"Game theory and Solitaire" Topic

I play Solitaire a lot on my computer. It's … relaxing, but frustrating. It also cuts into paintingtime, but…
I like the Free Cell version best.

I know that there are a lot of theoreticians and mathematicians with time on their hands who study things like this.
I have often wondered if, theoretically, ALL starting games are "winnable".
Failing that, is there a theoretical percentage that the "perfect player" should win?
Is "strategy" better than intuition?

I used to work with a woman who decided to start with game 1 in Free Cell and win them all in order. Unfortunately she had a stroke and retired on disability a couple of thousand games into the project. This does nothing to answer your question, I suppose, but this is the utter drivel page.

I don't know for sure, but I do know I've had games that didn't go past the first card or two, so I think that NOT ALL starting games are "winnable." Of course, it could have been operator error.

I have often wondered if, theoretically, ALL starting games are "winnable".

I would think not, although there's certainly a far higher percentage that are winnable than are winnable by ME.

I used to really like the TriPeaks version of Solitaire, which is apparently based on a Vegas card game, and eventually got up to an average of coming out a few bucks per game. It would be a slow way to make a living, but I suppose it would be better than nothing, if stranded in Vegas.

Doug

I used to work with a woman who decided to start with game 1 in Free Cell and win them all in order.

About ten years ago, I played and beat the up to a bit over #1700. I doubt I would finish all, what, 36K? At least I hope not!

I imagine I could engineer an initial draw that would be difficult. I seem to run into enough of them,.
Start with all the aces in the top row, and nothing but red cards in the bottom rows.

I play 'best 2 out of 3'. Sort of sets a 'time limit'…. ;-)

I like cake…….

Mmmmm… pie!

John, there are certainly unwinnable Free Cell games. Consider, for example, the column that starts King of Hearts, King of Diamonds, Ace of Spades, Queen of Spades, …

You can't move the Queen to play the Ace up, so you're stymied.

at over 2000 games played of freecell so far, I have not found an unwinable one yet. I used to play beleaguered castles with actual real cards (which is almost the same game, except the aces start already out) and could always win.

however, it does seem like you could construct a deal where there is no possible first move.

I like Spider better.I'm no genius,but even I have managed to win a dozen games at "expert" level.

It is actually a combinatorial path finding problem – each initial distribution of cards (the combinatorial part) is then followed by a set of path finding problems based on sequence of play. The combinatorial distribution of the cards in the piles defines the number of games while the possible paths represent the different ways a game can progress by the rules. The number of possible solitaire deals should be available via a Google search; it will be defined by the number of unique ordered ways one can shuffle a deck of cards (actually it is probably a subset of this if you use a '"draw one" kind of play because you have full access to the I dealt card pike, thus the order after dealing the tableau is immaterial. The problem is the sheer number of playable paths – probably countable but a huge number.

Flatland Hillbilly wrote:

The problem is the sheer number of playable paths – probably countable but a huge number.

Indeed. Stanislaw Ulam had the idea of the Monte Carlo method in 1946 while he was off sick from Los Alamos; he had been playing solitaire (Canfield), and wondered what the probability was of a game coming out. He pretty soon decided that enumerating the possible permutations was firmly in the "too diffocult" bin.

All the best,

John.

John -

Love the S. Ulam anecdote! It is here where you could use game theory to choose paths based on some "optimization" strategy – although we would have to classify such strategies as potentially being suboptimal given that one does not evaluate every possible playable path. In fact we could devise specific strategies of play based on perceived playoffs (e.g. winning strategies) for placement / selection of cards. One could use a computer to investigate the potential probability that a strategy leads to a win, but you would have to question whether the sampling statistics were sufficient to make a universally optimal choice.

John the OFM – one could postulate a distribution of cards in the tableau – most likely with no plays on the turned-over cards and then see if there is a distribution of cards in the turnover deck that would not play on any of the exposed cards on the tableau – would by definition be unplayable. The simple counter example shows an unwinnable deal. Now – just have to show that there is such a case. Assume that the turned over cards on the seven stacks are three jacks and four kings. We have 1 + 2 + 3 + 4 + 5 + 6 = 21 covered cards in the tableau. Let's assume this set includes all four queens, all four tens, and all four aces. These 12 cards represent the only possible plays, so all cards in the turnover deck would be useless. (Please check my logic here – feel free to correct me.)