Easy Difficulty (Alternative version)

“I think that’s enough Peak Stupid for now.”

I am about to lead my students down the mountain, but Ninja Monkey does a quick head-count and confirms one is missing. Through my peripheral vision I spot one of the Bad Idea Bears standing in front of a magic mirror (which nobody has noticed before). Wait a minute, he seems to be poking his finger through the glass. This would violate the laws of physics, even by Peak Stupid standards – unless Peak Stupid was stupider than I had previously thought.

“Don’t do it!” I yell. “Don’t –“

Dweet

Not even Ninja Monkey’s extremely fast metabolism is enough to stop BIB1 from walking through the magic mirror. He is gone forever, unless I have the courage to walk through the same mirror myself. But with BIB2 reduced to tears it seems we have no choice. I hope it’s not like that stupid veil thing from the Harry Potter movies.

There’s only one way to find out if you pardon the terrible cliché – I tell the rest of the gang we’re not descending Peak Stupid after all.

“Okay Bad Idea Bear Two, I want you to stand approximately nine and three quarters metres from the mirror. On the count of nine and three quarters I want you to run at full speed towards the mirror and then jump into it. Don’t be scared, you can do it.”

BIB2 reluctantly agrees.

“One two three four five six seven eight nine NINEANDTHREEQUARTERS!!!!”

Dweet

I am the next person to go through the mirror.

Dweet

BIB1 is looking at some more board games, unaware of the gravity of the situation.

“It’s safe!” I shout. “You can come – ”

Hang on, I’m not sure if my fellow students can hear me.

Dweet.

BIB2 materialises in front of the other side of the Magic Mirror.

Dweet … dweet …. dweet dweet dweet … dweet (etc).

Several of my other students appear one by one, and I breathe a huge sigh of relief.

“Head count,” I tell Ninja Monkey.

“No need for that,” he responds. I counted exactly 50 dweets.”

Despite the Ninja Monkey having Asperger syndrome, the Animal Kingdom still values his contributions to society. I’m more concerned about the Bad Idea Bears. Uh oh, something is weird. We seem to be in exactly the same place (or pretty close to it) after passing through the magic mirror. There are board and card games galore, and BIB1 is studying Snakes and Ladders. Of course, it takes me less than 3 nanoseconds to spot my favourite card game in the centre of the hall. The cards are already dealt.

“This is strange,” says BIB1.  –“It’s the same layout as before except every snake and ladder has been swapped. Once you get past square 88 it’s all ladders to the top”

“This is also strange,” says the Stockfish. “Black has the 16 chess pieces and White has the 12 checkers.”

“But White has the first move,” says the Dumb Bunny. “Does that give him enough compensation?”

A rare lapse of character sees the Eagle accidentally knock a brown die (with numbers 2,2,3,4,5,6) onto the floor. He quickly replaces it on the Backgammon table.

Connect Four is even weirder,” says the sloth as he hangs upside-down from a chair. “For some reason the pieces float upwards instead of down.”

Minnie Mouse soon discoveres Texas Holdem is again rigged – except the Magic Eye trick only works on cards 5 or lower. If you hold any other cards then you’re good – unless of course the flop comes something like 2-4-4 rainbow.

Dweet

“Monkey, did you count correctly?”

“Actually, that dweet was a semitone lower than all previous dweets,” replies Ninja Monkey. “My best guess is somebody passed the magic mirror in the other direction”

And sure enough, BIB2 is missing.

Dweet

Before I literally know it, BIB2 is standing in front of the magic mirror again.

“Bad Idea Bear Two,” I say. “We need to talk.”

The Eagle is seated in front of the Spider Solitaire table.

“Before you play, I should warn you Spider Solitaire is rigged – but in a good way.”

“87,72,65,84,84,72,69,70,85,67,75?” says the Eagle.

“I expect the game would be significantly easier than usual – for instance the probability of three cards of the same rank appearing in any row of 10 cards will be significantly less than usual.”

“There’s a better way to test your hypothesis,” says the Eagle. “Can I win this hand without any supervision from you? If I win, then there’s a good chance your hunch is correct.”

I give my best student the thumbs up.

The Eagle proceeds wins, but not without a struggle (I would have beaten the 67,82,65,60 out of that hand much faster, but at least his play is fundamentally sound). The cards magically arrange themselves into a new starting layout. The Eagle proceeds to win four games in a row. Only on the fifth hand does he finally lose a game, perhaps due to a lapse in concentration.

All my other students take turns experimenting with the Spider Solitaire cards, and I am happy to let the eagle supervise events. Meanwhile I rest myself on the floor in front of the Magic Mirror, to prevent any more shenanigans from the Bad Idea bears.

THE END

 

Choose Your Difficulty (alternative version)

“Are we there yet?” groans the Sand Griper.

“Do we have to do this?” asks the Dumb Bunny. Meanwhile the Eagle has no cause for complaint as she gracefully soars across the air.

“It’s good exercise,” I reply. Even a Spider Solitaire tragic like me has to get out once in a while.

I sit on a rock, giving myself a brief rest as the rest of the gang catches up. Ninja Monkey does a quick head-count and confirms I haven’t lost any of my students.

“If you judge this fish by its ability to climb a mountain it will live its whole life believing it is stupid,” quips the Smart 65,83,83.

