How Can I Win This Game?

In the opening phases of the game we are always concerned with turning over new cards and building in-suit. But in the middle-game or end-game things are different.

By this stage a decent player will be able to evaluate the position. After performing some multi-dimensional calculus on the back of an envelope, he she or it will be able to estimate winning chances and decide on a plan of action.

Unfortunately, an in-depth discussion of multidimensional calculus is beyond the scope of this post but a useful general principle is the following:

• If things are going okay, we should continue to play our normal game. Turn over new cards, build in-suit whenever possible, and start thinking about removing complete suits.
• If the game is going badly, start looking for miracles. You need them to win, and miracles never occur if you don’t look for them.

Conversely if the game is going extremely well, you might consider playing safe, but that’s another lesson for another time.

In the diagram position you don’t need a Grandmaster Title from the International Federation of Spider Solitaire to work out the prospects are bleak. The stock is exhausted, several cards are yet to be exposed etc, etc. But all hope is not lost if you excuse the terrible cliché. We can quickly obtain an empty column and turn over cards in columns a or h. Since we probably need good cards to win, we might ask ourselves “if we could call the next card what is the best case scenario when turning over column a or h?”

A closer look reveals all cards in the Spade suit are already exposed. Assuming we focus all our effort into removing a full suit of Spades how much luck do we need? Perhaps a good card or two in column a, or perhaps we can tidy things up a little and hope for luck on the next deal – no scratch that, the stock’s already empty.

It turns out we don’t need any luck – it is possible to remove the Spades without exposing any new cards. Of course, we need to expose cards to win the game eventually, but the point is we are guaranteed to remove Spades regardless of the permutation of unseen cards. One sequence would be: is <bg, id, ih, ia, jf, dj, cd, ch, jd, cj, d2=j1, hc, hc, fg, fd, fh, fa, d1=f1, f2=h2, hc, cj>. Whoosh – the Spade suit goes onto the foundations!

If you found this sequence of moves well done. Of course, it might be possible to do better than that – remembering that removing one suit is not synonymous with winning the game. But at least it’s a fallback position: we can choose this option if we find nothing better.

Avid readers might have recognised the exact same position from an earlier post, and would keenly deduce the game is winnable since I managed to beat it without undo. If you spotted this then again well done 😊