Game On/Short Story (7 Feb 2021)

“Oh I love trash!”, sings Oscar The Grouch. He is especially proud of the ever-growing stacks of cards in columns 1, 5, 9 and 10.

“But what is so good about the ever-growing stacks of cards in columns one, five, nine and ten?” asks Grover.

“Well,” replies Big Bird. “The more cards you have in those columns, the less you have in others. So it is easier to get spaces in columns 2,3,4 or 8. “This is why Oscar likes his trash piles”.

“That is true,” replies Grover. “But we did not get a good deal. We can not get more than one empty column.”

“But I want to know what’s the best move!” cries Elmo, who is clearly impatient with the discussion about how best to proceed.

Count Von Count walks in, together with a couple of human guest stars – today they happen to be Bart and George.

“Before we can work out the best move,” begins Count von Count, “we need to count the cards!”

Count von Count gets all the children to name the cards, starting from the left-most column and working towards the right. As the kids eagerly announce the rank of each card, Bart draws a tally mark next to the corresponding symbol.

“King! … Queen! … Jack! … Six! … Five! … Four! … King! … Queen! … Jack! … Ten! … Nine! …”

It takes a while, but Bart eventually ends up with the image below. Meanwhile, the others are busy contemplating whether it’s possible to remove a complete set of Clubs.

“We can do it!” shout the Bad Idea Bears. “We can remove a complete set of clubs!”

“Not so fast,” says George. “That would cost us our only empty column.”

“Besides,” adds Bart, “You ain’t welcome here, you’re from the wrong crowd.”

“Awwww” groan the Bad Idea Bears. They reluctantly leave the playing hall.

 It seems a better plan is to partially complete the Club suit and wait for better opportunities. If for instance we find the other Ace of Clubs, then we need not shift the Three in column 1. Or if we expose the second Club King then we could look forward to a new card more useful than the Eight of Spades.

“We should turn over a card in column 7,” says Big Bird.

“I agree,” says Count von Count. “There are four Tens unseen and that would give us two empty columns.

“Yes,” says Spider GM. “It is more important to take the card in column 7 than to remove the Club suit. Now it’s just a matter of working out the detailed sequence of moves.”

Spider GM is pleased that all his students are contributing to the discussion.

“Don’t forget,” says Count von Count, “that we are aiming to win this game with a score of 1000 or better. I believe we have played 143 moves so far.”

“Finally!” cries Elmo, as we start to move some cards around.

We reach the following position and are about to reveal what will probably be the most important card in the history of Four-Suit Spider Solitaire. If it’s a Ten then we’re in business.

And the final card in column 7 is … the Two of Hearts. It’s not the best card – then again it certainly isn’t the worst.

We now reach an all-too-familiar endgame scenario. We can easily get back a space in column 7, but we can’t turn over a new card. Fortunately there are still 10 cards in the stock, else it would be game over. How would you continue?

The Final Problem (short story)

SH and JW were at Holmes’ Baker Street diggings, reviewing the proceedings of today’s losing session with Moriarty. Heads-up Spider Solitaire had become the hottest game in town ever since the success of The Office, starring Creed Bratton. Yes, Bridge also had its fair share of followers in the good ol’ U. S. of A. but nothing could beat the strategic complexity of Spider Solitaire, which had twice as many cards.

In heads-up Spider Solitaire, two players alternate playing 10 hands and each hand is worth a certain stake agreed beforehand by the players. Whoever won more hands would win the stake multiplied by the difference in games won. For instance, if the stake was $300 per game, the maximum possible winnings for one player is $3000.

JW arranged two decks of cards in the critical position below, with the help of his photographic memory.

“This was the final hand of the night,” mused JW. “I had a difficult choice. I could turn over a card in column f or j. I chose column j, thinking to procrastinate the option of moving the 3-2 of Clubs onto one of the Fours. Of course I revealed the dreaded King of Spades, and never recovered. Do you think it was better to try my luck in column f?”

“Neither play was correct” replied SH. “Your plan did not meet the requirements of the position.”

