Solitaire Study (2012)
I love solitaire. It’s you against the universe. But it’s not a game of blind luck, as many people think. If played correctly, it’s actually a game of strategy and thinking ahead. The trick is to remember the cards and their order, and instead of immediately playing every playable card that comes along, to instead think about how playing each card will shift the deck. By not jumping at some opportunities, you can create other, more critical opportunities. Really it’s a game of opportunity management — like life.
In this respect, solitaire resembles chess in that you have to think many plies ahead. This can sharpen your mind if you play at your limit — and numb it if you try to play beyond your limit. Unlike chess though, you can’t bank on your opponent’s weaknesses. Each time, your opponent is baked in once the cards are dealt.
When most people play solitaire, they win roughly 20% of the time. But most people play with the goal of not missing any opportunity that comes their way. So I asked myself: What fraction of solitaire games are, at least in theory, winnable?
To answer this, you need to be able to, well…cheat. In other words, if you come to a dead end, you need to be able to go back and see if better choices could have been made. So I settled on Windows Solitaire — it’s widely used, it plays by fairly standard rules, and it comes with a back button.
Quickly, I learned that it is (usually) not difficult to map out all viable paths. This is because the game usually hinges on whether you can get to a single card or two. Sometimes though, the logic map can get very complicated, and take tens of minutes — and on rare occasions, a full hour — to untangle.
Once I had figured out how to do this, I (am somewhat ashamed to admit that I) played 1000 games in this way. 781 were winnable — if you made the right choices. The remaining 219 games I am fairly certain were impossible to win, hinging on cards that could not be uncovered.
Of course, I am only human, so this is technically only a lower limit — I would love to see someone code this logic mapping into a computer and check me. And in reality, many of the paths to victory were not obvious, and would not have been uncovered without the back button. But I conclude that
78% +/- 3%
of Windows Solitaire games (played under the default settings) are, at least in theory, winnable.
This study ruined computer solitaire for me — don’t even have it installed on my machine anymore. But I still like playing with actual cards (and no back button!) I play my own variant — a standard game of three-card draw followed by a single pity round of one-card draw. And I sometimes play it tag-team with others…though this can be painfully slow — this study made me an extremely quick solitaire player.