This has never been my experience until last night.

No “big deal,” right?

When playing with cards, my percentage is much lower, because there are moves where you have to make a choice that could be wrong statistically (you have two kings, which do you move off the stack. This would be very different for the Thoughtful Solitaire variant). I would guess that my percentage is 25% with cards. Also with cards it is a different game because half the time is spent shuffling.

When playing on my cellphone, I seem to win many more games, 30-40%, and have wondered if they are all “solvable” games but I think this is too hard to program. Perhaps it is just that I can focus on the game and not how annoyed I am by shuffling.

I figure someone math geek must’ve answered this question, but 30 minutes on google hasn’t yielded an answer yet…

My win percentage so far (only 50 games played) is about 34%.

This is somewhat misleading as the rules are never clearly defined. They are using very “loose” rules allowing a large percentage of games to be solved. The number of solveable games must obviously depend on the rules.

I usually deal a regular game of klondike, but with all cards face up. Then I also deal the rest of the deck in groups of three, so I can see the entire deck from start. The rules for how to play cards from the hand are more complex than most regular games of solitaire, so I will leave them as an exercise for the card players out there.

There is also a very neat computer game for Windows called K+ Solitaire. It is “Thoughtful Solitaire” with all cards showed from start, and it also has a really quick solution finder. Find it at http://www.greatgamesexperiment.com/game/kplus

In this game, the rules for which cards are allowed to be played can be very confusing (although the computer handle it for you). Take for example the following first cards:

1. 7 club
2. 2 heart
3. 1 hearts

4. 1 clubs
5. 5 diamonds
6. 1 spades

The ace of hearts and the ace of spades will be playable from the start. If you now play the ace of hearts (simulating in a regular game of Klondike that you draw three cards and play the ace of hearts), the 2 of hearts will now be playable. But also the ace of clubs since that would be playable in the next round (if you drew all the cards on the hand and then re-drew the first three).

But if you play the ace of spades now, the 2 of hearts will not be playable any more, since playing the ace of spades simulates you drawing three more cards (leaving the two behind) and playing the ace.

I don’t know if the solution finder will be able to find all solutions, but just clicking “new game” and then “search” will show that much more than 50% of all games have a solution.

The latest numbers form the wikipedia article is from the “ICGA Journal”, September 2007 where Bjarnason, Tadepalli and Fern show an algorithm that can solve around 80% of all thoughtful solitaire games in less than 4 seconds. They also show that between 82% and 91.44% of all Klondike games have a possible solution.

Tom is absolutely right about Yates.

Yates also writes about the Vegas version where you have three cards flipped, but limited run through the cards.

So where does that leave us? It doesn’t undermine my strategy. It does undermine my claim that the strategy is non-obvious, leaving the claim unproven.

Oh well.