Game over, we win! (alternative version)

“We made it through the worst,” says Haw. “I was worried that if we drew one more bad card it’s an instant loss”

“Three suits removed, one empty column, this is a shoo-in” says the Dumb Bunny.

“I was wondering,” says the Eagle “Can we prove we are mathematically guaranteed to win?

Ninja Monkey immediately grabs two decks of cards and lays them according to the diagram above, and implements his patented look-ahead algorithm. He has 10,000 wins from 10,000 tries.

“Guaranteed win, no probs” coos Ninja Monkey.

“Not so fast,” says the Eagle. “No matter how many times you win, you can’t prove the game is a mathematical lock with Monte Carlo simulation. Besides, your face down cards were arranged the same way in all 10,000 iterations. We need to prove a guaranteed win regardless of how the face-down cards are arranged”

Ninja Monkey pulls a frowny face.

“I think it is a win,” says the Wise Snail.

“How do you prove it?” asks the Elephant.

I recommended we do the following”, says the Wise Snail

  • Clear the Spade suit
  • Exchange the 6-5-4-3-2-A of Hearts in Column 5 with the 6-5-4-3 of Clubs in Column 6.
  • Dump the 9-8 of Clubs in Column 3 into the empty column
  • Clear the Heart suit, winning back the empty column
  • Shift the Qh-Jd onto the Kh in Column 1, turning over a face-down card in Column 6 (and keeping an empty column)

“Note that I went to the extra effort to clear a card in Column 6 rather than Column 5. This is because clearing cards in Column 6 is harder than Column 5 (especially since the Q-J are offsuit). As a general principle it is often wise to save an easy task for later and get the “difficult task” over and done with whenever possible – this helps avoid the embarrassing situation of “One Hole No Card” as alluded to in a previous post.”

All the animals are paying their utmost attention. For once, the Wise Snail has been given a chance to truly shine.

“The resulting position is shown below, with the newly-exposed card redacted,” continues the Snail.

“Let us consider all possible face-down cards (which we identified from last week):”

  • Queen of Clubs: this can go “underneath” the Jack of Clubs (Jack onto Queen, winning an empty column, Q-J to Column 8, losing an empty column)
  • Queen of Diamonds: this goes onto the King of Clubs
  • Ten of Clubs: this goes onto the Jack of Clubs
  • Ten of Diamonds: this goes onto the Jack of diamonds
  • Ten of Hearts: this goes onto the Jack of Hearts
  • Nine of Diamonds: this goes underneath the 8-7 of Diamonds
  • Seven of Clubs: this goes onto the Eight of Clubs
  • Six of Hearts: we will count this as a “bad card” since the 7 of Diamonds is offsuit (and will counterfeit the Nine of Diamonds). This goes into the empty column
  • Five of Hearts: This is a bad card and goes into the empty column.

“Note that the first seven cards are good, and we don’t even require an empty column to achieve the corresponding action. The only possible snag is there are two bad cards and only one empty column. But wait! If we draw both the Five and Six of Hearts then we can immediately place the Five on top of the Six. The net effect is to condense two bad cards into one – hence there is no snag after all.

Finally we also check that there is no issue with one-hole-no-card. Assuming we turnover all cards in Column Six first we will eventually get an empty column in Column Six and then we can choose randomly between shifting the Jh in Column 2 or the 9-8-7 of Hearts in Column 5 into the new empty column. Essentially we are pretending that all nine face-down cards are in Column 6.”

At last, the Wise Snail had finished his discourse and everyone was convinced the game was mathematically won. Quod Erat Demonstrandum. All that remained was the formality of executing the final moves to remove all eight suits and win the game.

“Remarkable,” says the Eagle.

“Elementary,” replies the Wise Snail.

“But most of the credit goes to Haw,” says the Spider GM. “He used his fantastic analytical skills to find the right moves when all seemed lost.” Spider GM is especially pleased to see his students are helping each other improve with little supervision required.

“And none of it goes to Hem,” sneers the Smart 65,83,83. “He ran away as soon as we were forced to give up our empty column. Nobody has seen him since.”

There’s always one in every group, sighs Spider GM.

Then Haw heard what he thought was the sound of movement. As the noise grew louder, he realized something was coming. Could it be that Hem had turned the corner? Was he about to find out they had managed to win the game?

