Tuesday, November 20, 2007

Losing to Yourself

Occasionally I play Solitaire on my iPod. After losing several games in a row (by lose, I mean I can't find anything more to do and I haven't finished the game) I wondered what percentage of games can be won and if there is any "better" methodology or rules to doing it that will yield a higher number of wins versus another.

Pure guessing leads me to believe that there are games that can't be won and that there are games that "could" be won if things are done in the right order, but can also be put into a state that you can no longer win from.

I am assuming that you are playing a "normal" game where you have 7 columns to work with (left most having one "up" card, the second having an "up" card and a "down" card ....), 4 foundation areas where you must place the cards by suit starting with Ace, and that you flip cards out of your deck 3 at a time (only able to play the top card). The version on my iPod default to NOT letting you move cards from the "foundation" areas but you could do it either way.

The puzzle I pose to everyone is to figure out what percentage of possible games are "winnable" or some approximation.

Also, can you determine any specific methodologies to increase the likely hood of winning a game over others?

Submitted by Me.

4 comments:

Kevin Berridge said...

I'm just pulling this from memory so take it with a grain of salt. I think my dad told me this a long time ago. Depending on the deck Solitaire can be unwinable before you even start. But Freecell can always be won. I think I remember being told that it hadn't been proven that Freecell could always be won, but that it was still true. I may search the web for some references to back that up if I find some time.

Anonymous said...

sheeeeesh, that seems like a hard question. to mask my ignorance I'll change the subject back to Free Cell and talk about something I can figure out ... I average 75-80% wins in free cell so I don't play Solitaire. I play Spider Solitaire sometimes but I only can win a small % of the time. Do any of you play those games with any regularity?

I have seen somewhere before analysis of some kinds of problems where a mathematician proves if a solution exists instead of finding the solution. I wonder if this field of mathematics could be applied to this complex game permutations to determine absolutely if a solution must exist for each deck permutation. I don't know where to begin on this. Also, the question of misplaying a winnable solitaire layout and making it unwinnable complicates the question. Interesting to ask, can one always misplay a layout so as to make it unwinnable?

Benjamin P Lee said...

I put some thought into this but didn't come up with anything spectacular other than proving to myself that there exists unwinnable games and games that can be won if done "correctly" and not done if done "incorrectly".

As it turns out, the wikipedia article I quoted actually had some information on the subject (stating that the exact percentage isn't known) and there were two interesting links on the subject (namely here and here).

The world may never know.

Benjamin P Lee said...

of course, you could always do something like this :-)