Match Summary (Alternative Version)

Once upon a time, there lived a Beaver in the Animal Kingdom.

The Beaver had just beat the highest difficulty level of Spider Solitaire – four suits sans undo. He felt he had played well after a difficult start, but it was hard to judge his overall ability at the game. After all, one wins and zero losses does not a large sample size make. And the fact none of his friends displayed any aptitude for the Royal Game certainly didn’t help. So, the Beaver decided to have a chat with his best friend, the Raccoon, who was known for his extensive knowledge of all things mathematics.

“It’s hard to judge your playing strength after one game,” said the Raccoon. “You need to play a large number of games to prove your victory wasn’t just beginner’s luck.”

“Suppose I played 129 games in a row,” replied the Beaver, plucking a three-digit number at random. “Then we can tally up my wins and losses and then we have a much better understanding of where I’m at.”

“Agreed,” replied the Raccoon. “Right now, the only thing we can agree on is you can play a hell of a lot better than I can.”

The Beaver chuckles, and he soon notices Captain Obvious is eager to join in the conversation.

“The only problem is it will take a long time to churn through 129 games,” says Captain Obvious. “Spider GM probably doesn’t wanna hear this but we all have better things to do in our lives than playing the Royal Game all day.”

“True,” says Raccoon. “Very True.”

Hang on, thinks the Raccoon. 129 happens to be a power of two plus one. This has me thinking – what if we can involve powers of two somehow? Let us say some games can be worth more than others. Suppose that each individual game was worth N victory points, where N was a power of two. A series of 129 games is equivalent to “First to 65 wins”. This should speed things up considerably. But Captain Obvious will gleefully point out Spider Solitaire is a game for one player, not two. Hang on (***thinks for a while***) I think I might have something.

“Okay I have an idea,” says Raccoon.

“What is it?” asks the Beaver and Captain Obvious simultaneously.

“Let us pretend Beaver is the protagonist,” says Raccoon. “Only Beaver can move any cards. I am the Antagonist and I am willing Beaver to lose.”

Using a stick, the Raccoon sketches a hypothetical cube with all powers of 2 between 1 and 32.

“Initially, each game is worth 1 Victory Point. If Beaver thinks he has a good position, then he can double the stakes. I must concede 1 VP or agree to play on for 2 VP. Similarly, if I think Beaver has a poor position then I can double the stakes and Beaver has the same choice of refusing or accepting.”

“Sounds interesting,” says Beaver. “But if my game state were really bad, can’t you just double the stakes after every move? That wouldn’t be very interesting”

“That is correct,” replies the Raccoon. “Therefore, I propose another rule: if either side doubles the stakes and the opponent accepts then the opponent has the exclusive right to make the next double.”

“So that means, if I get a poor position, you double, I accept, then I turn the game around, then I can redouble and play for four VP?”

“Quite correct,” replies the Raccoon.

“Wait a minute,” says Captain Obvious. “If first to 65 wins then is it possible to get more than 65 if the doubling cube is more than 1?”

“Yes,” replies the Raccoon. “It doesn’t matter if you’re above 65 or exactly equal to 65. And before you ask, it’s perfectly legit for someone to double near the end of the match regardless of the game state because the math says he has nothing to lose.”

“Just to touch base,” says the rot13(fzneg nff) as he gleefully pokes the rot13(nff) of Captain Obvious, “does that mean only Beaver can moves cards, but both Beaver and Raccoon participate in cube-decisions.”

“That’s correct,” says Raccoon. “Even though I don’t move any cards, I can still participate in evaluating the winning chances of a given game-state. Win-win for everybody since I get a chance to improve my game as well.

This idea proved quite successful, and soon Raccoon was discussing the implications of the doubling cube with his friends, many of whom were also avid mathematicians. They had independently discovered some interesting theory and concepts such as market losers, the Crawford Rule, Jacoby Paradox, Woolsey’s Law for Doubling and so on. Not surprisingly, much of this theory is well-known to expert Backgammon players today.

For the record, the Beaver managed to win 66-42, although that may have been a function of Raccoon’s limited understanding of the Royal Game (and hence sub-optimal decisions with the cube). At least it was a lot better than the 8-65 drubbing that Raccoon received when they reversed the roles of Protagonist/Antagonist. Initially the Raccoon thought the best equaliser for a mediocre player is to play each game at high stakes and hope to get lucky, even if the game state rot13(fhpxrq) since a long match would allow the antagonist to “grind” his way to victory. But the Beaver thought it was better to be aggressive with even marginal advantages – for instance if an intermediate player starts with six guaranteed turnovers or a “good five” then he should immediately double. Then at least he is fighting from a position of strength. If the protagonist thought his chances without a doubling cube were 50-50 then he is probably better off grinding and should hope to win on skill, not luck.

And the less said about Ninja Monkey’s first Match-to-65 and his infamous random move algorithm the better 😊

The End

A Far-Sighted Play (Alternative Version)

Jane Citizen had just finished packing her bags and was about to embark on the trip of a life time – if you pardon the terrible cliché. There was only one challenge left, and Antarctica was to be the toughest of all. Nail Antarctica and she would finally become a household name, revered for generations to come. Fail at the final hurdle and everything else would be for nought.

