gin/  

---

### Answer by username_1 on 2019-07-15. Score: 1

EDIT: this count is flawed, it doesn't recognize sets of three that include a spade. The correct number is given in the accepted answer. When the code is corrected, it gives the 136,694 unique gin hands, matching the accepted answer.

Original:

1 in 308,984, according to [Andrew Inwood's analysis](https://canadianandrew.wordpress.com/2016/09/13/odds-of-dealing-gin/), which includes [source code](https://bitbucket.org/ainwood87/gin/src/master/).

> **Comments:**
> **username_2**: Does that include being able to pick up a visible discard to make Gin on your first turn?  I'm inclined to think it doesn't, because I've done that twice, and I only play gin for an hour, once a week, for the past 4-5 years.  
> **username_0**: it does not.  Just the first 10 cards.  Getting a gin in the first turn (out of the first 11 cards) is a better (much harder question  
> **username_3**: This appears to count Aces as low-only, I assume this is why it disagrees with the other counts. See GinManager::SetUsableCards in https://bitbucket.org/ainwood87/gin/src/master/GinManager.cpp, which has nine types of length-five runs, when it should be 10.  
> **username_1**: Because Aces are low-only, in the standard rules of Gin (https://en.wikipedia.org/wiki/Gin_rummy#Objective)  
> **username_0**: @username_3, also the other counts use Ace as low-only.  
> **username_1**: Found it: it doesn't recognize three-of-a-kinds that include a spade, so undercounts the number of gin hands accordingly.  
> **username_3**: @username_1 Interesting. Either my memory of playing is wrong, or we were using non-standard rules. I didn't even notice the missing spade check.  
> **username_0**: @username_3, In the "official" rules aces are only low, however there are many variations where aces can be either high or low, for example TCC-Gin https://www.pagat.com/docs/TCCGinBook.pdf  

---