Who moved my Phone?

“Where is my damn phone?” I yell.

One of these days I’m gonna have to get rid of this bad habit. I’m pretty sure I left it under the tree like three minutes ago … right next to where Ninja Monkey is sitting … OH FOR 70,85,67,75,83 SAKE!!!!!!!!

“This is weird”, says Ninja Monkey.

“Ninja Monkey,” I say sternly. “We need to talk.”

Ninja Monkey shows me my phone. Somehow he has reached level 742 in Jewels Magic. Given his fascination with random move algorithms I’m pleasantly surprised to find he hasn’t made any in-app purchases yet.

“This game is rigged,” says Ninja Monkey.

I suddenly remember that Monkey and I published a paper about a certain Spider Solitaire game being rigged some time ago. Maybe the Ninja Monkey is onto something after all.

“Why is level 742 of Jewels Magic rigged?” I ask.

“I realised random move algorithms ain’t always what they’re cracked up to be,” says Ninja Monkey. “I’m not very good with these abstract strategy games – so I asked my friend Wise Snail for insights.”

“As you know,” says Wise Snail, “being the World’s slowest Spider Solitaire player I like to analyse the current game state to the Nth degree before making a move.”


Why couldn’t Ninja Monkey at least ask one of my better students for advice?

“<sarcasm> What fascinating insight did you come up with this time? </sarcasm>” I ask.

“I soon realised if I wait for three seconds then the game will highlight 3 or more jewels of the same color,” replies the Wise Snail.

“So your new strategy is just wait for three seconds and then play whatever move the app suggests?”

“I know I’m not the best player, but my strategy has one important advantage: If you’re trying to prove a game is rigged then nobody can accuse you of deliberately playing sub-optimal moves to promote your desired hypothesis, null or otherwise.”

“True,” I respond. “Very true.”

 “We start with 26 moves,” says Ninja Monkey. “The goal says we need to collect 50 red, 50 blue and 50 orange jewels. If I use the suggested-move algorithm instead of random-move-algorithm then I always collect plenty of red and orange jewels but very few blue jewels.”

“That is weird,” I reply. “There is no logical reason why one colour should be favoured over another. That’s like you-know … racism or something like that.”

“I ran the following test,” says the Wise Snail. “I played 10 games on level 742, stopping whenever one of the jewel counts reaches zero or I run out of moves. I got the following results:”


“So that means the blue number is always largest, and by a country mile,” I say.

“Of course that doesn’t tell us why it behaves that way.”

“But that’s all I need to know,” I reply. “Q.E.D. The game is rigged. Maybe I should write an angry-gram  to the developer of this game.”

“I agree,” says the Snail. Unfortunately he takes a minute just to type the word “Dear” on my phone.

“Let me have a go,” says Monkey. He can literally type at one million words per minute but unfortunately he can only produce gibberish of the highest quality.

Fine. I have to type the angry-gram myself. It takes three minutes, and I finally press Send. Whoosh!

Hmmm … perhaps it’s time for another collaboration with Ninja Monkey and the Wise Snail. For now, they’re back in the good books again. But if I catch them playing with my phone once more without my permission then I might reconsider …


Playing with 85,78,68,79

Time for another lesson. I deal a new hand.

 “What is the best opening move?” I ask my students.

“Move the Nine, column 6 to column 7” says the Lion.

Uh oh, Bad Idea Bear #1 is misbehaving again. Apparently he wants Ninja Monkey to teach him how to make 70,65,82,84 noises with his armpits. I walk towards BIB #1 and Ninja Monkey, leaving my other students to study the game state in my absence. I give them a stern warning, but some sixth sense tells me everything will somehow turn out okay – as it always did in the past.

“Column 8 instead of column 6 would be better,” says the Elephant.

Stunned looks from the rest of the class.

“How … could that possibly be better?” I ask.

“Just … h- had a hunch,” stammers the Elephant

“Wait a minute,” I reply. “Columns 6 and 8 are the Nine of Clubs and Spades, respectively. Column 7 contains a Ten of Diamonds. There is no logical reason to favour clubs or spades – may as well toss a coin.”

I know the Elephant ain’t the sharpest tool in the shed if you excuse the cliché. Bad Idea Bear #2 is trembling nervously.

