This is ONE OF 3 responses to VC 26 John 3 ("Solitaire")...
As promised, I have embarked on a study of the silly, time-consuming game of Solitaire.
My first question was "How often do I win?" I played 100 games, always accepting whatever the computer dealt and playing through to the bitter end. I won 13 games. In other words, I apparently tend to win roughly one game out of eight.
I strongly encourage other Archipelagoans to try the same experiment so we can get an idea of what our baselines are, and how much one player varies from another.
During my 100 games, I had time to meditate on some of the questions I raised in my last card. One of these involved whether it is preferable to draw from the board or the deck (when given a choice). Like everyone else I've talked to, my hunch is that it's better to draw from the board. I notice that when I lose games, it is not unusual to exhaust the deck, but it is quite rare to exhaust the board.
Like Janine, I generally make all possible moves before proceeding. Occassionally, however, I will purposely pass up a move. If I already have one black king on the board, and a black queen exposed as well, I may resist the chance to fill a void with the second black king and wait until a red king appears. My decision is such cases is also influenced by the dynamics of the deck. If I pass up this chance how likely is it that the same black king will come around again? Have I seen a red king in the deck?
Clearly, it is vital to keep churning the deck as much as possible. The earlier you can draw from the deck in a given pass, the more "churning" will result. Therefore, I will sometimes violate my rule of preferring the board to the deck if the card in question falls near the beginning of a pass through the deck. This is especially true if I happen to notice a vital card buried in the deck that I am unable to reach without such churning.
Once you've made your first pass through the deck, the sequence is revealed and, theoretically, you could take advantage of this knowldege. At the outset of the second pass you can predict all the cards that will be uncovered in that pass. A "perfect" player could uncover all those cards at once in his mind and consider them all when making choices. If a certain vital card is temporarily out of reach in the deck, he could use this information to plot a "course" to the card by making a series of (possibly odd) choices.
A computer program could approach this kind of perfection by projecting ahead whenever it encounters a choice. It could try both choices and project ahead (maybe through multiple passes through the deck) to estimate how many cards will be uncovered in either case. It could assign a point value to the projected plays, and even use knowledge of the cards uncovered so far to guess at the identity of hidden cards. After much grinding it can conclude that choice A will result in from 57 to 105 points, and choice B will result in from 49 to 190 points.
Chess programs work something like this. My question is, how much would all of this buy us? Would a very clever program win one game out of six? One game out of three? And, again, how many games are unwinnable from the outset?
Please keep those observations and theories pouring in. Research will continue!