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.


“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>


“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>


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.


“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.


Long-term Planning

If you have been following this blog regularly, you will recall the Project Manager had a very bad day at the office.

He achieved all his Key Performance Indicators. He got a healthy raise. Team morale is excellent, and his newest team members are especially enthusiastic about the next project. All the company’s clients are satisfied, and the CEO was in an especially good mood. But when he tried to apply his project management skills to the game of Spider Solitaire everything unexpectedly turned to 83,72,73,84. Where did he go wrong?

The attentive reader may have picked up the first move was a colossal blunder. The only suited move was the Ace of hearts onto the Two of hearts. But because those cards were in different halves of the tableau, neither Team Player 1 or Team Player 2 spotted it. I don’t know about you, but when a team of three people 70,85,67,75 up the very first move of the game it’s a pretty bad sign. Dividing a complex task into sub-problems is not trivial, and of course there are the overheads associated with communicating outputs between team members (as any project manager will know!).

Another (albeit less obvious) problem was that the number of face-down cards remaining is not a very reliable indicator of how well the game is going. Recall that the Project Manager realised the game was going badly when there were 20 cards left in the stock and he was nowhere near 18 face-down cards.

Although I didn’t explicitly mention this in the story, the Project Manager was implicitly assuming that progress should be about linear. Thus every time we deal another 10 cards from the stock we should expose at least C face-down cards, and C can be calculated using simple math (18 is not exact but it’s sufficiently close for purposes of the story). Linear approximation is unreliable, since one could very well have a game where things start badly, but once a critical suit is removed, everything opens up and a large number of face-down cards get exposed without the player even trying (because the game “plays itself” for lack of better expression).

Game Plan

A more serious problem is that the Project Manager assumed that the number of face-down cards alone was enough to estimate how well a game is going. This assumption is clearly wrong, and a good player should be considering a number of factors, such as how “clean” various columns are or how close we are to getting an empty column or a complete suit etc. Obviously this is far from trivial, but I recommend that a beginner should be thinking about a game plan like the following:


The items at the left indicate milestones. Thus, our first objective is to get an empty column. The next item of business is getting a number of suited builds (e.g. 6 of Hearts onto the 7 of Hearts etc). Next, we then remove a complete suit to the foundations. The good news is that once the first suit is complete, winning the game often becomes a formality. The labels R0 through R5 indicate rounds of cards dealt from the stock. The game starts at R0 and every time 10 extra cards are dealt we move to the next round. Once R5 is complete, the game is by definition either won or lost. The green bar at the top says that if we can obtain at least 1 empty column by Round 2 (or earlier) then we are “on schedule” to remove all suits before the stock runs out. If we can’t obtain an empty column by Round 2 then we have cause for concern.

The second green bar says we need at least 25 suited builds by Round 3, but also we cannot hope to achieve this until we achieve our first goal of 1 empty column, as represented by the tiny blue arrow. Obviously this is a simplifying assumption: one may get lucky with suited builds before an empty column is exposed, but this tends to be an exception. Once you get an empty column or two it is much easier to tidy up your columns and arrange cards in-suit with the usual “Tower-of-Hanoi” manoeuvres. Experienced players can experiment with more complex game plans, but if you’re a beginner it’s safe to assume that 25 suited builds ain’t happening until you get that empty column. Once you have enough suited builds, now is the time to start thinking about completing a full suit. The third and fourth green bars are interpreted in a similar manner.

No doubt those of you who are reading this at the office and snickering while the boss ain’t looking may have recognised the diagram as a Gantt Chart, named after Henry Grant (1861-1919), an American mechanical engineer and management consultant.

Multiple paths to every milestone

Recall the first milestone was getting an empty column. Note that I didn’t say we should focus on the column with fewest face-down cards. That would be putting all our eggs in one basket, if you excuse the terrible cliché. Often it is wise to keep an eye on several columns at once. We don’t need to have a plan for every letter of the alphabet, but it is much easier to clear a column if you have 2 or 3 potentially good columns (so a single 75,73,78,71 won’t 70,85,67,75 everything up). Similar comments apply to the other milestones.

In the previous story, Team Player 1 was pleased with the deal of R3 because he could get two in-suit builds without help from Team Player 2. This was fighting the wrong battle (although to be fair the damage was probably already done if you excuse the cliché). At this stage the team desperately needed empty columns and/or complete suits and they weren’t anywhere near achieving that.