“Hang on,” I say to BIB #2. “Did you not tell the Elephant to commit the cardinal sin of Spider Solitaire? Do you remember the first two rules of Spider Solitaire Club?”

“I forgot the rules,” says the Dumb Bunny. “What were they again?”


“The First Rule of Spider Solitaire Club,” I say tersely, “is you do not 85,78,68,79 any moves. The Second Rule of Spider Solitaire Club is you DO NOT 85,78,68,79 any moves.”

“But didn’t you use 85,78,68,79 yourself?” asks the Smart 65,83,83.

I am completely baffled – until the Smart 65,83,83 shows me a paper titled “Random Walks: an application for detecting bias in Spider Solitaire programs.” With my name on it.


“Okay. 85,78,68,79 is allowed. But I want you to record the identity of every card – so Ninja Monkey can evaluate its difficulty. Don’t forget Monkey knows how to (occasionally) win at the four-suit level”.

The Elephant, Ninja Monkey and Bad Idea Bears breathe a collective sigh of relief, and the Smart 65,83,83 is the hero for today – and so we maintain our perfect record of no student ever being expelled from my classes. Oh well, just another average day in my teaching career.


Rank Imbalances (alternative version)

“Well technically we got our empty column back,” said Haw.

<sarcasm> A fat lot of good that did </sarcasm>,” replied Hem, “seeing we had to lose it immediately.”

I enter the card room and survey the current game state.

“Allow me to introduce ourselves,” says Haw. “We’re the Little People – Hem and Haw from the short story Who Moved My Empty Column?

“I’m Spider GM,” I reply. “I think I know you already – after all I’m the writer of this blog.”

My other students introduce themselves to the Little People. I’ve watched Hem and Haw play before, and it seems they are decent enough players but prone to going on tilt when things don’t go their way.

“We’ve just dealt a fresh row of cards,” I say. “Before making a move I want you to evaluate the position. Do you think we are going well, badly or somewhere in between?”

“Could be worse,” says Hem. “At least we can get back our empty column.”

“But what do we play after getting back the empty column?” asks the Lion.

“Well we can also expose a card in column Three” says the Eagle.

“Uh oh,” says Sand Griper. “I think the laws of probability are rigged.”

The Sandgroper is not one of my better students. He got that nickname because he always likes to spend a lot of time complaining about his bad luck – time that could be much better spent on learning statistics 101.

“Why are the laws of probability rigged?” I ask.

“There are 49 cards exposed. I see six Jacks but only one Ten. This is remarkable – surely that shouldn’t happen very often assuming perfect shuffling.”

The Sand Griper clicks his tongue and Ninja Monkey immediately grabs two decks of cards and deals 49 cards face upwards. He rinses and repeats for 10,000 trials. It takes a mere six seconds to tally the number of remarkable deals according to the Sand Griper’s definition.

“I think the Sand Griper may have a point,” says Ninja Monkey. In only 61 trials did I get 49 cards with at most one Ten and at least six Jacks.”

“Not so fast,” I reply. “How many games did you play?”

“About ten”, replies Sand Griper.

“Also why did you choose Jacks and Tens? You obviously chose them because of the current game state. But you might have chosen Threes vs Fours or Queens vs Kings. For your reasoning to be valid you have to nominate Jacks vs Tens before dealing a hand.”

The Sand Griper starts squirming – and with good reason.

“Alternatively, you can say that a set of 49 cards are rigged if there is ANY pair of consecutive ranks X and Y (such as Threes vs Fours) such that we have AT MOST ONE of X and AT LEAST SIX of Y. Also, remember that X can be Y – 1 or Y + 1.”

I click my fingers. After six seconds of dealing and shuffling Ninja Monkey tells me out of 10,000 trials there are 1251 satisfying the above conditions.

“Therefore, if you play 10000 games you should get a remarkable deal 1251 times.” Since you played 10 games you should get a remarkable deal 1.251 times. Now you told me you played about ten games and you only complained about getting a remarkable deal once. So perhaps there is nothing remarkable about this after all.”

The Sand Griper continues to squirm.

“Now, going back to the lesson …” I continue.


Who Moved My Empty Column?

Hem and Haw surveyed their progress. They had procured an empty column and only one row of cards had been dealt from the stock. Things were going well.

