Minnie Mouse, the smallest member of the Duplicate Spider Solitaire club, wears second-hand bifocals that make her mix up same-colour suits, much to the chagrin of other players. Cy had been her chief victim.
“Now what?” I sighed. If I had a happy-face disc for every bad beat story someone told me then I swear I would never lose a game of Connect Four.
“The play had started well at my table. I had already turned over eight cards and I only needed one more good card to get an empty column.”
I nodded. Judging from the game state below, Cy hasn’t done anything majorly wrong yet.
“Alas, the next card in column 8 was the other Ten of Diamonds,” continued Cy. “Column 1 didn’t yield anything useful either, a Four of Spades underneath the Ace of Clubs.”
In this hand there is a stipulation saying no cards to be dealt from the stock. I presume this is to help students improve by focusing on one concept at a time.
“Game over, +100.” I said. “How did Minnie go?”
“Minnie started the same way, but then she moved the Ten of HEARTS in column nine onto column 2.”
“Thinking it was the Ten of Diamonds,” I said.
“Minnie turned over a Nine of Clubs in column 9 and that was all she wrote, if you pardon the terrible cliché. It wasn’t even close.”
“I’m okay with terrible clichés,” I replied. “I use them time and time again.”
“Minnie’s play was wrong on two counts,” insisted Cy. “Not only did she misread the suits, but her goal was to expose as many cards as possible, not build sequences in suit.”
Actually Minnie’s play was correct. There are three guaranteed turnovers in columns 1,8,9 even if the worst possible cards turned up – provided the cards were played in proper order. Cy’s impulsive play meant that he was no longer guaranteed to turnover a card in column 9. If he shifts the Js-0h in column 9 first then the turnover in column 8 will not run away.
One might even make an argument of shifting the Ace in column 1 first. This “kills” column 5, but column 7 contains a suited 2-A. Therefore, we will only regret this move if we turned over two Threes (whereas we only need one King in order to regret shifting the Js-0h). The important point is Minnie’s play was better than Cy’s.
“Has anybody managed to expose all the cards for a single hand yet?” coos the Smart 65,83,83.
“Don’t ask,” replies the Dumb Bunny.
“Shush!” I say. “There are still animals playing.”
Duplicate Spider Solitaire is a fun variant, particularly for lousy players who never get close to winning a game at the highest difficulty level. Certain stipulations are also provided such as “score 10 points per turnover” or “do not deal any cards from the stock.” Therefore, if you get into a complete mess you can always hope your measly score is enough to beat the others players who must play the same lousy hands. You gain match points whenever you perform better than anyone else.
Unfortunately I am not aware of any existing Duplicate Spider Solitaire clubs anywhere in the real world. Perhaps some of my Bridge friends would know of one (or are willing to start one!). If so, then please leave a comment below 😊
I could use a bit of sleep. It all started last night after the Bad Idea Bears suggested a long poker session with the usual suspects. After some thought I agreed, but only because they actually behaved well during the last week. One thing led to another and … anyways, you get the gist. Hopefully today won’t be too much of a disaster.
“Here is an interesting position,” I say. “What would be your play here?”
I pull out my i-Phone and show the position to my students. It’s a pity we don’t have whiteboards and chalk in the jungle.
The monkey takes out two decks of playing cards. After three minutes he is the first to offer an answer.
“I say it doesn’t matter what move we play. I’ve played 100 games thanks to my usual extremely-fast-metabolism and I estimate the winning chances are exactly zero”.
“I believe we call this a self-fulfilling prophecy,” I reply. “Perhaps, if we thought that victory was actually possible and adjust our strategy accordingly then our chances would increase.”
Unfortunately most of the students are sympathising with the Monkey. After all, nobody in the animal kingdom has managed to beat the game at the four-suit level.
“Anyone else have a better opinion? How about you Mr Snail?”
“I need some more thinking time,” says the Wise Snail.
Hmmm … this lesson ain’t off to a great start. Not surprisingly, the Wise Snail is the slowest player in the Animal Kingdom. At least I will give him credit for being a better player than the Monkey since the Snail hasn’t lost 50 quintillion games in a row.
“The position isn’t that complicated,” I reply. “There are only 11 cards in play and 5 legal moves.”
“Yes, but with 11 cards in play we have 93 cards unseen.”
“Well, we know that in Freecell the chances of winning is exactly 100% or 0% assuming perfect play,” replies the Snail. “This is because all cards are exposed. In Spider, if we ever reach a game state with only 2 hidden cards then the winning chances must be 0%, 50% or 100%. With 3 hidden cards, the winning chances will be some number divided by three …”
“Three factorial is six,” says the Smart 65,83,83. “Some number divided by six.”
“Whatever,” continues the Wise Snail. “Similarly one can compute the exact winning chances for any number of face-down cards”.
“I see where you’re coming from,” I reply. “Unfortunately with 93 face down cards, there are 1.156 * 10^144 possible permutations if we ignore cards with identical suit and rank. We only have half an hour remaining in this lesson.”
The Wise Snail pulls a frowny face.
“I wanna flip a coin, since there are no in-suit builds,” offers the elephant. “Unfortunately there are 5 legal moves and we don’t have a coin with five sides.”
Okay, +1 for humour but not exactly the answer I was after.
“Four of Hearts onto the Five,” says Bad Idea Bear #1.
“Only three more good cards and we get an empty column!” adds Bad Idea Bear #2.
“We can eliminate some moves,” offers the Jaguar. “Moving either Eight onto the Nine is equivalent, so pretend there is only one Eight. We shouldn’t move a Four onto the Five since that means we only have two guaranteed turnovers, not three. Therefore it’s a choice between 9-8 or 6-5.”
“That’s good,” I say. “Finally we’re getting somewhere.”
“So we don’t need a 5-sided coin after all,” says the Monkey.
At least the monkey is paying attention this time and knows a thing or two about humour. The Smart 65,83,83 gives the Monkey an oh-so-polite wink.