“But it was one column or the other,” said JW. “Might as well have flipped a coin. At least Moriarty allowed me to boop after conceding. We found that column 6 would have revealed a Nine of Hearts, also a bad card.”

SH put down his pipe and narrowed his eyes, as though about to admonish a poor student for repeated failures.

“How many times do I have to tell you – when you have eliminated the impossible, whatever re- ”

“How many times do I have say that smoking is bad for you!” retorted JW.

“I can’t help it!” snapped SH.

After some robust discussion they eventually reached a bargain: the great detective would give up smoking and his protégé would pay more attention to his teachings.

“The laws of Spider Solitaire do not compel you to reveal a card whenever you have an empty column,” said Holmes. “Consider the play of <hb,eh,ce>.  It is much easier to win back an empty column when you have 7-6 in-suit rather than offsuit in column e. With six Queens unseen, we can also reasonably hope to clear column b. Moreover if we can reach the Jack of Spades in column h then we might get four turnovers. There is also the potential for developing a suit of Hearts. It would be nice if we can obtain a run of Hearts from Jack to Ace, but the rules unfortunately don’t allow that – so this is the best we can do. We only need to win back one empty column and find at least one missing Queen of Hearts on the next row of 10 cards to put ourselves in fine shape.”

“Amazing, Holmes. I would never have considered that play.”

“Elementary.”

The Watering Hole

“Thank you for leading me to the Watering Hole,” says the Horse. “Unfortunately I rot13(fhpx) at Spider Solitaire.”

Despite my best efforts, I can’t make my newest student to think more than two moves ahead. Through my peripheral vision I notice a demotivational poster saying “Training is Not the Cure for Stupidity”. The horse looks dejectedly at the cards on the table. He has just been forced to deal a new row of cards and has no idea what to do. He takes another swig from his glass. It seems drinking is not the cure for stupidity either.

“I was the local champion at Klondike,” continues the Horse. “Got the hang of it pretty quick …”

“Local champion,” sneers the rot13(Fzneg Nff). “Only because you were up against the likes of the rot13(Qhzo Ohaal), Bad Idea Bears and Ninja M-”

“YOU’RE NOT HELPING!” I yell.

I angrily swipe the cards off the table and glare at the rot13(Fzneq Nff). Fortunately Ninja Monkey is able to restore the correct position in less than three nano-seconds thanks to his photographic memory and extremely fast metabolism.

First of all, let me begin with the response from Bart Wright:

I’m finding this really fun — applying all those competing considerations that only arise in a real game.

This is where the game often starts getting tricky… sometimes the moves before the first “deal” feel like following a chess opening, and here I go off the opening and have to think harder. I know sometimes I get to a position where I say, “Darn, if I could think far enough ahead I bet I could do better, but I can’t pull off the mental effort required”. But I don’t think this is one of them.

Bart says the moves before dealing a row of 10 cards feel like following a chess opening and in some sense, he is right. Before the first deal, all face-up cards are always in descending sequence (a knowledge bomb from Edifying Thoughts of a Spider Solitaire Addict) so analysing a particular position is not so difficult. But after dealing a row of cards, the descending sequence property is lost, and it takes much more effort to determine minimum guaranteed turnovers, let alone the best move.

In this case, we have only two guaranteed turnovers – that’s the bad news. The “good” news is we probably don’t have to think too far ahead to determine the best play.

Bart also mentioned that in the last post, I shifted the Q-J of Diamonds from the King of Diamonds in column 5 to the other King of Diamonds from column 1. He thinks it’s better to leave it in column 5 because of the consideration that we get an empty column if we remove a full set of diamonds. The reason I moved it to column 1 is to avoid a possible long-term problem with “One-Hole-No-Card,” a situation where you can’t reveal a new card despite having one or more empty columns. I’m still not sure about my decision – but what I do know is that anyone who plays long enough will eventually encounter the situation of One-Hole-No-Card.

To determine the best move, we need to visualise several moves ahead and also calculate (or at least estimate) various probabilities, such as chances of drawing a good card.

Meanwhile the Horse unsuccessfully tries to stifle a yawn as Bart and I study the cards in front of us. We all know yawning is contagious, especially when it’s the Bad Idea Bears setting a bad example.