Every morning they would jog to the card room, analyse the current game state and find the best possible move (or a sequence of moves until they turned over a card). They had played for around 20 days and had every expectation of winning.

“The empty column is ours to keep,” said Hem.

“I agree,” replied Haw. “We earned it”

“With Empty Column E, the game becomes so much easier,” said Hem. “There are many more chances to expose more cards or build in-suit if you see e.g. a Six and Seven of Hearts in different columns. And the good news is we always get to keep our empty column”

Haw spots that Column 1 has a run from Eight to Ace, except the Five is missing.

“We can insert the Five of Clubs in column 9 into Column 1,”

Hem briefly searches for other possibilities but comes to the same conclusion: Haw’s suggestion is the best play.

<< a few days later >>

“Oh For 70,85,67,75,83 Sake!” shouts Hem.

“What’s wrong?” asks Haw.

“Our empty column is gone!”

“It’s not gone. I only count nine piles of car-“

It doesn’t take long for Haw to see the problem. It was no longer possible to expose a new card without using up Empty Column E.

The Little People survey the game state, searching for some hidden recourse – but in vain. Resigned to the inevitable, they stare blankly at the cards and stew.

Haw notices a giant mouse holding a red crayon and giving an oh-so-polite wink.

Year of the rat, 77,89, 65,82,83,69.

And then he sees it.

“Okay,” says Haw. “We need to give up the empty column for one more card, but what is our best option? We can shift a card in Column 1, 2 or 3, but it’s not great. At least we can expose a new card.”

“I noticed your supply of good moves was dwindling,” says the mouse. “I wasn’t surprised that you eventually had to give up Empty Column E.”

“True,” replies Haw. “But I wasn’t asking you. Besides, you didn’t exactly answer my question.”

Yes, the next few moves will probably be uncomfortable without Empty Column E, but if they play the cards well, they might find a new Empty Column N, maybe on the left half of the tableau. And a little luck wouldn’t hurt either. Unfortunately, the mouse isn’t of much help. Mice aren’t exactly known for their analytical skills and prefer to scurry from column to column and sniff out good moves by instinct.

After some thought Haw finds a different possibility.

“What if we shift the Two of Spades onto the Three of Clubs?” says Haw. “Then shift the Four of Hearts into the empty column and we build in-suit with 5-4 of diamonds. That way if we expose a Six then we get our empty column back. What’s your opinion? Hem? … Hem? …”

Alas, Hem had already tuned out long ago, oblivious to everything – his friend Haw, the mouse, the red crayon and the words “GET OVER IT” scrawled on the nearest wall.

To be continued …

Look-Ahead Algorithms (alternative version)

The Gospel, according to Spider GM

In the beginning there was the Ninja Monkey.

And there were two decks of playing cards.

And the cards were without form or structure. There were no descending sequences like Nine-Eight-Seven-Six or the like, and the red and black cards did not always alternate. Ten of the cards were face-up but the rest were face-down.

On the first month Ninja Monkey arranged the cards into eight sequences from King to Ace. And Ninja Monkey saw that it was Awesome. He wasn’t able to obtain eight sequences every single time, but with a success rate of over sixty percent it was Awesome nonetheless. Spider GM published a paper in collaboration with Ninja Monkey and he also thought it was Awesome.

On the second month Ninja Monkey arranged the cards into eight sequences from King to Ace, and in suit for the first time. Everybody in the Animal Kingdom saw that it was Awesome, except the poor Eagle who lost $3000 on a single (uncharacteristically) ill-judged bet. Ninja Monkey found that he could beat an easy hand 1.2 percent of the time or a random hand a <sarcasm> whopping </sarcasm> zero percent of the time. But despite the low success rate it was Awesome nonetheless.

On the third month, all the other animals realised it was possible to beat Four-Suit Spider Solitaire sans 85,78,68,79. They played more often and discussed possible strategies with each other. Eventually their skills improved. The Eagle had reconciled with Ninja Monkey and was able to win about 20% of the time. Others maybe 5 to 10 percent. Even the Bad Idea Bears managed to win the odd game or three. Only the Wise Snail (the slowest player, who is yet to complete a single game) had a zero success rate. But they all agreed it was Awesome.