The eagle remains silent. He knows the answer, but wants to give the other students a chance to contribute.
The lion raises his front paw. It’s always a pleasure to witness the insights of the lion, one of my better students.
“If we move 9-8,” roars the lion, “then assuming we turn over a bad card we have to choose 6-5 next. But if we start with 6-5 then we can choose between 5-4 or 9-8 later. 6-5 it is.”
This is a good insight, but not the answer I intended.
“Every player knows that building in-suit is more desirable than off-suit,” I say. “When we build off-suit then (at least in the first few moves) most of the time we are effectively losing an out, assuming our goal is to expose as many cards as possible.”
“For instance, if we move a Ten onto a Jack then a Queen is no longer a good card. There are a number of exceptions: for instance, moving a Queen onto a King does not lose an out for obvious reasons and if we have e.g. a Two and a pair of Threes then again we avoid losing an out. Once all the easy moves are exhausted we have to choose carefully.”
I briefly glance at my notes, just checking I have the right game state.
“We have three guaranteed turnovers with 9-8 and 6-5-4. For simplicity let us ignore the fact we have duplicate Fours and Eights. Clearly we won’t move the Four onto the Five as that will bring us down to two guaranteed turnovers. Well done to the Jaguar for spotting this. Hence the choice is between 9-8 and 6-5.”
“Let us pretend that we have to make two moves before exposing any face-down cards. For instance, we might move 9-8, then 6-5 then turn over the cards underneath the Five and Eight. Or we might move 6-5, then 5-4 then turn over the cards underneath the Four and Five.”
Uh oh. The Sloth is snoring. I think nothing of it: after all he’s not the sharpest tool in the jungle out there if you excuse the terrible cliché and/or mixed metaphor. In fact I don’t recall the last time he didn’t fall asleep.
“Observe that in the first case we have lost two outs since Tens and Sevens are not as good as before (even though they are still good). But in the second case we only lose one out (the Seven). Therefore the correct move is 6-5. Well done Lion!”
“Roughly speaking, making two moves before exposing face-down cards corresponds to a worst-case scenario when a useless card comes up (e.g. an Ace). If a decent card came up then we might reconsider. For instance, after moving 6-5 we might expose a Two and then we must choose between 5-4, 2-A or 9-8.”
The Eagle is desperately trying to suppress a chuckle. Something is out of character: my best student doesn’t exactly have a reputation for lame puns, knock-knock jokes or pranks.
“As a general rule,” I continue, “building a long off-suit sequence of cards means you generally have more safe moves before you start losing outs. For instance if you had 3-4-5-6-7 within the first ten cards then playing 7-6 loses an out, but then you can build 6-5-4-3 within the next three moves without losing any extra outs. Of course the fickle Spider gods might eventually give you an Eight and an empty column, and you find you are still unable to move the 7-6-5-4-3 onto the Eight –”
I’ve just realised that EVERYBODY HAS FALLEN ASLEEP EXCEPT THE EAGLE. Maybe quitting my day job and teaching various animals how to play well at Spider Solitaire ain’t what’s it cracked up to be. Or perhaps my teaching skills need a bit of work. Or perhaps I should learn to say “NO” to the Bad Idea Bears whenever I have to teach the following day.
“Marking assignments, the bane of every teacher,” growls Ms. Spider, as she angrily scrawls the word “DREADFUL” on a sheet of paper. “This goose just divided by zero.”
I’ve always enjoyed math, but I am all too aware that it represents a bugaboo for many ordinary folk. Not everybody can have higher than average IQ and not everybody can play piano and solve Rubik’s Cube at the same time. I agree we have to Make Math Great Again.
“I s’pose I could improve my presentations skills or learn Statistics 101,” admits Ms. Spider.
“I confess I never studied stats at uni,” I respond. “I had to pick it up all by myself.”
“Learning stats 101 sounds too much like work. Surely there must be a better way.”
“You could make the exams and homework easier,” I suggest.
“We can’t make it too easy,” responds Ms. Spider. “I’m sure the good students wouldn’t mind an extra challenge or two,”
I steal a glance at the goose’s assignment. Yes the goose is below average, but one of the assignment questions are badly worded. Another question has kilometres as a typo for metres, and I have to suppress a chuckle. I can see why some of Ms. Spider’s students call her the WWMT.
“Actually,” says Ms. Spider, “I was toying with a more radical solution”
“We could give different exams to different students”
“What a revolutionary idea!” I exclaim. “Nobody has ever thought of this before!”
“From each according to his abilities … “
“From each according to his needs,” we chant in unison.
I am impressed: this Spider is clearly well-educated, not just in mathematics. She knows her clichés and sayings.
“Does that mean,” I ask, “if an awesome student correctly answers 40 assignment questions in a row then he will get a very difficult exam?”
“Hang on, what if an awesome student deliberately flunks the assignments …”
“Well … we could give the exam less weight than assignments,” the Spider responds somewhat nervously. “Then there is no advantage to tanking the assignments.”
“For this to work,” continues Ms. Spider, “we have to come up with some way of measuring the difficulty of certain questions.”
I mull over this for a while. We all know that students can be graded according to some chosen system. For instance, a math student can be Outstanding, Exceeds Expectations, Acceptable, Poor, Dreadful or Troll. But how can we grade certain questions?
“Which of these problems is harder?” asks Ms. Spider.
“I think both are equally easy. After all, I participated in the International Mathematical Olympiad many years ago.”
Somehow, I think that was not the answer Ms. Spider expected.
Behind us, a monkey, eagle, mouse, elephant, lion and jackal are enjoying some Texas Holdem. As usual, the monkey has squandered away all his chips early, and the Eagle is schooling the rest of the field, having accumulated more than half the chips in play. The Spider eyes them warily: clearly they should not be privy to our discussion.
“You see,” says Ms. Spider. “Sometimes I find it hard to judge the difficulty of a single question. For instance, I expect problem X to be easier than Y, but for some reason the reverse holds when I mark the assignments.”
