Intermezzo

In Microsoft Window’s Spider Solitaire I found an unusual feature/bug: if a player completes a suit he receives a 100-point bonus but is not penalised 1 point for the move. For instance, suppose we have K-Q-J-T-9 of Hearts in one column and 8-7-6-5-4-3-2-A of Hearts in another and our score is 458. If we clear Hearts our score becomes 558, not 557. Another example: suppose we have no completed suits, a score of 400 and our target is to win with 1000+ points. The maximum number of moves we have is 208, not 200.

Note that clearing a suit is automatic, so we don’t have the option of completing the suit but refusing to move it do the foundations. In rare circumstances this option may be desirable, but giving an example is left as the proverbial exercise for the reader.

Here’s another fun question: what is the theoretical minimum number of moves required to beat Spider Solitaire if the cards fall perfectly?

To avoid accidentally revealing spoilers, I will insert the lyrics for one of my favourite anti-smoking songs.

Once a stupid smoker camped by a billabong

Under the influence of L.S.D.

And he sang and he smoked while his mates were drinking alcohol

You’ll come a smoking will kill ya with me

Smoking will kill ya smoking will kill ya

You’ll come a smoking will kill ya with me

And he sang and he smoked while his mates were drinking alcohol

You’ll come a smoking will kill ya with me

Up rode the smoker mounted on his thoroughbred

Down came the troopers one two three

What’s that illegal drug you’ve got in your tucker bag?

You’ll come a smoking will kill ya with me

Smoking will kill ya smoking will kill ya

You’ll come a smoking will kill ya with me

What’s that illegal drug you’ve got in your tucker bag?

You’ll come a smoking will kill ya with me

Rot13(shpx) said the smoker he committed suicide

You’ll never catch me alive said he

And his ghost may be heard as you pass by the riverside

You’ll come a smoking will kill ya with me

Smoking will kill ya smoking will kill ya

You’ll come a smoking will kill ya with me

And his ghost may be heard as you pass by the riverside

You’ll come a smoking will kill ya with me

The simplest viewpoint is to consider in-suit builds because the game is finished if and only if we have exactly 96 in-suit builds.

Each move gains at most one in-suit build (e.g. 6 of Hearts onto the 7 of Hearts). Dealing a row of 10 cards can gain at most 10 in-suit builds. We start with zero in-suit builds and can deal from the stock five times. To obtain 96 in-suit builds we require a minimum of 5 deals (worth 50 in-suit builds) plus 46 moves to pull off the Holy Grail of Four-Suit Spider Solitaire. That’s 51 moves in total. Well done if you answered 51 moves.

Assuming we start with 500 points, our final score is 500-51+800 = 1249 points … plus an 8-point rebate for the feature/bug described above. That’s a grand total of 1257.

And what happens to our score if we deal a row of ten cards and automatically remove two or more suits? Even I don’t know the answer to that one 😊

Exercise for the interested reader: get two physical decks of playing cards and deal a hand of Spider Solitaire. Ignore the identity of face-up cards (so if you see an Eight of Hearts, you can pretend it is the Four of Spades or any other card of your choosing), so you are effectively distinguishing only between face-up cards and face-down cards. Remember that you cannot deal a row of ten cards if you have at least one empty column. Play out the hand and verify that victory can indeed be attained in exactly 51 moves.