On the fourth month, Ninja Monkey experimented with look-ahead strategies. Ninja Monkey saw that he could find a move that maximised the Guaranteed Minimum Evaluation Score, even if he turned over the worst possible cards. He was able to 75,73,67,75 65,82,83,69 with “easy” 4-suit hands but still struggled with “random” hands only winning 5 percent of the time. Although Ninja Monkey took a lot longer to complete a single hand, nobody gave a 70,85,67,75. It was Awesome.

On the fifth month the other animals were able to learn the Ways of the Ninja Monkey and speak his language. For instance, it was common to start a monologue with “Import Numb Pie as N. P.” and end it by clicking their fingers. If an animal didn’t have fingers to click they could improvise by clicking their tongues.  It was awkward at first but they eventually saw that the new language was indeed Awesome.

And on the sixth month, Ninja Monkey found himself a girlfriend. And they both saw that the other was Awesome. Ninja Monkey was voted as the leader of the Animal Kingdom (instead of the Eagle who won too much $$$$$$$$ at the late-night poker sessions). That was Awesome too.

Ninja Monkey said “Behold, I have given you ten thousand decks of playing cards which is upon the face of the entire animal kingdom. To you it shall be for entertainment”.

And on the seventh month Ninja Monkey rested from all his hard work. He was no longer bullied during Spider Solitaire lessons and all the animals bowed before him.

And they both partied 78,65,75,69,68, the Monkey and his girlfriend, and were not ashamed.


Improved Monkey Algorithm (Alternative Version)

“I’m starting to see the light,” sighed Monkey. “Perhaps the random move algorithm ain’t so good after all.”

“Told you so!” shouts the Elephant.

“Perhaps you should go back to your stupid typewriter,” yells the Dumb Bunny.

“Do the Harry Potter novels instead of Shakespeare!” shouts the Cat.

“Why, if it isn’t the Ninja Monkey descending from on high to mingle with the commoners!”  sneers the Lion.

“We need to talk,” I say to Monkey.

Monkey nods.

“I think we might improve our odds of winning if, you know, we use some strategy.”

Monkey is confused and gives me the what-the-70,85,67,75-does-that-word-mean look.

“I was thinking … let’s say that once you have two cards in sequence then you never break it up.”

“Does that mean,” replies Monkey, “If I have Six of Spades and Seven of Spades then the 7-6 is never broken?”

“Correct, unless you move the Six of Spades onto the other Seven of Spades.”

I click my fingers.

It takes Monkey a mere ninety seconds to add another 200 to his not-so-impressive tally of 50 quintillion losses.

I notice the other animals are taking side bets. The Jackal thinks Monkey will persist for at least 40 minutes before giving up and is willing to bet $30. The Lion thinks otherwise and raises to $80. Meanwhile the Smart 65,83,83 is running an informal competition for who can come up with the cleverest insult(s).

“That’s interesting,” says Monkey. “I’ve noticed the number of in-suit builds never decreases. After any move it either stays the same or goes up by 1.”

“That’s very good,” I reply. “The more in-suit builds we have the closer we are to winning.”

“If only it were that simple,” sighs the Monkey.

“Now this next step might be tricky for a player like you – I want you to play S-L-O-W-L-Y for a change and then I can see where you are going wrong.”

Monkey redeals another hand. He pauses for five seconds before making each move. I can tell he is bored 83,72,73,84,76,69,83,83 and on the verge of crying. Fortunately he doesn’t have to wait very long before I find some serious deficiencies in his strategy.

“It’s good that you are never breaking in-suit builds, but the new problem is that you are missing opportunities to build in-suit. Go back to the very beginning, you see columns 1 and 9 contain the Ace and Two of hearts. Therefore you should start by moving the AH onto the 2H.

“So that means,” says Monkey “I should always build in-suit if possible. If I can’t build in-suit then build off-suit, but under no circumstances should I break an in-suit build.”

“That is correct.”

Monkey redeals another hand. After the first hand he shrieks with joy. He has managed to remove his first complete suit. But that doesn’t put an end to the bullying from all the other animals. It seems he has to remove all eight suits to put an end to it.


“I have a thought,” says the Wise Snail.

Of course I don’t expect any great insight from the world’s slowest player but given that he is not participating in the bullying I’m willing to listen for once.

