How Can I Win This Game? (Alternative version)

It was a pleasant Sunday afternoon. The sun was shining and he had plenty of spare time on his hands. True, there was the small matter of a chemistry assignment due tomorrow, but that could always be done after dinner. A perfect time to play some more Spider Solitaire.

The play had started well, but things started to sour when four Kings appeared in the third deal. The fourth deal brought no luck either with no face-down cards unable to be exposed. Resigned to his fate, Joe Bloggs reluctantly dealt the last row of ten cards and surveyed his prospects.

How can I win this game? Joe asked himself.

There was some good news: an empty column (or “hole” as he liked to say) was available in the ninth column. And he could turn over a card in Column h. But at this stage of the game Joe realised he would need a good miracle or three to win.

“What is the best card I can hope for in Column h?” Joe asked himself.

This brings him to the bad news: there would be plenty of calculation to look forward to, and given the stock was empty any mistake, no matter how small, could be fatal.

Suddenly Joe Bloggs spots a bird staring at him through the window.

She’s been wallowing in the mud for way too long. Don’t ask me why.

Joe Bloggs briefly considers giving the poor thing a nice warm bath.

“Oink oink,” says the bird.

“87,72,65,84 84,72,69 70,85,67,75?” replies Joe Bloggs.

Through his peripheral vision, Joe Bloggs notices a flock of shiny pigs floating in the air. Thirteen of them shift into the foreground and form the shape of a happy face. After winking at Joe Bloggs, they chase each other in circles for a good half-a-minute. Then they gradually accelerate until whoosh – they shoot up towards the sky!

“Oink oink,” repeats the Bird.

Joe Bloggs stares at the bird again. Perhaps she is trying to tell him something, but he can’t work out exactly what. His chemistry assignment? That wouldn’t make much sense.

Joe studies the cards again. He soon notices that every card in the Spade suit is visible in the tableau. An Ace in column 5 or 6, Deuce and Three in column 6, Four-Five in column 8 and so on. Perhaps it is possible to remove a complete suit of Spades with the correct sequence of moves, regardless of the permutation of face-down cards. Not likely, given they were scattered all over the place, but perhaps his best shot anyhow.

“Aha,” says Joe Bloggs, after some thought. “The correct move sequence 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>”

Joe Bloggs executes the move sequence <bg, id, ih, ia, jf, dj, cd, ch, jd, cj, d2=j1, hc, hc, fg, fd, fh, fa, d1=f1, f2=h2, hc, cj> and whoosh – he triumphantly slaps the Spade Suit onto the foundations!

True, his position was still very bad after removing the suit of Spades but no matter. He had already won the war: thanks to this hand his skill had improved considerably and the actual result of this game was rendered moot.

The virtues of procrastination

We’ve all been there. Your Chemistry assignment is due tomorrow. You’ve got to prepare for your English Exam next week. You need to do the dishes. It’s baby’s bath time again. Gotta start looking for a job. Time to install Tensorflow on your machine and understand Neural Nets and Deep Learning 101. Or maybe all of the above. Oh well, one more game of Four-suit Spider Solitaire sans 85,78,68,79 can’t hurt can it?

Spider players rejoice! Your favourite game is one of a select few where procrastination can be a virtue. Here is a simple example:

proc_1

There are two obvious options: either we can expose a new card in column 3 (shifting the Spade Five on the Club Six) or move the Diamond Queen onto the king of the same suit. Which is the better option?

Suppose we build in-suit with the Diamond K-Q. A little thought shows we then have nothing better than to shift the Spade Five and turnover a card column 3. Therefore we may as well start by turning over column 3 and seeing what happens. Here are a number of possible scenarios:

  • We turn over the Diamond Queen (recalling there are two decks, so this is indeed possible). This means we get to turnover a second card in column 3 and build the K-Q of Diamonds.
  • We turn over the Spade Queen. Again we get another turnover (albeit off-suit), which is probably worth more than building in-suit.
  • We turn over a Nine of any suit. This Nine goes onto one of the three Tens and we get another chance for either of the first two scenarios.
  • We draw an Eight of any suit. This is a bad card and we have nothing better than to build the K-Q of diamonds.

In effect we are procrastinating the act of moving the Diamond Queen onto the King. It probably should be done at some point, but we lose nothing by waiting. In all the above cases, procrastination either gains something over non-procrastination or breaks even.

You might have noticed there was a further option of moving the Two of Clubs onto either Three in columns 7 or 9. Again there is no reason to do this immediately, so we procrastinate by leaving the Two of Clubs alone. The advantage becomes apparent if column 3 reveals two Deuces in a row.

Opportunities for procrastination frequently arise during the course of play. Each individual opportunity represents only a small edge, but the cumulative effect of these small edges can become significant over a large number of games.

Now that you have studied this example in great detail and have suddenly became a Master Procrastinator I think you might enjoy studying the next problem:

proc_2

The obvious move is to complete a run of hearts using columns 6 and 7. Even better: Microsoft is kindly highlighting this move for us. And we also expose the last hidden card in column 6. The only downside is we expose the ace of clubs. Aces are generally undesirable since nothing can be played onto them. Since this game is going well, one ace will probably not hurt us. But we may as well try to avoid it if at all possible. If you’ve suffered too many bad beats in Texas Holdem and you think Spider Solitaire is out to get you then you probably know what I’m talking about.

Of course we know by now that the most obvious move is not always the best. Looking around for other options, we notice we can get two empty columns by shifting the 3-2 in column 4 onto the Four of Hearts in column 6. But that is a Pyrrhic victory since we don’t get to clear Hearts. We have to give back one of the empty columns just to reveal a new card.

Oops: I’ve just noticed that if we do get the second empty column then we can tidy things slightly by swapping the Ten of Clubs in column 4 with the Ten of Diamonds in Column 9 (note this is not possible with only 1 empty column). Okay, Microsoft is no longer highlighting the obvious move but we can live with that.

proc_3

So it’s decided then: NOW we can safely drag the 3-2-A of Hearts onto the Four, clear the suit and reveal the last card in column 6.

Actually it is possible to improve this plan slightly. Can you see it? (hint: it involves procrastination).

You know the drill by now: No peeking at the answers below (deliberately or otherwise) until you’ve had an honest crack at this problem

image-8

The correct move is … Ah 70,85,67,75 it. I can’t be bothered completing this post. I’ll do it tomorrow 😊