I mull over Ms Spider’s words. I am not really in a position to judge, given I have never marked any student assignments.
“I have an idea,” says Ms. Spider. “Let’s draw a table”
“For simplicity,” says Ms. Spider. “Let’s assume each question is either marked correct or not correct, hence there are no partial marks. I use blank instead of 0 for ease of reading. Sam is an awesome student since she answered most questions correctly. Owen is a Stupid student because he only scored 2 out of 9. Each individual is represented by a single row.”
“But there is no reason we can’t do the same with columns if you pardon the double negative. For instance, only six people solved problem 8 but nine solved problem 9. Therefore problem 9 is harder than problem 8 …”
“So even if you don’t understand the questions themselves you can still say things like Debbie is better than Anna”
“Exactly,” replies Ms. Spider.
“With 18 students and 9 problems, you don’t have a lot of data”
It’s a stupid observation, I know – but I am only trying to buy time as I try to digest her ideas.
“Well, the same logic applies if we had 1800 students and 900 problems.”
“I think I understand,” I say. “It’s like some kind of Mechanical Turk. Previous students have tried these questions (and of course you don’t have to pay them to do these exams!), so you can work out which questions are easy or hard.”
“Wasn’t the Mechanical Turk some kind of fake chess-playing machine by Wolfgang von Kempelen? What a disgraceful idea! I would never try to cheat chess players like that”.
Okay, didn’t see that one coming. We need to agree on a definition of Mechanical Turk.
“Do you think your students will eventually find out their exam papers are different?”
“That shouldn’t be an issue,” says Ms. Spider, as she squirms in her seat. “If a poor student finds out, he has no reason to complain. If a good student finds out then deep down in his heart he already knows he is better than the poor student, so the exam result doesn’t matter.”
Somehow I think her logic is very, very, unsatisfactory. But I do know that many of the greatest insights precisely come from those who are willing to suggest ideas that sound utterly outrageous. For instance Rivest, Shamir and Adleman are your average computer scientists, but with a bit of luck they might one day become famous, known to every student of cryptography. So I should cut her some slack.
In fact, I am more than looking forward to the results of her revolutionary teaching methods. After all, I’m not the teacher and I don’t set the exams. I was especially careful not to suggest any drastic ideas of my own. If the radioactive 83,72,73,84 hits the fan and grows to fill the size of the entire house then I am more than happy to watch, knowing my 65,82,83,69 is fully covered.
Hooray! I have finally quit my day job and found something I really enjoy: teaching students how to play 4-suit Spider Solitaire well. According to legend, nobody in the Animal Kingdom has managed to beat the game at the highest difficulty level. Even the Ninja Monkey with an amazingly fast metabolism couldn’t achieve it despite 50 quintillion tries (and counting).
In my first class I have 6 students: a mouse, lion, Jackal, Elephant, Eagle, and last but not least, the monkey.
I have already gone over the basics: empty columns are good, suited connectors are good, but aces and kings are usually not your friends. I notice the monkey is taking copious notes. He is an ideal teacher’s pet, if you excuse the lousy pun.
“Take a look at this position,” I say. “Do you think we should win with correct play?”
“I think so,” replies the mouse. “I would bet 3 dollars.”
“That means you think it’s not possible,” quips the lion.
“What do you mean?”
“Your bet is too small,” replies the lion. “If you thought this is a win, you would be betting $30, not $3.”
“I would raise it to $60 at least,” offers the Jackal.
“Yeah sure,” says the elephant.
“We do have 4 suits removed and two empty columns. Sixty dollars says we win this.”
“I wouldn’t bluff if I were you,” replies the Elephant. “Look at that pile of 83,72,73,84 on Column 4.”
“Come on guys,” says the eagle. “I think we need to analyse this seriously. This game is about math, not people or animals.
I turn my attention to the monkey, who as so far been silent.
“What’s your opinion?” I say, putting him on the spot.
The monkey looks embarrassed.
“This would be easier if it were one-suit.”
Everyone laughs. The monkey looks like he wants to kill himself.
“But that’s way too easy!” exclaims the mouse. “Even I would go all-in.”
“The monkey raises a good point,” I say.
Stunned silence. All the other animals look at each other, unable to believe what they heard.
“Okay,” I continue. “Let’s change the rules: the game is one-suit but we cannot remove suits to the foundations until all cards are exposed.”
“But that’s cheating!” shout all the animals in unison (except the monkey). “You’ve already moved four suits to the foundations”.
Don’t ask me how the animals manage to speak in perfect unison without proper rehearsal. I guess everyone has their own unique talents.
“For purposes of this exercise, let’s assume I changed the rules mid-game and you have to Deal With It.”
The animals discuss this for a few minutes.
“K to 3 in column Five,” says the mouse. “9 into column Seven. 10 to A onto the Jack in -”
“Not-so-fast,” replies the eagle-eyed eagle. “There are two aces in column 4.”
“But we can create another empty column,” says the Jackal. “4-3 in column Eight onto 8-7-6-5 in column Nine.”
“Once we reach the 4 of Clubs the rest should be easy. Column 2 becomes empty and 4 of Clubs into Column 2 etc.”
“And it doesn’t matter what order the hidden cards are in.”
I am pleased that all my students are participating in the discussion.
“So we can win at 1-suit,” I say. “Note that if we couldn’t win with 1-suit we can deduce it probably won’t be possible at 4-suits (unless we can quickly complete a suit).”
All the animals nod in agreement.
“Now back to the original problem,” I say. “How to continue at the Four-Suit level?”
The animals quickly discover the right plan. Once the King of spades lands in an empty column we can recover an empty column by moving the 8-7-6-5 onto the Nine of spades. We then have to shift the Nine of spades and Ace of clubs into two empty columns. Then we have to hope we have enough empty columns to finally shift the 10 of Hearts and reach the Four of clubs. Of course, all this is easier said than done, if you excuse the terrible cliché.