Here are a few options to consider:

  • Five of Spades onto the Six of Diamonds, the easiest turnover.
  • We can shift both Threes in column 3 to expose a second card.
  • Jack of Hearts onto the Queen, Four of Hearts onto the Five of Hearts, Five of Diamonds onto the Six in column 1. Seems very attractive with three more in-suit builds.

But there’s a catch: we also wanna “insert” the Queen of Hearts in column 2 between the K-J in column 7. If we choose the last option, we will end up with Ks-Qh-Jh in column 7 and 9s-Qh-Jd in column 8 (unless we reveal some good cards). It is clearly more desirable to have Ks-Qh-Jd and 9s-Qh-Jh, so column 8 is easier to shift later on. Therefore we have to sort out the K-Q-J mess first.

In other words, we have to sacrifice many moves before turning over a single card in column 6, and this not only hurts our goal of 1000+ but also may affect our chances of winning the game since we commit ourselves to several irreversible moves before gaining information from the new card.

For this reason, Bart suggests we turnover column 3. Note that “killing” the Five of Spades in column 10 isn’t a big deal because we already have a Five in column 9. We would only regret it if we turned over two Sixes – that is heavy odds-against with only two guaranteed turnovers.

Unless anybody other than Bart can come up with a different suggestion within the next few days, I’m turning over a card in column 3. Any takers?

“Hi,” says the rot13(Fzneq Nff). “I’m rot13(Fzneq Nff)”

I’m Bart,” replies Bart. “Rot13(Rng zl fubegf!)”

Uh oh, I think we’ve all had a bit too much to drink, including myself. Then again, we could all use a bit of laughter after what’s been a rotten year.

THE END

Winning with score of 1000+ (short story)

Oh goodie! I have three more students signing up to my Spider Solitaire classes. This time they are humans.

“Hi, I’m Simon”

“Spider GM,” I reply. “Nice to meet you”

“I like to see the game as a logical puzzle,” says Simon. “With sufficient thought we can deduce the proper play in any given position – or at least something reasonably close to optimal. I call this logical deduction”

Simon is a down-to-earth bloke who clearly knows the game. He plays guitar way better than I do. And he can play a mean game of Starcraft. A teacher’s pet if you pardon the terrible cliché.

“I’m Mark,” says Mark.

“I’m Spider GM, nice to meet you”

“I like the use of rot13(haqb) …”

Uh oh, Mark is probably not one of my better students. But he is an approachable dude with a wry sense of humour. He definitely knows his Cryptic Crosswords. I once gave him “At first condemn our very feeble excuse for everything that follows constant negative press (7)” and he got the answer in, like, less than three nano-seconds.

“especially with a variant that requires the player to complete all eight suits with a score of 1000 or better,” continues Mark. “So if I make a bad move, I can still rot13(haqb) but lower my score since each move or rot13(haqb) costs 1 point. Rot13(haqb) also makes sense in a Spider Solitaire Speed-solving championship. I call this rot13(ovshepngvba).”

“I call it blooper-reeling,” I reply. Mark and Simon are known for their witty banter and occasional pranks – and unlike Starcraft I can mix it with the best of ‘em.

I have never been a fan of rot13(haqb) and I have certainly never heard anyone use the term of rot13(ovshepngvba) to describe the cardinal sin of Spider Solitaire. Still, I will concede Mark has a point. With a target score of 1000+ or better, rot13(haqb) can only be used sparingly so we could still have some interesting scenarios with non-trivial decisions. But I have already started this game, so no rot13(ovshepngvba) for now. Maybe in a later game …

“I’m Eugene,” says a third person.

“I’m Spider GM … hang on, you’ve brought a chess set with you. Another one of my hobbies!”

It doesn’t take long for us to set up the pieces. My other students watch with great interest. Despite having an International Master title, Eugene somehow rot13(jubbcf zl nff) ten times in a row. This guy is something special.

I take my king in my right hand and offer it to Eugene, as though it were a Christmas gift.”

“It’s your game,” I say. “Take it.”