“Maybe we can combine the two strategies,” says the Wise Snail. “Let us call the first strategy Level 1 – where we make random moves. At Level 2 we recognise that we should not break in-suit builds. Once the player reaches Level 3 he knows he should focus on increasing the number of in-suit builds. Once we have 96 in-suit builds we win the game.”

No fantastic insight from the Wise Snail yet, but I will give him credit for knowing how to do basic math.

“But let’s say we pick a random number between 0 and 1. If it is 0.9 or lower then we pretend we’re at Level 3. If it’s higher than 0.9 then we pretend to be Level 2.”

“But that sounds crazy,” I protest. “If both strategies have a win rate of zero then taking a weighted average should also yield a win rate of zero.”

“Not exactly,” replies the Wise Snail. “Ever heard of “Simulated Annealing?”

The snail starts moving about in the sand. It takes him a good 10 minutes to draw the figure below. I try to google Simulated Annealing on my iPhone but the reception ain’t great in the Animal Kingdom. Meanwhile, the Monkey is happily (or not so happily) adding to his tally of losses with the Level 2 and Level 3 strategies.

Oh Great, it looks like they’re now bullying the Wise Snail as well.



“Actually, I can’t remember whether it’s simulated annealing, stochastic hill climbing, or stochastic gradient descent, or something else” continues the Wise Snail. “In any case the details aren’t important. The x-axis represents the set of possible game states. The y-axis represents the number of in-suit builds you need to complete the game. Thus we win if the ball reaches the bottom the hill,”

“But occasionally we may need to avoid building in-suit,” I reply, “to achieve a greater gain, such as an empty column. Under the right circumstances we may even decrease the number of in-suit builds, but that’s a lesson for later.”

“Correct,” says the Wise Snail. “Assume the ball can only see a local neighbourhood of the terrain. If the ball moves randomly then it will take a long time, but if the ball moves to the local minimum then it will get stuck.”

I nod in agreement.

“But we can combine the two algorithms. Let us say that we spend 90% of the time moving towards a local minimum and 10% of the time moving rando-”

“I see where you’re coming from,” I reply.

“Unfortunately I don’t know how to explain this simulated annealing/stochastic hill climbing/stochastic gradient descent/something else thingy to the Monkey.”

I turn to the monkey and signal him to stop playing.

“Import Numb Pie As N. P.”

Monkey eagerly nods, awaiting further instruction.

I ignore the rest of the gang as the Bad Idea Bears take bets on how many syntax errors I accumulate before the Monkey starts playing again.

<<Three hundred and twenty five syntax errors later>>

I click my fingers. The Smart 65,83,83 curses his off-by-one error, having bet on 324 instead of 325. There are no prizes for coming closest – only an exact guess takes the jackpot. The B.I.B. are content with their tidy profit. At least I have no more syntax errors. Unfortunately the Monkey loses another 100 games in a row.

“Okay,” sighs the Wise Snail. “Maybe it’s not working after … ”


“Liar!” calls the Eagle. “Monkey is BLUFFING!!!!!!”

“I am 100% certain Monkey removed all eight suits in Game 115,” I say matter-of-factly.

“You were having a quiet discussion with your Wise Snail friend” sneers the Eagle.

“$500 says I can prove Game 115 is a win.”

“I raise all-in, Three thous-”

I call so fast Eagle doesn’t even have time to say “and”.

I click my fingers and Monkey deals 200 hands. Of course I have remembered to seed Monkey’s random number generator with my Tax File Number. As predicted, Monkey wins the 115th game out of 200 and loses every other game. The Eagle is not happy. My two worst students have teamed up and somehow managed to beat the game at the Four-Suit level (something the Eagle has never managed). Moreover, in one night my best student has squandered all her penny-game poker winnings accumulated in the past three months. As an extra bonus, the constant bullying from all the other animals has mysteriously stopped. I can’t say everybody lived happily ever, but at least it’s a step in the right direction 😊


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.


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.



Fool of a Goose!

“Another one of life’s disappointments”, sighs the Silly Goose.

The goose forlornly sits under a tree, with a handful of peanuts and a piece of cardboard saying “Down on my luck”.

“What have you done this time?”

“It all started when I was trapped in some contraption”. started the Silly Goose. “With a number of sliding bars, hot lava, cold water, a big pile of gold and a big smiling cheetah.”