The monkey brings out a set of cards and arranges them into the diagram position. He tries and tries but to no avail. Despite his repeated failures the other animals are amazed at the monkey’s dexterity and eidetic memory as he quickly reorders the cards into the starting position without error.
“Let me have a try,” says the eagle.
The eagle quickly discovers a truly remarkable solution to this problem, which this blog is unfortunately too small to contain. All the animals applaud loudly as he smacks the last suit onto the foundations with a satisfying thud.
“How the 70,85,67,75 did you do that?” asks the Monkey.
Uh oh. I’m beginning to have doubts about the quality of the monkey’s copious notes. His strategy is still as lousy as before. He is not really a model student after all.
“Let me have a look at your notes,” I say.
I confiscate the monkey’s book and riffle through his “oodles of doodles”, none of which have any artistic merit. I am about to 83,80,65,78,75 the monkey in front of everybody and rip his doodles to shreds. But at the last minute I suddenly remember that I owe the monkey a tremendous debt. Without him I wouldn’t have been able to publish a paper in the International Journal of Arachnids, Primates and Other Predatory Species. Then I stumble upon a very strange picture:
So the monkey does have occasional flashes of brilliance when doodling after all. Okay, the happy star isn’t exactly centred properly, but it’s not a bad job for someone with only pencil and paper. I doubt that any human could produce art like that. I return the book to the monkey and bow before him.
Seeing that the monkey got off without even a warning, I guess it’s only fair that the last word belongs to Shakespeare: All’s Well That Ends Well.
I like my new job. Okay, the pay isn’t great and the diet leave much to be desired, but at least I’m my own boss and I get to set my own hours. All the animals are easy going and real friendly, and we can cuss and swear with impunity. And best of all, nobody smokes around here (because smoking is bad for you). 70,85,67,75 89,69,65,72!
Here we are in the dreaded Blue Screen Of Death. It is reputed to be the hardest version of the game, and even the Spider GM loses over half the time. And it’s got an ominous picture of a Spider web in the background. It ain’t called the BSOD for nothing if you excuse the terrible cliché. And we’re not aiming just to escape: we’re here to destroy the thing.
I am in the ninth column. Scanning the tableau I find only
one other card of adjacent rank: the Jack of Spades. Perhaps he knows something
I don’t (not likely since my rank is higher but you never know). I know from
sad experience that the occasional victory is not enough to destroy the BSOD.
“Well, we do have The Prophecy,” says the Jack of Spades.
“A Prophecy?!?!?” I ask. “I didn’t know we had one. How do
“I had a strange dream. After we exited the White Screen in
Part Two of this trilogy I heard voices.”
“What did they say?” I ask impatiently.
It is clear all the other cards are paying full attention.
Otherwise the Four of Hearts would have already moved onto the Five of the same
suit by now.
“Now if you are to break the Spider’s curse,” the
Jack of Spades intones solemnly, “the value must be five percent or worse.”
“But – but that sounds lame.”
“True. But it’s the only prophecy we’ve got,” replies the Jack. “Or more precisely, it was the only thing I heard that vaguely sounds like some kind of prophecy.”
I repeat the prophecy in my head several times, trying to
make sense of it but to no avail.
“Hang on,” I say. “This prophecy is written in the iambic
“You’re right,” says the Jack of Spades. “I wonder if that
has any signif-“
“But the Ninja Monkey has reproduced the entire works of
Shakespeare, so surely he knows a thing or three about iambic pentameter.”
The monkey enters, as if on cue.
“Good point,” says the Jack of Spades. “Maybe he can help us decipher Monkey the want
prophecy to play! Monkey want to play! Play play play play play!”.
“Or maybe not,” I reply.
Ninja Monkey has taken maximum weirdification to the next level. This time he has brought along a friend named Ninja Mouse. Ninja Mouse controls a small arrow on the screen using his telekinetic powers, while the monkey caresses the mouse’s fur (presumably to keep him warm in this miserable cold weather). Spider GM clicks his fingers and the fun immediately begins.
And I must say, the monkey and mouse are
75,73,67,75,75,78,71 65,82,83,69. They have all of us sorted into the
foundations in less than two seconds. They start another hand and again we’re
sitting pretty in the foundations in less than two seconds.
“It’s all too good to be true.”
Now it’s my turn to hear voices – but to be fair, I should
probably pay more attention to whatever’s inside the back of my head. Then I
notice with horror the Monkey and Mouse aren’t playing properly. We’re neatly
arranged in complete runs from Ace to King, but in different suits. They are
pretending the game is one-suited. Clearly the Spider GM has given them the
wrong instructions. And as luck would have it, the Spider GM is nowhere to be
“Ah, there it is, the 70,85,67,75,69,78,73,78,71.”
Hang on, I got distracted. I was supposed to be figuring out
something. What was it again? Oh that’s right: the value must be five percent
or worse. But what is this value? Perhaps every time we win a game (preferably
Four-Suited sans 85,78,68,79) the Spider’s value decreases. The value could be
a company’s market capitalisation. If that ever goes below 5 percent of GDP then
we’re quids in … okay I’m clutching at straws if you pardon the cliché, but
it’s hard to find a better explanation when the arrow is moving us from one
column to the other at a million miles an hour (another terrible cliché I
know). What I do know is that Monkey’s strategy is not improving, even with the
Mouse’s help. If anything, it seems to be getting worse.
Then I pick up on something unusual. I started 100 consecutive games in exactly the same position: top of column Four after the third round of cards is dealt from the stock. It occurs to me that Spider GM has done this on purpose, and has given the monkey some special instructions. I’m not exactly in the mood to try to work out what the Grand Master is aiming for. At least the Monkey and Mouse play with their usual dexterity and I won’t have to wait too long until this saga is over. They complete 4000 games in a mere 2 hours.
Uh oh. This can’t be good.
“What’s wrong?” I ask.
“Monkey is sad. Monkey is losing”.
