Suzanne:

With both you and Janine on the case we cannot fail to make significant inroads into the dark continent of solitaire!

There seems to be unanimous agreement that taking from the board is favored over taking from the deck. There is some disagreement, however, as to which direction we should favor when raiding the board. Suzanne prefers right to left so as to more deeply penetrate the higher piles to the right. Janine seems to prefer left to right so as to open holes for kings as soon as possible.

I am not convinced that it matters. Essentially, all buried cards are equally mysterious; a vital card could be anywhere. Uncovering a hole is like uncovering an invisible "overlord" card that a king can submit to. The only difference, then, is that the overlord "card" is always at the bottom of each pile, so we know in advance the consequences of exposing it; uncovering the tops of deeper piles has far less predictable results.

One thing is certain, however. Some spreads are unwinnable right from the start. Consider the case in which a two of spades is exposed atop the rightmost pile. Suppose that the following three cards are buried beneath it: the ace of spaces, the three of hearts, and the three of diamonds. In this case there is no way the two can ever be pulled from its position and the other three cards are already in their common grave. If the gods of chance dictate this initial arrangement there is absolutely nothing we mortals can do (short of cheating) to circumvent destiny.

And of course this is not the only way a spread could be unwinnable. There are many arrangements involving multiple piles that forbid all victory. The questions I have are A) how can I identify whether or not a certain sequence of cards is unwinnable? and B) what percentage of initial spreads are unwinnable?

I have no idea what the answers are. But I have devised an algorithm that will shuffle cards in such a way that the initial spread is guaranteed to be winnable. The trick is to start from the winning position (all four suits arranged from ace to king) and play the game in reverse, moving at random within the reverse rules, until an initial spread is formed. This method would provide a fantastically high number of initial spreads, all of them guaranteed to have at least one path to victory, and it would be fairly easy to program.

UPDATE

Since writing this card I have completed a tool for the first stage of solitaire research. For a description of this project and details about how YOU can participate, see this issue's installment of Mr. Wizard!