Eugene is puzzled. “I thought the pieces were supposed to go back in the box.”

“You never watched the Queen’s Gambit?”

“Never heard of it.”

“Name of a movie, or more precisely, a mini-series. Named after the opening of course – White plays d4, Black d5, White c4.”

Eugene struggles to locate the squares d4,d5,c4 on the chessboard.

“But – but there’s nothing defending the pawn on c4,” says Eugene.

I suddenly realise Eugene was wearing a “magic hat” during our 10-game series. If my intuition is correct, he will probably call it rot13(purngvat). Eugene can play a mean game of chess (or several), but doesn’t understand basic social principles such as Maintaining Eye Contact 101.

“Wait a minute,” I say. “You’re the guy who also plays Sudoku?”

“Yes,” replies Eugene. “Been a while.”

I quickly scribble a Sudoku grid with only the digit in row 5 column 5 missing. There are no quirky rules like thermometers, arrows, disjoint sets, killer clues or sandwiches. It takes him a good minute or two to deduce the missing digit is a Six.

In the distance I notice the Bad Idea Bears giggling to themselves. They hold a strange device that was clearly meant to communicate with Eugene during our chess games. I later find out the BIB thought it would be hilarious to troll Eugene by deliberately giving him the wrong digit in the easiest ever Sudoku puzzle in history. Normally I don’t condone this sort of behaviour but given that they exposed yet another cheat in this sorry state of the world I can forgive them today. However, if this trend continues …

The End

Tower of Hanoi (alternative version)

“I can’t do it,” sighs the Ninja Monkey.

“Now what?” I ask

“It’s the legend of the Flowers of Hanoi,” replies Monkey. “Something I learnt from the Bad Idea Bears.”

“I know you often mention the Flowers of Hanoi during Spider Solitaire lessons,” says Bad Idea Bear #1. “We asked our friends about it, and eventually figured out the rules.”

This cannot be good. Yes, the Bad Idea Bears have inquisitive minds, an essential quality for anyone who does a Ph. D., but it’s a pity their math fundamentals are 83,72,73,84.

In front of the Monkey are a pile of five flowers, surrounded by a large square. Each flower lies atop another flower of slightly smaller size. There are two more squares of the same size, but do not contain any flowers.”

The Bad Idea Bears say I should be able to shift all the flowers to one of the other squares in 30 moves, but the best I can do is 31.”

“Shouldn’t be too hard,” I say. “After all, thanks to an extremely fast metabolism you are able to complete 200 games of Spider Solitaire in three minutes if you pretend it’s played at the one-suit level. But this puzzle only involves five flowers instead of 104. How hard can it be?”

“But there’s a catch. You can only move one flower at a time – and no flower can be on top of a smaller flower.”

“Of course if this were Spider Solitaire then you can do it in one move, since all flowers are the same colour.”

“Yes that is true,” chuckles Ninja Monkey. “The game does have similarities with Flowers of Hanoi. I find I often need to make many moves just to expose one more card. But perhaps my Random Move algorithms aren’t all they’re cracked up to be.”

“Don’t be too hard on yourself. You’ve already achieved a lot with Four Suit Spider Solitaire. Everybody treats you with respect, and we won $3000 dollars from the Eagle last …”

“For 70,85,67,75,78 sake,” says the Eagle. “You don’t need to bring that up every third day of the month.”

“Why do the Bad Idea Bears think it’s possible in 30 moves?” I ask.

“I was wondering about that as well,” says the Bad Idea Bear #1. “But we finally figured out the pattern. We started by considering what happens with fewer than 5 flowers.”

BIB #1 draws a large circle in the dirt. He chooses two random points A and B on the circle and draws a line connecting the points. The two resulting regions in the circle are labelled 0 and 1.

“With only one flower, it takes one move to shift all flowers from one square to another,” says BIB #2

I nod in agreement. So far no ground-breaking discoveries yet.

BIB #2 draws a new circle in the dirt but with three vertices A,B,C and lines connecting all pairs of points. Now there are four regions numbered 0,1,2,3.

“With two flowers, we need three moves to shift all flowers to a different square.”

Again I nod in agreement.