Oh well, at least Monkey has fixed his bad habit of
talking too fast and interrupting everybody else before they finish their
“Please don’t cry,” I say. “I want to help you – I
can teach you how to play well at Four-Suit solitaire. I beg you, please slow
down and only move a card when I tell you to.”
Spider GM kneels down and gives him a hug. Awwww …
Unfortunately it looks like I won’t be teaching the Monkey how to kick
65,82,83,69 at Four Suit Spider any time soon. Oh well, so much for becoming
the hero and saving the world.
“What happened?” I ask the Grand Master.
“Something is wrong with the Blue Screen of
Death,” he replies. “The longer you play with it … the more
difficult it is to win.”
I sense the Grand Master is also distraught, as he
struggles to choose his words carefully.
“What do you mean?” I ask.
“Let me explain. Ninja Monkey played 40 hands and pretended the game was 1-suit, not 4-suit. He repeated each hand 100 times-“
“I gathered that,” I say. “I wasn’t born
three days before yesterday.”
“So on each hand,” continues Spider GM,
“we can estimate the chances of winning to be such-and-such percent.”
I nod in agreement.
“Would you care to pick two numbers between 1 and
40?” asks the GM.
“3 and 15”.
“Monkey won Game Three 88% of the time and Game Fifteen 45% of the time. That’s an inversion because Game Three is harder than game Fifteen. Pick again.”
“Okay, 5 and 32”
“That’s another inversion. Monkey won game Five 47% of the time and game Thirty-Two 11% of the time.”
“Hang on,” I say. “If the games are sorted
by increasing winning percentage then there would be no inversions.”
“Correct, and if they are sorted in reverse order then
there would be 780 inversions”.
I do a quick calculation: 40 * 39 / 2 = 780.
“Also correct,” I reply. “On average there
should be 390 inversions.”
“Ninja Monkey says he got 468 inversions. That’s a lot bigger than 390”
Maybe that was bad luck,” I reply. “Besides, how do
we know that a difference of 78 is reasonable or not?”
“But this is where statistics comes in. We can show
that if the game were not biased then 468 or more inversions in 40 hands would
occur less than once per 20 trials.”
I’m starting to get lost. At least the GM is talking English and is not saying something stupid like “Import Numb Pie As N. P.”
“Can you explain in more detail?” I ask.
Spider GM clicks his fingers. Ninja Monkey gets a large sheet of paper and cuts out 40 rectangles, numbered from 1 to 40. He then shuffles and deals them in a row. He counts 370 inversions and writes the number 370 on another sheet of paper. He then shuffles again and deals a new permutation of numbers 1 to 40. This time he gets 423 inversions, higher than the expected value of 390. He writes the number 423 next to 370. He rinses and repeats for one hundred thousand trials. Then he draws a pretty graph. Needless to say, all this in less than 25 seconds after Spider GM clicked his fingers. Only for 3558 trials is the number of inversions 468 or greater.
“You see,” continues Spider GM, “the null hypothesis
says each hand occurs with equal probability. Assuming this is true, the
chances of getting 468 or more inversions is 0.036. In statistical language we
call 0.036 the p-value, which happens to be less than 0.05. Therefore 468 or
more inversions is significant at the alpha equals 0.05 level.”
“What does that mean in layman’s terms?” I ask.
“It means we have evidence that The Game Is
Rigged,” replies the Spider GM, adding a triumphant emphasis on the last
“Hang on, what’s so special about 0.05? Why not 0.01
or some other number?”
Spider GM stands up and points to the exit. As Monkey and Mouse immediately scurry away stage left, the Grand Master clenches his fist and glares at the Blue Screen Of Death. I have barely enough time to convert 0.05 into a percentage and register that the prophecy has just been fulfilled.
Spider GM is a tower of strength as he slams his right fist
into the computer screen.
He is a demigod who can do no wrong, and who gives a
flying 70,85,67,75 if his right hand is bleeding profusely? Everything turns
into a blur and I feel like we are being time-warped to somewhere new (why does
this happen in every part of the trilogy?). But at least the curse is broken,
so hopefully this can only be for the better.
Fast backward to 1965. No Limit Texas Holdem is the hottest game in the animal jungle, and personal computers and mobile devices haven’t been invented yet. A group of monkeys cheerfully shove large stacks of chips across the table without apparent rhyme, iambic pentameter, or reason. I guess I can try to reverse engineer the rules of Texas Holdem as the dealer turns over each card, but after listening to the Grand Master explaining Statistics 101 I am mentally exhausted. I surrender to their unbridled joy and delightful unconcern as a chimpanzee bangs away at the piano. The music sounds absolutely atrocious but nobody cares when everybody has a jolly good time. The Spider GM has no trouble maintaining law and order during poker nights. Nobody throws a tantrum after a bad beat and all the monkeys handle the cards and chips with the utmost care. Everybody lives happily ever after – except the guy(s) who designed the Blue Screen Of Death.
Yes, this really is a true story. The monkey correctly reproducing
all of Shakespeare’s works, the mouse’s telekinetic powers and cards moving by
themselves and speaking perfect English are all true. Even the part where I
smash the computer screen with my right fist is true. And so is all the math
and statistics. Okay, so I lied about time travelling back to 1965 but
everything else is kosher.
I will however admit to never winning anything in a short
story competition in my entire life. Not even an Honorable Mention. So if
anyone can give me tips on improving my writing then please leave a comment or
Part 2 of my Spider Solitaire story. They say that having said ‘A’, one must say ‘B’ (and perhaps ‘C’) so here goes:
<sarcasm> Great </sarcasm>
I am no longer a rectangle-shaped card. I have been reduced to a black letter Q on a White background. I live in a bland world of letters and numbers. This has nothing to do with a game show based on Countdown. I miss the Green Screen already. I knew I shouldn’t have swallowed the blue and orange pills at the same time. What was I thinking?
“I told you so”.
I wish that stupid voice at the back of my head would Just.
Without warning, a cute monkey suddenly appears out of
Enter Ninja Monkey
“Monkey is happy!”