“You’re not helping!” growls the lion. The long trek has clearly taken its toll and even the Bad Idea Bears are not in the mood for jokes. I allow a few minutes break for everyone. We have only another 400 metres to go.

“Are we there yet?”

I turn to the Sand Griper.

“Okay, to make this trip a bit more entertaining I will let you play a game called 20 questions.”

The Sand Griper perks up – not something I see every day.

“The rules are simple,” I say. “You can ask as many questions as you like – except ARE WE THERE YET can only be used twenty times”.

The Sand Griper returns to being his usual grumpy self. Apparently he’s also not in the mood for jokes.

Finally I see a wooden sign and everyone soon reaches the top of the mountain, including the stockfish.

We immediately enter a tunnel. We follow the path and soon find ourselves at a large Games Room. All the animals marvel at the immense variety of board and card games, ranging from the prosaic Snakes and Ladders to the ever-popular Die Siedler von Catan or the ethereal strategic complexity of Risk. Not surprisingly the usual suspects are keen for a game of Texas Holdem after a long trek up the mountain.

“This is different,” says the Stockfish.

Stockfish is looking at a chessboard, except there is something unusual about the Black pieces.

“White has a large advantage” says the letter Alpha.

“Not so fast,” says the Dumb Bunny. “Black only needs to capture the King to win, but White has to capture everything.”

“I say White is completely winning,” replies the letter Zero.

The Eagle notices something unusual about the adjacent Backgammon board: one of the Green dice has the numbers 1,2,3,4,5,5 instead of the usual 1,2,3,4,5,6.

“Oooh look!,” I squeal. “My favourite game!”

Even better – the cards are already dealt, sparing me the arduous task of setting up the start position.

The Wise Snail seems pleased with the initial position. There are four guaranteed turnovers and two guaranteed in-suit builds.

“Jack of Clubs onto the Queen,” says the Elephant. “It’s in-suit and we also have a spare Queen.”

“Well done,” I reply. “You’re learning fast – no wait, I think this game could be rigged.”

“Why is the game rigged?” asks the Eagle. “Yes, there are two exposed Aces but …”,

“My favourite card!” squeals the letter Alpha. Clearly, he is new to the game. But from what I’ve heard these Letters and Numbers are capable of learning a new game with only four hours of self-training.

“But you have taught us many times the initial position is a poor indicator of whether a game will be easy or difficult,” continues the Eagle. “Besides you have four guaranteed turnovers and two in-suit builds.”

“There are other indicators,” I reply. “Remember the backgammon board with the faulty Green Dice, and what about the chessboard with unequal armies? If that’s not rigged then I’m challenging RIGGED whenever somebody plays it in Scrabble!”

“Look at this!” squeals Minnie Mouse. “Texas Holdem is also rigged. Take the Queen of Spades from the deck. Hold the back of the card to your nose. It should be blurry. Focus as though you are looking through the image into the distance. Very slowly move the card away from your face until the letter Q appears …”

Meanwhile the Bad Idea Bears are engaged in a fierce battle of Snakes and Ladders. They eventually realise that every square between 83 and 88 (inclusive) contains a snake and no ladder reaches a number higher than 88.

“So does that mean every single game here is rigged?” asks the Eagle.

“I will assert with 95% confidence every game is rigged, including Spider Solitaire,” I reply. “Welcome to Peak Stupid. But at least we know the game is rigged before moving a single c-”

“But that’s outrageous!” says the Eagle. “I refuse to play”.

“I know you are one of my top students but I want you to understand carefully: I have no problem with the game being “rigged” if the player knows in advance the cards are not properly shuffled. Think of it as an extra challenge – we already know it is possible to beat four-suit Spider Solitaire without boop if the cards are properly shuffled.”

It takes some convincing, but my students eventually agree to play the game out.

< several moves later >

  • Round 1: three Kings appear simultaneously
  • Round 2: A very awkward Q84KA84Q20 with lots of evens.
  • Round 3: three Threes
  • Round 4: four Fours
  • Round 5: at least I didn’t draw five Fives. But three Sevens and three Tens are awkward.

“You’re right,” says the Eagle. “You correctly predicted the game would be rigged. I’m not sure whether trips and quads in every round is a true indicator of difficulty and we haven’t even considered the permutation of unseen cards in the tableau but it is apparent someone did put in the effort to rig the cards”.

“Despite our best efforts we couldn’t win without the help of boop,” I say. “We obtained two empty columns at one stage and came close to completing the Heart suit. Pity that both Jack-of-Hearts were hiding behind two Kings in Column Four though.”

Hang on, I think to myself. Stockfish’s fishbowl has somehow moved right by a good half-a-meter when nobody was paying attention. I soon figure out this mischief was due to Ninja Monkey (thanks to his extremely fast metabolism and lightning reflexes he was able to avoid suspicion for quite a while). But at least I’ve worked out how the stockfish was able to ascend the mountain without violating the laws of physics.

The End

Blue Screen of Death: part 3 of trilogy

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.

Blue screen of death

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 you know-”

“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.”

“Humph.”

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 pentameter.”

“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 found.

“Ah, there it is, the 70,85,67,75,69,78,73,78,71.”

Spider GM nowhere to be found

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 sentence.

“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 four words.

“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.

This image was shamelessly stolen from the infamous Computer Error Song

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.

THE END

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.

If you still don’t believe any of this please check out my paper on Spider Solitaire.

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 three 🙂