Uh oh, I think to myself. This can’t be good.

“I can’t remember the name of the game. Perhaps it was ‘War Horse’ or something like that.”

“What happened?”

“My friend, the monkey, pulls a few sliding bars at random. I plead with him to slow down and think, but to no avail. The monkey is about to pull the last handle but soon realises the error of his ways.

I have a feeling someone or something is watching us, but I am too engrossed in the Goose’s story to care.

“Fortunately, I was able to escape … by waking up in a cold sweat.”

From the Goose’s body language, I can tell this isn’t the end of the story.

“The next day, I decided to have some fun with the local Dupe Spider Solitaire club, run by the same Cheetah.”


“It’s really convenient,” continues the Silly Goose. “Everyone is real friendly. Free nibbles and drinks. Best of all you don’t have to manually shuffle the cards. The cheetah gives you preset hands. He arranges which opponents you play. You pay 250 peanuts to enter, and he gives you a bonus 250 peanuts, so you effectively start with 500. Lovely chap the cheetah. He organises everything for you.”


The Silly Goose then mumbles something about the easy-going Cheetah having an engaging personality, but by this stage I wasn’t really paying attention. I’m not even sure if the goose is aware of the literal meaning of “dupe” in Dupe Spider Solitaire.

“It all started well enough. I started with p500 . It costs p25 to play a game. Score more points than your opponent and you win the peanuts. I won the first ten hands … “

(btw, p is the official symbol for peanuts, just like how we use $ for dollars).

“That puts you on p750 if my math is cor-”

“Um … I never made it past p700.”

“How is that so? I have a math Ph. D. There is no way I could muck up an elementary math problem.”

“Math Ph. D.’s have been known to make elementary mistakes,” retorts the Silly Goose. “It happens to the best of us”.

“Yes I know that,” I reply tersely “But look! p25 times 10. That means we add a zero to make p250 …”

And so we argue and argue and argue and argue and argue. It takes me a good few minutes to realise there is a thing called “rake”. In a standard casino the rake may be anywhere between 2.5% to 10% for a poker session. So if a player wins a pot of say p100 and the rake is 5%, then he only really wins p95 instead of p100. The Cheetah actually has a rake of a whopping 16%, and this means the Silly Goose’s math was correct. Okay, I will give the Silly Goose credit for getting something right for a change.

“When did you realise something was wrong?” I ask.

“I only realised my goose was cooked after losing four hands in a row against Ninja Monkey. By that stage I only had five peanuts left.”


I look at the handful of peanuts sitting in front of the Silly Goose. She indeed has only five peanuts left.

“Fool of a Goose!”, I mutter to myself in a not-so-authentic Gandalf impersonation.

“I’m sorry,” murmurs the Silly Goose.

“It’s okay,” I say. “I know you can play a decent game of Spider Solitaire, compared to most of my other students. But from now on, just stay at the local Dup-LICATE Spider Solitaire Club.” Make sure the D-word has nine letters, not four. Only play with people you know. And don’t ever play with big money. And if it’s organised by an animal that sounds like C-H-E-A-T-E-R then you should run, run, run!”

Oops, I just realised the Cheetah is the fastest animal in the animal kingdom. At least the Goose didn’t pick up on my faux pas as she nods sheepishly (even though she is a goose, not a sheep).

“What is that?” I ask, pointing at the Silly Goose’s new toy. I hadn’t noticed it before, since it was hiding under the down-on-my-luck piece of cardboard . No harm changing the subject, I guess.

“That’s a special Spider Cube. At least I won the lucky door prize at the Dupe Spider Solitaire club.”

“Lucky door prize?”

“Yes,” replies the Silly Goose. “For every ten hands you play you get an extra ticket, hence more chances of winning. Oh, I’ve heard you can wield a mean Rubik’s Cube – I’m hopeless at these things”.


Typical Cube Scheme, I think to myself. At least it wasn’t a Rubik’s Pyramid. But I have to admit the pictures of little spiders on each sticker are so cute  😊

I am curious as to what possessed the Silly Goose to live up to her name. My curiosity doesn’t long. Thanks to my peripheral vision I quickly notice the Bad Idea Bears hiding behind a tree and snickering to themselves.