“Why are you-”
“Monkey write the complete works of Shakespeare!”
Ninja Monkey reveals a large wad of papers. I glance at the contents. I immediately recognise a passage from “Twelfth Night”. All the words are correct. The punctuation is perfect and words are all formatted nicely. Now that is impressive.
“How long did it take you to complete all works of Monkey Shakes
is speare? diligent! Monkey is hard working! When monkey don’t succeed, monkey
try try again!”
“Which part of how long did it take you to complete Ooh! all
Ooh! works Monkey of wants Shakespeare to don’t win you at understand? Four
Suit Spider Solitaire!
It’s hard to communicate effectively when the monkey is jumping up and down and opens his mouth before I have a chance to complete my sentence. Not to mention Monkey failed to answer my question and wants to change the subject. At least he mentioned Four Suit Spider Solitaire, one of few things I am good at. With a bit of luck, I might be able to teach him a thing or two. I wish the monkey would stop simulating fart noises with his armpits though.
“You see,” continues Ninja Monkey. “Animal kingdom says it
can’t be done! Nobody has managed to win with four suits! Monkey want to prove
we can do it”.
Gathering some courage, I ask the monkey how many times he
played Spider Solitaire.
“Fifty quintillion games!”
“But – but that’s more than the number of But permutations
Monkey on never Rubik’s gives cube up! Monkey is diligent! Monkey fail! But
Monkey try try again”.
I do a double-take. I managed to beat Four-Suit Spider Solitaire on my first attempt. But the monkey has played more games than permutations on a Rubik’s Cube and hasn’t won a single time. I feel the urge to exercise my free will and punch the little 70,85,67,75,69,70 in the face. But I can’t escape the voice inside my head that squeals “he’s so adorable”.
Hang on: I’ve just noticed I no longer have a suit. I am not
the Queen of HEARTS. I’m just a queen. Why didn’t I pick that up earlier? I
“Waitaminute” I say.
“Wait a minute what?”
At least we’re not talking simultaneously anymore. I’ve
figured my best chance at civil communication is talking really fast and pretending
every sentence is a three-syllable word.
“Grand Master wants monkey to play one-suit! Monkey always
obey the Grand Master”
Enter Spider GM.
Let me get this straight: I’m in a sans-free-will virtual
reality created by the Ninja Monkey. Meanwhile the Ninja Monkey is in his own
sans-free-will virtual reality created by the Spider Grand Master. Somehow this state of affairs is less than
First things first: let me try to work out why Spider GM wants
his pet monkey to play games at the 1-suit level. My best guess is that playing
a simpler version of the game will give Ninja Monkey some valuable insights for
strategies required to beat the game at the highest difficulty level.
“Import Numb Pie As N. P.” intones the Grand Master.
Monkey nods, eagerly waiting further instruction.
“For Foo In Range One Thousand, Game State Initialise
I don’t recall foo ever being in the English language. Even
if it was, I wouldn’t understand what Spider GM is saying anyway.
Spider GM is a human being. His voice is firm but polite. I
have no idea what the incantation means, but at least there is no animosity
between the two. I have to remind myself that this simulated reality inside a
simulated reality could have been worse.
After what seems an eternity SpiderGM clicks his Right-hand fingers
“Eek! Line Twenty-nine Syntax Error!” squeals Ninja Monkey.
“Oh for 70,85,67,75,83 sake!” says Spider GM. “Let’s try that again.”
“For Foo In Range One Thousand SEMICOLON, Game State …”
Yawn. Last time we were in the Green Screen and I thought my
fellow friends are weird. I have since revised my opinion.
Finally after many syntax errors, incessant cussing,
unsuccessful finger clicking, and immense frustration Spider GM has everything
working. He clicks his fingers one last time the monkey gets to work.
Exit Spider GM
Spider Monkey moves the Three in column 2 onto the Four in
Column 10. He turns over a King. He then slides the Jack in column 3 to the
Queen in column 4 revealing an Eight. Everything is a blur. I don’t even have
time to verify the monkey is making legal moves. After what appears to be
juggling 104 cards without a single mistake, Ninja Monkey has sorted all the
letters and numbers into eight complete sequences from K to A. All this in less
than two seconds. But Ninja Monkey ain’t done yet. He shuffles the cards and
deals another hand. Again he has all of us neatly arranged in eight sequences.
At this rate he will have completed 100 games inside three minutes. They don’t
call him the Ninja Monkey for nothing. Unfortunately the monkey doesn’t win
The something strange happens. In one game everything seems
to freeze. I soon register that Ninja Monkey is oscillating an Ace between two
adjacent columns. It turns out Ninja Monkey has only one legal move on the
tableau and he has already exhausted the cards in the stock. The poor thing is
stuck in an infinite loop but doesn’t realise it. After half a second Ninja
Monkey concedes the game and starts a new hand.
At least Ninja Monkey doesn’t throw a tantrum after losing,
something humans could learn from. None of the letters and numbers show any
signs of wear and tear. He is a fast player and has won more than half the
time. So I have to give NM credit for doing something right.
Finally after a thousand games all is said and done. I have
a chance to survey the game state of the final hand. Ninja Monkey has removed
two suits, but the tableau is a mess and the game is indeed unwinnable. But the
monkey is content with his efforts. I ask the monkey if he can rewind back a
few moves for some good ol’ post-mortem analysis and see where he went wrong.
But to no avail of course.
Enter Spider GM
“Monkey win sixty two percent! Sixty two percent!”
Ninja Monkey runs towards the Spider GM and gives high five.
Then he jumps into the air and gives Spider GM a high ten with both feet. His
hygiene is perhaps not the greatest but Spider GM doesn’t seem to care. One of
the number Fives jumps up and Ninja Monkey gives him a high five as well.
Unfortunately there is no such thing as a high queen. Spider GM gives him a
reward of 621 peanuts.