The Bad Idea Bears draw three more similar diagrams but with four, five, and six vertices and lines connecting all pairs of vertices.

“Continuing in this manner,” says BIB #1, “we find seven moves are required to shift three flowers, fifteen moves for four flowers and thirty moves for five flowers. In every case Ninja Monkey has found a solution with the correct number of moves – except the last one.”

I examine the BIB’s artwork carefully. They have indeed correctly counted 30 regions in the last diagram. And they can draw diagrams faster than the Wise Snail, I’ll give them that.

“At first we thought it should be 29 regions in the last diagram,” says BIB #2 “but we eventually figured out that no three lines should intersect at a single point. Unfortunately Ninja Monkey has never been able to do it in 30 moves. He can do 7 moves with three flowers and 15 moves with four flowers but the best he can do is 31 moves with five flowers.”

I look in the Monkey’s direction – unfortunately he seems to have knocked himself out, and it doesn’t take long to work out why.

Oh well. At least I was brought up right by Mom and Dad. For one thing, I never scratch my 66,85,77 and/or pick my nose in public.

THE END

How Can I Win This Game? (Alternative version)

It was a pleasant Sunday afternoon. The sun was shining and he had plenty of spare time on his hands. True, there was the small matter of a chemistry assignment due tomorrow, but that could always be done after dinner. A perfect time to play some more Spider Solitaire.

The play had started well, but things started to sour when four Kings appeared in the third deal. The fourth deal brought no luck either with no face-down cards unable to be exposed. Resigned to his fate, Joe Bloggs reluctantly dealt the last row of ten cards and surveyed his prospects.

How can I win this game? Joe asked himself.

There was some good news: an empty column (or “hole” as he liked to say) was available in the ninth column. And he could turn over a card in Column h. But at this stage of the game Joe realised he would need a good miracle or three to win.

“What is the best card I can hope for in Column h?” Joe asked himself.

This brings him to the bad news: there would be plenty of calculation to look forward to, and given the stock was empty any mistake, no matter how small, could be fatal.

Suddenly Joe Bloggs spots a bird staring at him through the window.

She’s been wallowing in the mud for way too long. Don’t ask me why.

Joe Bloggs briefly considers giving the poor thing a nice warm bath.

“Oink oink,” says the bird.

“87,72,65,84 84,72,69 70,85,67,75?” replies Joe Bloggs.

Through his peripheral vision, Joe Bloggs notices a flock of shiny pigs floating in the air. Thirteen of them shift into the foreground and form the shape of a happy face. After winking at Joe Bloggs, they chase each other in circles for a good half-a-minute. Then they gradually accelerate until whoosh – they shoot up towards the sky!

“Oink oink,” repeats the Bird.

Joe Bloggs stares at the bird again. Perhaps she is trying to tell him something, but he can’t work out exactly what. His chemistry assignment? That wouldn’t make much sense.

Joe studies the cards again. He soon notices that every card in the Spade suit is visible in the tableau. An Ace in column 5 or 6, Deuce and Three in column 6, Four-Five in column 8 and so on. Perhaps it is possible to remove a complete suit of Spades with the correct sequence of moves, regardless of the permutation of face-down cards. Not likely, given they were scattered all over the place, but perhaps his best shot anyhow.

“Aha,” says Joe Bloggs, after some thought. “The correct move sequence is <bg, id, ih, ia, jf, dj, cd, ch, jd, cj, d2=j1, hc, hc, fg, fd, fh, fa, d1=f1, f2=h2, hc, cj>”

Joe Bloggs executes the move sequence <bg, id, ih, ia, jf, dj, cd, ch, jd, cj, d2=j1, hc, hc, fg, fd, fh, fa, d1=f1, f2=h2, hc, cj> and whoosh – he triumphantly slaps the Spade Suit onto the foundations!

True, his position was still very bad after removing the suit of Spades but no matter. He had already won the war: thanks to this hand his skill had improved considerably and the actual result of this game was rendered moot.

The Big 104 (alternative version)

The Grand Master, the principal adviser to the King, had maintained a blog about Spider Solitaire for a whole year.

