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Orchard: A 9 card solitaire game» Forums » General

Subject: 9 cards versus 18 cards rss

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Jim Adams
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Not to be all statistics nerdy, but with the double sided 9 card deck there are 512 possible 9 card hands. With the single sided 18 card deck there are 48,620 possible 9 card hands. I made one of each and haven’t noticed any difference in play yet, e.g., one deck producing higher scores than the other. I realize the constraints of the original 9 card contest dictated the original double sided deck. Is there any reason in the design of the original cards to suggest the decks should play differently in the long run?

Great game! My best score to date is 42 with the 18 card deck.

Thanks!
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Neil O'Rourke
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Howdy Jim,

Most importantly - I agree with your assessment. Great game in a small package. It has been my 2018 goal to have the lowest weight and transport footprint with the most fun to be had.

To spare the people who don't want the math below: The biggest difference in the 18 card option is that there are strong symmetries between the front and back of each card. Note card 1 and its flip side card 2; Four trees can be overlaid - RB/YY.

Here's my math by presenting permutation, because order matters. When I tracked your numbers I found 18C9 = 48,620. Also, there are 512 or (2^9) ways that the cards can be oriented (front vs back).

In a 9 card layout; the first card can be any of the 18 possibilities.
Cards 8 and 7 - order does not matter. Orientation can be any of 4 options multiplied by 4*(8C2)=(4*28)=112.
Cards 6 and down to Card 1 also get placed in order.
So...
18*112*12*10*8*6*4*2=92,897,280 total permutations for the deck's order.

For an 18 card layout - in short order:
18*17C2*15P6=8,821,612,800
Nearly 95 times larger options with this option.

+Points if you read this far.

TL;DR - Great game. High number of possible decks.

Neil.
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Jim Adams
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ve6neo wrote:
Howdy Jim,

Most importantly - I agree with your assessment. Great game in a small package. It has been my 2018 goal to have the lowest weight and transport footprint with the most fun to be had.

To spare the people who don't want the math below: The biggest difference in the 18 card option is that there are strong symmetries between the front and back of each card. Note card 1 and its flip side card 2; Four trees can be overlaid - RB/YY.

Here's my math by presenting permutation, because order matters. When I tracked your numbers I found 18C9 = 48,620. Also, there are 512 or (2^9) ways that the cards can be oriented (front vs back).

In a 9 card layout; the first card can be any of the 18 possibilities.
Cards 8 and 7 - order does not matter. Orientation can be any of 4 options multiplied by 4*(8C2)=(4*28)=112.
Cards 6 and down to Card 1 also get placed in order.
So...
18*112*12*10*8*6*4*2=92,897,280 total permutations for the deck's order.

For an 18 card layout - in short order:
18*17C2*15P6=8,821,612,800
Nearly 95 times larger options with this option.

+Points if you read this far.

TL;DR - Great game. High number of possible decks.

Neil.

I hadn’t looked at the symmetries on the paired cards, e.g., card 1 versus card 2. Good observations! It’s fun to analyze games (which I count as “playing”, too) when they are simple enough to yield to straightforward calculations.

Thanks!

Jim
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Cheryl Leon
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Haha, that is awesome that you guys figured that out! I was curious. Looks like the nine-card set up gives me plenty of options. LOL! So I'll stick with that since it matches the logo glued to my Altoids box 🤣
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