I always knew the one-suit level was ridiculously easy, but
I never expected that a player with very poor strategy could still win more
than half the time. Despite the monkey’s atrocious record of zero wins and
fifty quintillion losses at the four-suit level I still managed to learn
something from him. I’m not sure how that will make me a better player, but it
is a fun fact to know. Spider GM seems especially pleased with his experiment
also. Maybe there is hope for humankind, monkeykind, letterkind, numberkind and
all other kinds of kinds in this world after all, and it’s not all doom and
gloom (if you pardon the cliché) just because we live in a virtual reality
controlled by someone else.
Spider GM moves his hand towards the three icons on the upper
right corner of the White Screen and clicks his fingers. Everything disappears
into nothingness in less than half a nano-second, leaving me wondering where me
and my fellow Letters and Numbers will end up next time. At least I have a new
friend to root for. Here’s hoping Ninja Monkey can finally win at Four Suit
Spider Solitaire and do the animal kingdom proud!
Okay, so after three weeks it seems that most of my readers/followers have some experience in writing short stories but none of them have any experience in playing Spider Solitaire. Nobody has left a single comment so far. So maybe my next project should be to play a game of Spider to the best of my ability, then pretend my move sequence is the plot of a really lame story, told from the viewpoint of one of the cards in the tableau.
THE GREEN SCREEN
So here we are in the Green Screen (for lack of better
name). Our task is to somehow escape from this simulated reality and teleport
back into the real world as physical objects. Perhaps we have to follow a white
rabbit, enter a night club, meet a hot 67,72,73,67,75 named Trinity and take
things from there – which would be insanely cool. Or I could be completely
Ten of us have been chosen as the “Starting Hand”, whatever that means. I don’t know which ten they are, mainly because I am still asleep. I don’t even know my name because my memory has been erased. All I know is I am rectangle-shaped and my back is blue. I am in the Fourth Column, covered by one other rectangle-shaped thing. There are 54 of us, and we have to somehow escape.
Ever heard of The Maze Runner by James Dashner? Or the movie of the same name directed by Wes Ball? The protagonist, 16 year old Thomas, wakes up in some intricate maze along with several other boys. He has to work out his role in their society (as does everyone else), work out the rules of the maze as they go along, solve a number of puzzles … only to find out once they escape there are more challenges ahead (it’s a trilogy after all so what do you expect?). Okay, that’s probably not the greatest analogy but it’s the best I can come up with right now. At least I am not a Slopper and there are no toilets to clean every day.
Apparently my name is Queen Of Hearts. Goodie – at least I’m
a human. Most of my friends are numbers. 83,85,67,75,83 to be them. I’ve moved
onto the Diamond King. It’s not the same suit, but at least I have someone to
call a friend. I no longer feel alone. It also means I am further away from the
dreaded Queen of Spades. She’s always grumbling about too much demand for
something and not enough supply. Or the other way round. Whatever. I was never
any good with Economics at School. I would later learn it’s not just her –
everyone here often grumbles about cards of the same rank for some strange
reason. <sarcasm> That’s what friends are for right? </sarcasm>
These guys are weird.
Okay I get it. Cards arrange themselves in descending order.
At least that explains why the Kings and Jacks seem to treat me with respect.
All the other spot-cards don’t seem to care much about me. I watch as the other
cards gracefully dance around the tableau. Apparently they know the rules
better than I do.
Just for fun, I try to scamper across to the adjacent column, onto the Ace of Diamonds. No – the laws of physics don’t like that, and I am immediately whizzed back to my original position. Rules are rules.
What the 70,85,67,75 was that?!?!?!? Ten new cards just
popped out of nowhere! So that’s worse than I thought: if we don’t escape from
this contraption then ten new cards will periodically appear every 5 minutes or
so and eventually the whole place will get flooded – it’s probably not
something I’d wanna think about … and I’ve just been covered by the King of
Spades. I’ve heard plenty of bad stuff about them. They tend to appear at the
worst possible moments. They sit on your face and stay there forever – or at
least it feels like forever. I don’t mind the kings so much, but I much rather
have their 65,82,83,69 next to me instead of on my face. At least there are no
monsters in this world, unlike The Maze
Oh, and I’ve just noticed my twin sister has appeared in
column 1. It then occurs to me: there are TWO decks of playing cards. I was
expecting something like a single deck plus two jokers, and once the jokers
turn up then Good Things Will Happen. Jokers can move onto any card, and any
card can play onto a joker. But apparently they don’t exist in this Green
Screen. At least empty columns seem to be useful: any card can use them, not
just a king. That’s almost as good as a joker.
I scan the tableau. There are two-dozen cards yet to be
turned. They don’t know the laws of physics that govern the Green Screen. They
don’t even know their own name. The exposed cards are dancing around, apparently
making no effort to free them. Ten more cards will magically appear on the
tableau every 5 minutes or so. At this rate, they will never see the light of
day, if you pardon the cliché. I was one of the luckier ones, having started
near the top of a column. I was able to observe most of the proceedings so far.
At least I have some idea of what’s going on.
“Stop moving around aimlessly!” I yell.
“We’re not moving around aimlessly!” said the Five, Four,
Three, Two and Ace of Diamonds, all in unison.
“We need to come up with an overall grand plan.” I said “We
need to consider the state of the whole board, not just a single col-”
“We’ll sort ourselves into suits first” said the Nine,
Eight, Seven, Six, Five and Four of Spades also in unison. “Then we can take it
I watch as they gracefully leap from an empty column onto
the Ten of Hearts. It now occurs to me why the cards were “wasting time”
organising themselves into suits. In the early rounds, cards were able to move
only one at a time; maybe two or three if we were lucky. In mistaking the trees
for the forest, I succeeded in missing the details. I feel stupid.
Still, I think that there is some truth about “thinking
about the bigger picture”. I start to wonder, what happens if we get a complete
run from Ace to King, all in the same suit. I’m a bit rusty at Texas Holdem but
I believe that is called a straight flush. The Club suit is looking good.
