Just yesterday I received an email from Dr. Douglas Furton, a Physics Professor at Grand Valley State University.  Dr. Furton had read my blog post about One-Handed Solitaire in which I used simulations to find the probability of winning such a game.  Finding himself interested in this problem, he contacted me and requested to see my R script.  Sadly, my R script from two years ago (when I wrote that post) is no longer with us.  Let this be a lesson to me that I never forget: always save to Dropbox!

But Dr. Furton’s email put a bee in my bonnet, so I ended up writing new code which is here.  Now, it seems my new code gives me an answer that contradicts the answer that I had arrived at in my post from 2 years ago. I am finding that the probability of winning a game of one handed solitaire is about 0.0071, rather than 0.00206.  This was disconcerting to me, and I even wrote the code over again from scratch.  But again, I came to the same new answer of (roughly) 0.0071.

So now I challenge you, dear reader, to write up your own code and let me know what answer you get. If you get something pretty different than 0.0071, please send me your R script, and let’s see if we can settle this!

There are a lot of interesting questions that are left unanswered about one-handed solitaire.  For example, if you get to immediately discard your first four cards, do you have a higher chance of winning than otherwise?  Do you have a higher/lower chance of winning one-handed solitaire if your deck is missing n cards?

Dr. Furton was interested in finding out about the distribution of cards that are left over at the end of a game.  Someone who has zero cards left over has won, while someone who has 30 cards leftover did not get very close…  Here is what Dr. Furton got using this code:

Lastly, I wrote some much faster code that you can look at here.

Have fun with this stuff, and don’t forget to learn from my mistakes and always backup your R scripts!

[Update from 2/5/2019 : I am not thinking about / working on this problem any more!]