Long-term Planning (alternative version)

It has not been a good week. Company profits are down, the project is three weeks late, team morale is low, customers are saying nasty stuff on their Twitter and Facebook. The latest performance review was 83,72,73,84. And the less said about yesterday’s WHS incident the better. But at least Project Manager Two’s crack team of procrastinators haven’t forgotten how to play a mean game of Spider Solitaire. They could win about 20% of the time sans 85,78,68,79 whereas Project Manager Two’s significant other would only win about 10% of the time – on a good day.

“Okay here’s the plan,” says Project Manager Two. “Tom will focus on exposing as many cards as possible.”

“What about building in-suit?” asks Tom.

“68,73,67,75 will alert you whenever it is possible to increase the number of in-suit builds. But he will only focus on reversible moves.”

“You mean things like Seven of Hearts onto the Eight of Hearts when the Seven is already on a different Eight?” asks 68,73,67,75.

“Correct,” replies Project Manager Two. “Remember the virtues of procrastination. Only build in-suit at the last min-”

“But if the move is reversible then procrastination doesn’t matter, right?” asks 68,73,67,75.

“Correct. Remember we are only aiming to win; the number of moves is irrelevant. In any case it looks like you’ve got the gist.”

“What is my task?” asks Harry.

“Your job is to look for opportunities to remove complete suits.”

“Does that mean I have nothing to do in the early rounds?”

“Not exactly. It is still possible to monitor the progress of individual suits even if all 13 cards haven’t appeared. For instance if we have a run of A-2-3-4-5-6-7-8-9 of clubs after the first round then we expect a strong chance of completing the suit before round 3 say.”

“Let’s do this!” say Tom, 68,73,67,75 and Harry in unison.

game2_image1

“We are guaranteed to turn over 3 cards,” says Tom. “Which I believe is average.”

“We’re nowhere near completing a single suit,” says Harry.

Well DUH,” replies 68,73,67,75.

<several moves later>

game2_image2

“We have two empty columns,” says Tom.

“Alert – well sort of,” says 68,73,67,75. “We can shift the 5-6 in column Five to one of the three Sevens. Technically not reversible, but unlikely to cost. This allows us to align the K-Q of diamonds and K-Q of spades.”

“But can we procrastinate?” asks Project Manager Two.

“You’re right,” replies 68,73,67,75. “Even if only one empty column instead of two we can still align the K-Q of diamonds and spades. Therefore we have no need to do so immediately

“We don’t have any long runs in a single suit,” says Harry. “It will probably take a few rounds before we can remove any suits.”

“Let’s get some numbers,” says Project Manager 2.

“There are 25 cards unseen. We are guaranteed at least 4 turnovers before the next round,” says Tom.

“We have 8 builds in suit,” says 68,73,67,75. “It’s easy to get four more builds if we choose not to procrastinate, assuming we refuse to give up empty columns.”

Project Manager 2 checks his Gantt Chart. He is pleased with his team’s progress and instructs Tom, 68,73,67,75 and Harry to continue on with “business as usual”.

<several moves later>

game2_image3

Tom is about to shift the 8 of diamonds onto an empty column and build the 8-7 of hearts in-suit onto the J-0-9 when Harry suddenly calls out “Alert!”

“We have King through Six in spades in column 5, we can add the 5-4 column 4 at the expense of a hole. No Ace of Three unfortunately. The club suit is also coming along nicely with King through Seven in columns One and Four. We also have the 6 and 4-3-2”

Tom briefly considers shifting the K-Q-J of clubs onto an empty column to extend the spade suit to K through 4. Yuck. Maybe if it didn’t expose another Ace then he might consider it. J-0-9-8-7 of hearts it is.

<several moves later>

“Alert,” says 68,73,67,75. “Move the queen from column Nine to Six, then shift the other queen from Column 10 to Nine. Add the Jack-Ten-Nine from blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah and at the end of all those complicated manouevres we have an extra in-suit build K-Q in hearts. And every one of these moves is reversible!”

“Well spotted,” says Tom. “How the 70,85,67,75 did you do that?”

“It’s the only part of the game I’m good at,” replies 68,73,67,75. “But remember we’re all part of a team. We all do our bit.”

“That’s why y’all bow to the master,” chuckles Project Manager Two.

“Alert,” says Harry. “Every card in the spade suit is now visible.”

It doesn’t take long for the crack team of procrastinators to organise a complete suit of spades and remove it from the tableau.

game2_image4

“I’m sorry,” says Tom. “I really need to go. I’ve already booked my tickets for a piano concert tonight.”

“You’re perfectly welcome to leave,” replies Project Manager 2. “With one suit removed and three empty columns, we are well on track to win this game. I’ve decided we will leave this game for today and complete it on Monday.”

Unfortunately, procrastination turned out to be a very poor decision. On the next week the Project Manager discovers to his horror that all the games on their PC’s have been disabled and they are no longer able to complete the game.

THE END

Solution to procrastination puzzle

Apologies for the delay in posting the solution.

The correct move is to shift the K of hearts in column 6 onto the empty column to expose a new card, and then clear the suit with the 3-2-A. The difference is if we expose the Three of hearts then we have two empty columns instead of one. Of course the odds are small since there is only one Heart Three unseen, but nothing to be lost by trying!

Note that if you were scoring according to number of moves instead of playing a “pure game” (i.e. just winning) then you would probably not procrastinate and save a move. Since the game is going so well, you would probably expect to win anyway.

Oh, in other news I have just lent  Steve N Brown’s book to my work colleague so I expect to see some big improvement in her play in January 2020. Bring it on!

Happy procrastinating

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 😊