Advanced Strategy

As you gain more experience you may enhance the Gantt Chart. For instance, once you get an empty column, you may decide your next task should be a second empty column, 25 suited builds or work on both simultaneously. Similarly, you might decide that once you remove a full suit, you may add a task of finding a second suit. Or you might decide that 25 is not the correct number and replace it with something slightly higher or lower, and so on. An example game plan for an advanced player could be something like this:


Finally, one should remember that a Gantt Chart is a living document, written in English not Latin. If a game is progressing badly (or conversely if an unexpected opportunity presents itself), it may be wise to adjust it accordingly.

The main advantage of having a Gantt Chart is it gives the player (or team of players!) a rough idea of where they stand (in terms of winning chances), hence they know when a change of strategy is required. So the fact that our Project Manager had a Gantt Chart at all indicates he is doing something right! Without a Gantt Chart, it is too easy for a player to drift into a lost position without understanding where he went wrong. This leads to the worst of both worlds when a player loses a game and also fails to learn anything from his defeat.

Until next time, happy Spider Solitaire playing!

All pigs fed and ready to fly

“It’s been an excellent year,” said the Chief Executive Officer. All the staff members are beaming with pride.

“Another month ends. All targets met. All customers satisfied. Our new team members are especially eager and enthusiastic.”

Everyone laughs as the CEO reaches the final slide of his Powerpoint Presentation: a picture of Santa Claus riding into the subset, but with the usual reindeer replaced with flying pigs.

“I would like to thank y’all for the hard work you have put in,” continues the CEO. “Today will be a very special day. Every staff member will be allowed to goof off the rest of today and play as much Spider Solitaire as they want.”

The Project Manager groaned inwardly. As if he needed to be reminded of his failure at that blasted game, especially at the 4-suit level. His significant other could boast a win rate of 20%. He was lucky to obtain half that rate, even with the help of 85,78,68,79.

Despite the many years of tutelage from his wife, the Project Manager was unable to see the board as a whole, especially with two decks of cards. The game was way too complex, especially considering that exposed cards were not necessarily always in descending sequence and half the cards were face-down.

Hang on he thought to himself. Maybe if he organised a team of players instead of a single person then the chances of victory would increase. Divide and Conquer, if you excuse the cliché. At least that would give him an advantage over his significant other. She always played solo.

“I know the feeling,” said Team Player 1. “I’m reasonably ok at Freecell and we all know Klondike is boring, but I really 83,85,67,75 at Spider.”

Team Player 2 can only nod in agreement. He only learnt how to play the game a week ago.

“We need to approach the game systematically,” said the Project Manager. “It’s tempting to rush in and play the first move that springs to mind but I think if we can work as a team it will be better in the long run.”

Team Players 1 and 2 nod in agreement


“So here’s the plan,” says the Project Manager. Team Player 1 will focus only on columns 1-5 and expose as many cards as he can. Team Player 2 will handle columns 6-10. When both of you are stuck I want you to report your progress, and I will take things from there.”


“I only turned over one card,” says Team Player 1. “I need a Five, Eight or Queen from Team Player 2 … or an unlikely Deuce-Three combination”.

“I got two cards,” says Team Player 2. “I need a Deuce, Ten or King from player 1.”

“Excellent,” says the Project Manager. “Jack of Clubs onto the Queen of Hearts.”

They expose a Deuce of Clubs.

Team Player 1 is more than happy to shift the Ace of Clubs in-suit onto the Deuce in column 5. Unfortunately Team Player 2 has nothing else to report.

“This is going well,” says the Project Manager. “Ace of Hearts onto the Deuce, in suit!”

<<several moves later>>


“I think we’re in trouble,” says the Project Manager.

“Why is that?” asks Team Player 2.

“There are only two rounds left in the stock,” replies the Project Manager. “According to my Gantt Chart, we should have only 18 face-down cards remaining. But we’re not even close.”

“We got a good deal this round,” offers Team Player 1. “At least my half of the board is good. I can build in-suit with the 9-10 of diamonds, then build in-suit again with the 2-3 of diamonds without any help from Team Player 2.”

<<several moves later>>


“Well that was 83,72,73,84” sighs the Project Manager.

It’s all over but the groaning. The Project Manager catches the next bus home and reflects on his crushing defeat. He can’t remember having a less productive day at the office.

“Hi Hun, I heard the good news from your work colleagues …”

“Ngrrmph,” replies the Project Manager.