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

 

A closer look at Choose Your Difficulty (Alternative Version)

“Allow me to introduce myself. I’m Spider GM, the creator of this blog.”

“My name is Gravelsealer Geoeyes,” says the gnome.

“And I’m Captain oBVIOUS,” says the dude with the words Captain oBVIOUS emblazoned on his shirt.

“And we are the Fu Kung Pandas,” say FKP1 and FKP2.

“That’s amusing,” says Caption oBVIOUS. “You only have to change one vowel and then it almost sounds rude.”

The gnome, Captain oBVIOUS and I are happy to accept the Fu Kung Pandas’ hospitality.

“Gravel-something-whatever is a strange sounding name,” I say to the gnome. “Where did you get that from?”

“It was chosen by a Dungeons and Spiders Random Name Genera-”

“Dungeons and WHAT Random Name Generator?”

“It’s like Dungeons and Dragons, but instead of fighting monsters you play games of Spider Solitaire”

“I’ve heard of D&D, but never really liked it when I was a child. But D&S sounds like it could be right up my alley!”

“It’s pretty simple really,” replies Gravelsealer Geoeyes. “Every time you win a hand you gain Experience Points or XP.”

Captain oBVIOUS deals himself a hand of Four-suit Spider Solitaire. It quickly becomes oBVIOUS his skill is very poor: he never looks beyond the first line of play he sees.

“Are you allowed to use boop?”

“Allowed to use WHAT?”

“Sorry, that’s an Erfworld reference, which may be ahead of your time. It’s a euphemism for 85,78,68,79 which is frowned upon by good players like yours truly.”

“Captain oBVIOUS seems to be doing well,” remarks FKP1 as he proceeds to steam some buns.

77,89 65,83,83 I think to myself. FKP1 knows much more about cooking than the fundamentals of the game.

“85,78,68,79 is not allowed otherwise the game it too easy,” says Gravelsealer Geoeyes. “The good news is you get to choose your difficulty level and number of suits.”

“So that means if you are relatively new to the game you would probably select 1-suit, correct?”

Gravelsealer Geoeyes nods in agreement.

After a delicious meal of noodles, buns and whatnot, The Fu Kung Pandas bring in a large sheet of paper for us to study:

Experience Points Table

“This is the table for XP,” says FKP1.

“To work out the number of XP, simply identify the row and column corresponding to difficulty and number of suits respectively,” adds FKP2. “Of course, you only get the XP if you win”.

Missing values as usual,” I groan. “The bane of every data scientist.”

I thought NaN means you win a slice of nan bread,” says FKP1. “That meal was delish!”

“Not a Number means there are no hands for a given difficulty level and number of suits,” replies FKP2. “For instance there are no Grandmaster hands for the 1-suit level.”

“The number of XP increases whenever you increase the difficulty level or the number of suits,” says Captain oBVIOUS.

Hang on, I think to myself. 3000 is not larger than 6000. I soon realise the last row is labelled “Random” which makes sense after all.

“So what happens after you win enough XP? Do you level up?” I ask.

“Whenever you gain enough XP an epiphany occurs,” replies Gravelsealer Geoeyes. “For instance, my first epiphany was to realise the tremendous value of empty columns. I have pretty much mastered the 1-suit level but struggle a bit with 2-suit. And don’t even mention f-”

“And what happens after you get enough epiphanies?”

“The player with the most epiphanies becomes the Grand Doctor of Spider Solitaire.”

“That sounds easy,” says Captain oBVIOUS. “All you have to do is keep beating easy 1-suit games and you can get as many epiphanies as you want – oh for 70,85,67,75,83 sake!”

The captain concedes a miserable defeat. He has exhausted the stock, 30 cards in the tableau are still face-down and no empty column was attained at any stage of the game.

“Yes,” says Gravelsealer Geoeyes, “but I don’t wanna grind all day – that sounds too much like work. Besides, if everybody spends 12 hours a day playing Spider Solitaire then someone is gonna miss out”

“But if you are willing to take lessons, then hopefully you can get there faster by beating 4-suit games half the time,” I reply. “Thirty dollars an hour – hang on, something is wrong with this table.

“What The 70,85,67,75?” say Gravelsealer Geoeyes, Captain oBVIOUS and the Fu Kung Pandas in unison.

“If you look closely, the XP gained for a random deal is equal to the XP gained for the lowest permissible difficulty for the same number of suits, which makes little sense,” I say.

“For sake of argument,” I continue, “let us assume we have 400 hands at the four-suit level. 300 of these are solvable and are arranged in order of increasing difficulty from left to right. The remaining 100 are unsolvable and occupy the right-most 100 deals in random order. An Expert deal would choose randomly out of the left-most 100, but a Random deal would choose randomly out of the entire 400 hands. Clearly it should be easier to beat an Expert deal than a Random deal, and therefore the latter should be worth more XP than the former. In practice, the overwhelming majority of games are winnable, even at the Four-suit lev-”

Gravelsealer Geoeyes gives me the dreaded “you-lost-me-at-four-suit-level look”. Then again, I don’t wanna be too harsh on a player who refuses to 85,78,68,79.

It doesn’t take long for me to convince the gnome to start taking lessons. Life is good 😊

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

Estimating the difficulty of a Spidew Solitaiwe hand (continued)

Everything seemed to be going well until Parson hit an unpleasant snag. Four dreaded kings turned up simultaneously after dealing the third row from the stock. And there was no chance to turn over another face-down card without the help of boop.

