For some reason, I’ve been thinking about Klondike solitaire probabilities a lot lately. Primarily, I’m wondering what the likelihood is that a game will have zero legal plays. I’m certain it happens, but it’s got to be pretty rare. It’s a complex game, though, so here’s my plan towards solving it:
- Given two non-ace cards, what is the chance that one cannot be placed on the other, using standard Klondike rules?
- Given three non-ace cards, what is the chance that none can be played on any other?
- Given seven...?
- Given two (three, seven) cards, what is the chance that there is no legal play (placing one on another or moving an ace to the foundation)?
There are more steps after that involving the eight deck cards, but it gets pretty complicated pretty quickly. I’ll be happy just getting this far.