“Thank you, Grand Master, for this most wonderful blog,” said the King. “I enjoyed reading your silly stories. However I can’t claim it has improved my game tremendously so I can only offer you a small reward.”

The King gives the Grand Master a sack of wheat.

“How dare you offer such a modest reward for the world’s best blog on Spider Solitaire!” replied Spider GM. “As far as I know, I am the world’s best player of Four Suit Spider Solitaire sans boop. This is a travesty!”

“What nonsense!” retorted the King. “I have several men who can wield a mean deck of cards – or two.”

The King corrected himself at the last minute, recalling that Spider Solitaire was played with 104 cards, not 52.

The Grand Master offered to play a 30-game match against each of the top ten players chosen by the King. A 30-game match would consist of 15 games by each player, Four-Suit sans boop and whoever won more games would win the match. Spider GM offered “draw odds” to every player, meaning that if both won the same number of games it was tantamount to the Spider GM losing the match. Not surprisingly Spider GM wiped the floor with each and every one of them.

Sensing the King was utterly humiliated, the Spider GM suggested the following deal: he had to publish one blog post for the first card, twice that for the second card, twice that for the third, and so on. Once all 104 cards in Spider Solitaire were accounted for, Spider GM would enjoy 104 consecutive nights in a palace with 104 dancing girls per night. Spider GM was allowed to count the 104 articles he had already written towards the however-many-were-required needed to reach his end goal.

The King knew the arrogant 66,65,83,84,65,82,68 had a couple of blog posts lined up already, perhaps between 50 and 100, but reluctantly agreed to the bargain.

THIS IS GONNA BE WILD, the Grand Master thought to himself. He was well on the way to completing the next square, which will be marked 128.

youarehere

THE END

30th Anniversary Celebration (alternative version)

It had been 30 years since the Ninja Monkey become the first dude in the Animal Kingdom to beat Four-Suit Spider Solitaire. The affable Tim Croofs had decided to throw a massive party of Solitaire binge-playing and every monkey, his dog and literally every millipede on the planet was invited. As an extra incentive every win would be worth double the usual Experience Points.

Captain oBVIOUS was keen to try his new strategy of becoming the Grand Doctor Of Spider Solitaire. Recall that whoever has the most experience points would become the Grand Doctor Of Spider Solitaire, and the captain reasoned that all he had to do was beat enough 1-suit hands to gain as many XP as he desired.

Meanwhile, Gravelsealer Geoeyes was struggling with the 2-suit version of the game. He could win just under half the time. The dog on the adjacent table was faring even worse. It was not very smart – it could only beat one game in three.

It was not just Spider Solitaire. Several other games were being played, such as the well-known Freecell, Klondike, Pyramid and the like.

A number of dumb bunnies were playing Snap. Apparently, the Bad Idea Bears thought it would be a hilarious prank if they told them the first player to win ten games in a row would earn 10,000 experience points (and several epiphanies would occur at the same time).

Not surprisingly it was the Eagle showing everyone else how it’s done. With a 25% success rate at the four-suit level he was easily top of the Experience Points Leaderboard.

The Wise Snail arrives three hours late to the party. He signs up, and then he waits …

And waits …

And waits …

And waits …

And waits …

“Sorry,” says Captain oBVIOUS, as he taps the Eagle’s shoulder.  “You’ve got to hurry up.”

“Shush, I’m trying to think,” replies the Eagle. “This is a critical point of the hand.”

“The playing room is packed with people and animals,” continues Captain oBVIOUS. “Half of them are waiting for the organisers to print more playing cards. Thank you for your patience and underst- ”

The Eagle notices with horror that the playing room is indeed packed with people and animals and half of them are waiting for the organisers to print more playing cards. I can’t remember the last time my best student was shown up by Captain oBVIOUS.

“The room may be packed, but at least there’s no deadly virus ravaging the Animal Kingdom,” quips the Smart 65,83,83.

“You’re Not Helping,” growls the Lion, who is also waiting for a game.

“*** Sigh ***” sighs the captain. “I guess I’m not becoming the Grand Doctor Of Spider Solitaire after all. Several other players are playing non-stop and they seem to be more skilled than me.”