Parson laboriously noted the identity of all face-down cards he managed to uncover so far. He decided it was best to start afresh and determine how best to prepare for the four kings in round 3.

“Boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop”, says Parson.

All cards magically return to their starting position.

At long last Parson is able to enter a critical endgame with only 20 face down cards. Despite having one suit removed and an empty column, Parson knows he’s in trouble. One more bad card would imply a certain loss without the help of “boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop boop”. Parson glances at his watch (displaying his stats) and suddenly realises he doesn’t have a lot of Move left. Maybe the liberal use of boop isn’t what it’s cracked up to be.

He sighs with relief after turning over a much needed Ten of Spades in Column 1. With luck on his side, Parson has no trouble untangling the remaining cards and winning the game (albeit with only 3 Move remaining). The Dwagon Spidew collapses to the floor, as though mortally wounded. Parson does the same, but more through relief and sheer exhaustion instead of being mortally wounded.

“You have done well,” says the Monkey.

“Thank you,” replies Parson.

“Unfortunately, you are not a Doctow of Spidew Solitaiwe.”

“But, but … I worked my boop off for three booping hours. I earned my victory! True, I used boop too much and was lucky to not run out of Move but …”

“Boop is not the problem,” replies the Monkey. “The problem was your hand was Too Easy.”

“You. Are. Boo. Ping. Kidding. Me,” grunts Parson. He could explode any minute now (if you excuse the terrible cliche).

“As soon as you exposed all the cards, I did some complex calculations in my head and determined an expert should win two games in fifty. To become a Doctow of Spidew Solitaiwe you need to win a hand with an estimated win rate of zero games in fifty”.

“So … does that mean I was doomed as soon as I dealt the starting hand?”

“Yes and no,” replies the Monkey. “You are not a Doctow of Spidew Solitaiwe but at least you are still alive, unlike the many skulls and skeletons that are barely a distance of 1.5 metres away from you.”

Finally Parson could take it no more.

“70,70,70,70,70,70,70,85,85,85,85,85,85,85,85,67,67,67,67,67,67,67,75,75,75,75,75,75,75,75!” shouts Parson. He remembers the Monkey’s warning about swearing three nano-seconds too late.

The Dwagon Spidew suddenly springs to life and lunges towards Parson. The Spidew thrusts his fangs into Parson’s face. What happens next is not pretty.

THE END

Estimating the difficulty of a Spidew Solitaiwe hand

That thing is hideous, Parson Gotti thought to himself.

The Dwagon Spidew eyes Parson warily and he returns the favour. It probably came from the city of Ruhan (in some dark corner of the Universe where HYGIENE is apparently not allowed in Scrabble). At least Parson wouldn’t have to engage in physical combat. All he has to do is arrange two decks of cards into eight complete suits from Ace to King.

“So that means no illegal moves, keep a distance of at least 1.5 metres and the Dwagon Spidew won’t mess with you,” said Parson.

“And most important of all, no swearing,” added the Monkey.

At least the monkey is on my side, thought Parson. How useful a mentor the Monkey is remains to be seen. Parson deals 54 cards onto the tableau and leaves the remaining 50 in the stock.

Parson glances at a number of skeletons and human skulls strewn over the floor. The Dwagon Spidew’s modus operandi is pretty simple, he thought. Simply wait for the human victims to perish from exhaustion, hunger, frustration, PTSD, whatever, or all of the above if they can’t finish the game.


Parson examines the starting layout. He counts only three guaranteed turnovers. Years of experience taught him the average guaranteed turnovers should be closer to four not three. But at least two of them would come from in-suit builds. And there were no Aces or Kings.

Parson shifts the Seven of Hearts exposing an Eight of Clubs, then shifts the Eight of Hearts (column 2) exposing the Four of Clubs, a second bad card.

“Oh for Boop’s sake!” mutters Parson.

The Eight of Hearts magically reverts to its original position in Column 2 and the Four of Clubs is face-down again.

“Wait – what is this boop?”

The Seven of Hearts returns to its original location in Column 10 and the Eight of Clubs is face-down again. Parson had returned to the starting position.

“So every time I say boop the game will boop a move – unless I am already at the starting position.”

The Dwagon Spidew nods in agreement. Alas, half the human population (including Parson) had difficulty pronouncing a certain word rhyming with “One Two”. And a vaccine for the dreaded Dysarthria virus wasn’t happening any time soon.

Parson moves the other Eight of Hearts on to the Nine of the same suit. At last a good card – the Three of Hearts, which can now play onto an off-suit Four in column 8.

Parson hears an ominous rumbling sound in the distance. On second thoughts, it was only his stomach telling him it’s time to eat.

“I couldn’t boil an egg to save my life,” grumbles Parson. He had long regretted living with his parents for 30 years.

At this point a hard-boiled egg magically pops out of nowhere and Parson eagerly grabs it with both hands. Phew, one less thing to worry about. Nom, nom, nom, nom, nom, nom, nom, nom, nom.

At length, Parson is able to secure his first empty column (not surprisingly with the considerable help of boop). His curiosity is piqued by the following thought: “how can I estimate my chances of winning without boop if I were a much better player than I currently am?”. But back to the task at hand. How to defeat the Dwagon Spidew?

(To be continued …)