YOWZA!!!! All the Clubs have escaped! A triumphant C major chord pierces the dreary silence and fills us all with hope. Three suits to go, this should be easy as … no wait a minute. I’m still covered by the Jack of Clubs. My twin sister is still sitting in column 1. I remind myself there are two decks in this game. And we are still covered by a King. The King of Spades can move into an empty column, but for some reason he seems reluctant to do so. I guess we just have to wait then.
Okay, I get it now. Two decks of cards make 104. We started
with 54. Every now and again, 10 new cards magically appear out of nowhere.
After 50 cards are added, we have the right number to complete two full decks. Without
two full decks, there is no way we can complete suits from Ace to King. So
those cards appearing out of thin air are a blessings in disguise, if you
pardon the cliché. I’ve finally figured this out. Who needs jokers when you’ve
got the smarts like me?
Of course if more than 104 cards appear in play then we are REALLY 83,67,62,69,87,69,68.
“Off with the hearts!” I yell.
Everyone looks at me in disbelief. This isn’t the right time
for a lousy pun.
“We have a complete suit from Ace to King”, I continue.
“King-Queen-Jack-Ten in the second column, Nine-Eight in the right …”
“I’m not sure if that will work” said the Three of Clubs.
“Even if it did work, it will cost three empty columns just to reach the 7 of
Hearts in column 9”.
“There’s no choice. We’re gonna use up at least two columns
to expose a card”, said the ace of spades.
“Even if it doesn’t work”, I say, “we still get to partially
tidy up that mess in column 9 which is worth something. Spider is not all about
turning over as many cards as possible”.
Yes, I just contradicted myself about earlier feeling sorry
for the two-dozen face down cards that don’t know the laws of physics that
govern the Green Screen. I get that.
The Nine of Spades leaps from column 2 into an empty column,
taking the 8-7-6-5 with him. He is clearly eager for the Nine of Hearts in
column 9 to take his spot on top of the K-Q-J-T of the same suit.
“Not so fast” says the Nine of Hearts. “The Spider Grand
Master does not look kindly on 85,78,68,79,73,78,71 moves”.
“Who is this Spider GM you speak of?” I ask.
I shudder at the thought that we are being controlled by
some “higher being” and we are pawns in a bigger chess game (or cards in a
solitaire game if you wanna take things literally). Then again, if there is a
higher being who is a GM at Spider Solitaire and he is playing to the best of
his ability then that can only increase our chances of winning. So perhaps we
shouldn’t be complaining.
The Jacks, Queens and Kings engage in a long discussion.
This is a critical point in the hand. Make the wrong decision and we are
trapped forever. All the little cards shy away from discussion: they are unable
to visualise a long complex sequence of moves. They know full well it is better
to remain silent and be thought a fool than – well you know the rest of the
“Okay, I’ve got this”, I say. “Queen of spades goes to King.
Rearrange cards so that we have Nine through Ace in column 9. Clear the hearts,
dump the six of diamonds to an empty column. We still have one empty column
left. Swap Ace of Spades with Ace of Diamonds, move the 3-2-A onto the 4 of
spades, four of hearts onto 5 of diamonds … Oh 67,82,65,80, we don’t have an
“Yes we do”, says the Eight of Clubs in column 2.
Of course we do. We cleared the hearts. Duh.
We execute the plan. Fortunately we have visualised everything correctly and things go as expected. I no longer feel stupid. I farewell my twin sister as her suit gracefully whizzes to the bottom left of the Green Screen. Only six more triumphant C-major chords to go and we are done. Looks like we got this!
As expected there are no further difficulties and victory is
a mere formality. Just for fun I do a little endgame calculation. There are ten
cards missing. As long as nothing stupid happens like all even cards on the
last deal …
Clubs = A4 Diamonds = 67TJ, Hearts = 2, Spades = 3JK. Yep, this is a lock.
“So what happens after we win?” asks the Eight of Clubs.
“Well, we go back to the physical world as plastic cards”, I
“Would we become inanimate objects?”, asks the Nine of Spades. “Would we lose the ability to talk to each other and move around according to certain rules”
“Perhaps,” the Three of clubs says, “we would be fondled by
grumpy old computer-illiterate farts in a retirement village who only know how
to play Klondike.”
Always the cheery one,
I think to myself. Maybe going back to the real world ain’t what it’s cracked
up to be after all.
“Or perhaps,” adds the Two of Diamonds, “one of us gets a
68,73,67,75 pic after a bad beat in Texas Holdem.”
The Seven of Hearts gives the Two of Diamonds an
oh-so-polite wink. No card higher than a Nine is amused.
I rest my case.
At this very moment, the last ten cards magically appear
onto the tableau. We easily clear the remaining suits and win the game.
Some lame music plays and two pills immediately appear on the table. I’m supposed to choose one and swallow it. The Orange pill means we all stay in the Green Screen. The Blue one means we go back to the real world as inanimate objects. Both options 83,85,67,75.
I hold one pill in each hand and recite to myself: “Eenie meanie minie moo, smoking very bad for you, drinking is bad for you too, eenie meanie … ah 70,85,67,75 it”.
In one last act of defiance, I swallow both pills
simultaneously. Hah!, bet they didn’t think of that did they? A burning
sensation sizzles my tongue, and I feel ill. I feel the system crashing about
me, as I teleport to God-knows-where. The colour drains from the Green Screen
and I throw up. I believe it’s called a technicolour yawn except it looks more
like 50 Shades Of Gray. Okay, I probably shouldn’t have done that.
THE END … or perhaps not?
OKAY THAT PROBABLY DIDN’T WORK
So there you have it. There’s probably a reason or three why I haven’t won any meaningful short story competition yet. But at least I had a go. Do you guys think I have potential as a budding short story writer? Or should I stick to just playing Spider Solitaire to the best of my ability, and leave the writing to the Short Story GM’s? On second thoughts, if I can improve your win rate at Four-Suit Spider by a substantial amount then I don’t care how lousy my short story is bwahhahahahahahahaah 🙂