“More skilled than I,” quips the Smart 65,83,83.

“Oh For 70,85,67,75,83 Sake!” shout several animals in unison.

wedidit

“We did it! We did it!” shouts Tim Croofs, oblivious to the numerous players as they grumble about not enough cards and too much overcrowding.

“MOST NUMBER OF GAMES PLAYED IN A SINGLE DAY, WE BROKE THE RECORD  70,85,67,75, 89,69,65,72!!!!!!!”

“LET’S DO IT AGAIN! AND AGAIN! AND AGAIN!”

Tim Croofs and organisers high-five each other and live happily ever after.

THE END

Spider Solitaire Notation (alternative version)

The streets were littered with random animal and human body parts. An arm here. A leg there. A lizard’s tail, a cat’s paw. A pair of bunny ears to the right, an ox-tongue to the left. A human kidney, a lung. Careful, don’t step on the occasional monkey brains … uh oh, somebody even managed to lose his 68,73,67,75 after, shall we say, some rather poor decision making. The city was not exactly known for good hygiene, and a vaccine for the mystery virus wasn’t coming any time soon. But the White Bishop knew he had been one of the luckier ones. He only had a nose missing.

Despite many years of debate and discussion, there was no consensus on whether the Knight or Bishop was the stronger piece on the Chessboard so they had decided to settle things over a game of Spider Solitaire, or more precisely a series of games. It was well known the Knight could wield a mean deck of cards or two, but the Bishop felt he was equal to the challenge.

They would both play 100 games each, and whoever won more games than the other would win the match. As compensation for being wheelchair-bound, the Bishop gave the Knight odds of half-a-game. Thus, if they both won the same number of games, the Knight would be declared the stronger player.

notationexample-05172020

“<ji>”, says the Black Knight.

The White Bishop obediently moves the Four of Clubs onto the Five of Clubs, exposing the Three of Diamonds.

“<eh>”.

The White Bishop moves the Seven of Spades onto the Eight of Spades, exposing the Four of Diamonds

“<ie> – oops I mean <je> … <if> … <if> … <fi>”

And on and on it went. The quadriplegic would announce his moves according to their agreed notation and his anosmia-stricken best friend would play them out. They had even mastered the lingo for supermoves, (borrowing from the simpler game of Freecell) and superswaps. When it was the Bishop’s turn to play, the Knight would only watch. Of course there would be no 85,78,68,79 for either player. All the other chessmen watched in awe, admiring the skill of both players as they navigated the good cards and bad.

< several games later >

The Knight had won 47 games out of 100. With his concentration waning near the end he probably should have won a couple extra games. But at least he didn’t have to worry about making further errors. Everything depended on the Bishop who had won 47 out of 99. The latter had reached an endgame with only six face-down cards remaining and the stock empty. At first the prelate was about to concede the game and the match, but he eventually realised he could expose one face-down card with a complex sequence of moves. But he would have to hope the newly-exposed card was good. Finding nothing better, the Bishop executes his plan and is about to turn over a card, but then pauses.

Just turn over the 70,85,67,75,73,78,71 card and get it over and done with, the Black Knight thinks to himself.

“I feel it is most unfair, for the entire match to be decided by a single card.”

“The match is very close,” replies the Knight. “I calculate the odds to be exactly 50:50. The next card will determine the outcome of the game and the match. Get a good card and even the Ninja Monkey can’t 70,85,67,75 it up with random moves. Draw a bad card and you have no plan B.”

The Bishop checks his card-tracking sheet.

“There are three good cards and three bad cards. Doesn’t get much closer than that”

“JUST 70,85,67,75,73,78,71 TURN 70,85,67,75,73,78,71 THAT 70,85,67,75,73,78,71 CARD 70,85,67,75,73,78,71 OVER so we can work out the winner and go home.”

“We both played 100 games and neither player has managed to demonstrate any statistically-significant superiority over the other,” continues the Bishop. “I don’t see any point in completing the last game.”

After some thought, the Black knight replies “All right, we’ll call it a draw.” 😊

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