Maximum Deadwood

For those of you who’ve read the Gin Rummy Deadwood Distribution on the previous post, we know the average deadwood dealt on a hand is 57. 

To the left of the graph we reach zero deadwood.  It’s easy to imagine being dealt a hand that has no deadwood.  Wouldn’t that be nice!

 

To the right of the graph we almost reach 100 deadwood, but not quite. 

 So, what the maximum deadwood is for a hand?

 

Deadwood Refresher

Let’s have a quick refresher on counting deadwood.  Deadwood are any cards in your hand that you can’t use in a group or run. 

Kings, Queens, Jacks and Tens count as 10 deadwood points and all other cards count at face value.  Aces are 1 deadwood point. 

Take the sum of the points for each unusable card in your hand and that is your deadwood points.

An important point to remember is that you can’t use the same card in a group and a run at the same time.

 

*** Spoiler alert!  ***

Take some time to figure out the highest amount of deadwood points or scroll down to see the answer.

 

1,000 Words Worth

Here’s a snapshot of the maximum deadwood in a hand from Yimmaw.com

Cards are laid out by suit from left to right in ascending order.  This view is pre-sorted which makes it easy to pick out groups and runs.  Groups go up and down, runs go from left to right.  No need to slide cards around in your hand.

This hand is a combination of the highest five cards.  There are 2 Kings, 2 Queens, 2 Jacks, 2 Tens and 2 Nines.  Not a single group or run. 

It’s 100% pure deadwood for a whopping 98 points!

You can’t add in another Ten, Jack, Queen or King because that would create a group of 3 cards reducing the deadwood by at least 30.  Using a smaller card, like an 8 or 7 would only bring the deadwood total down.

 

What is the Probability of getting the Max Deadwood?

There are 15,820,024,220 possible 10 card hands you can be dealt.

 

To figure out how many combinations of 98-point deadwood hands is tricky.  I wrote a script using the AI system to output all possible combinations.  It found 1,584 in total. 

15,820,024,220 divided by 1,584 is 9,987,389. 

 

Bottom Line

You might encounter a 98-pointer once every 10 million deals. 

While this looks daunting there are 11 cards that can improve your hand.  Hopefully you’ll pick up a few before your opponent knocks!