“See you honey,” said Jane.

“Best of luck,” mumbled John Citizen, his eyes fixed firmly on the computer screen.

Jane glared at her ne’er-do-well partner. All he did was spend countless hours on that damned computer. Even washing the dishes once in a blue moon was beneath John’s dignity. But she grudgingly admitted John had a very high IQ and could play a mean game of Spider Solitaire at the four-suit level without undoing any moves.

“It’s not all about luck,” retorted Jane. “Preparing for the Seven Seven takes many months and years of preparation and dedication, instead of sitting at the compu-”

“Why is it called the Seven Seven?” asked John, hoping for a change of subject. “I know it’s the highest peaks and volcanic mountains on each of the seven continents. But something like Seven Tallest seems a more logical name.”

“That’s beside the point,” replied Jane. “Men are always useless. All they do is eat, drink, sleep and play Spider Sol-”

“Oh, give it a rest,” snapped John as he reflexively clicked the ‘minimise window’ icon of his beloved game. “We both know there are worse vices than playing Spider Solitaire at home. Besides, this feat was completed by only seven others, all men.”

“Your general knowledge is commendable, but history has proved again and again that in the last few decades women have made great strides towards gender equa-blah blah blah blah blah blah blah blah blah blah. Blah blah blah, blah blah blah blah blah blah blah. Blah blah blah …”

Joe Bloggs had tuned out as usual. At long last, his partner has left and Joe could finally concentrate on the cards in front of him.

The latest episode of I’m a Married Man, Get Me Out Of Here! was off to a lousy start for several reasons: John had accrued zero turnovers in round 1 and far too many Kings for his liking. But at least he had obtained an empty column after taking several good cards in column 5. The obvious option was “ef,be” to take out the last unseen card in column 2. But John’s gut instinct sensed this was wrong. It would be difficult to turnover more cards with the help of a solitary empty column.

John noticed that there is only one Queen visible. However, even the Ninja Monkey would know what to do if the next turnover was a Queen of any suit. The real problem was Sevens. There are several Eights visible but buried beneath Kings – but only one Seven of Hearts visible in column 3 (yes, mind the gap in column 8!). In other words, there were seven Sevens unseen, either face-down in the tableau or in the stock. If the last card in column 2 was a Seven, John would be considerably embarrassed with no Eight available just when he needed it most. And if several Sevens suddenly appeared in the next round, John would be in more trouble than the poor dude who fell into a crevasse in May 2021.

John knew from experience that winning is not all about luck. Preparing for the seven Sevens would require many moves and plans of preparation and dedication – cards don’t magically become useful or useless just because the random number generator spat out the power of a prime number.

Aha! John realised he could turnover a card in column 10. True, this places a King in an empty column but there were legit hopes of getting the last face-down card in column 2 or 4. But “ef,je,jf,ja” or “eg,je,jg,ja” would free up two Eights which might augur well for the future. If the next card in column 10 was any Queen or Seven then John would suddenly be back in the game. Several other cards would allow a single turnover – and another shot at a Queen or Seven. So it was decided then: John would dump the King of Diamonds into the empty column and pray for luck …

Will 2022 Be Year of the Ninja Monkey?

“Twenty Twenty Two Gonna Be Great Year!” shrieks Ninja Monkey.

“How so?” asks the Wise Snail.

“Twenty Twenty Two – My Year! Year of Monkey!”

“You don’t have to jump up and down all the time,” gripes the Sand Griper. “It’s annoying.”

“Besides,” roars the Tiger, “you have no evidence to back up your claim. According to the Chinese Zodiac, it’s MY year. The formula for Tiger years is 12x + 6 for any whole number x. Substitute x=168 and you get 2022. Quod Erat Demonstrandum.”

“Tiger is right,” says the Elephant. “I may not be the sharpest tool in the box when it comes to Phil Hellmuth’s menagerie of poker animal types, but I can remember every sign of the Zodiac and which year corresponds to which animal.”

“Not so fast,” says the Ox. “Chinese New Year starts on February not January, so I still get to enjoy approximately 30 more days of fame.”

“To add insult to injury,” adds the rot13(fzneg nff), “the formula for Monkey years is 12x for any whole number x. That means you are the maximum possible distance in either direction from one of your good years – therefore 2022 is the worst possible year for the monkey”

“Monkey don’t care, Monkey don’t care! Monkey invent his own Zodiac!”

“But you can’t invent something out of the blue just because a few unpleasant facts got in the way of a really good story” says the Eagle.

Ninja Monkey presents his own version of events: there are exactly 337 animals in today’s meeting. Each animal represents a different species – if we conveniently ignore the fact Ninja Monkey brought his GF along. Ninja Monkey assigned himself the year 0, his GF the year 1 and the rest of the animals different years in no particular order. How convenient it was that 337 happened to be a prime divisor of 2022. Quod Erat Demonstrandum.

“The monkey raises a valid point,” says the Wise Snail. “If the Zodiac caters for only 12 animals, then the vast majority of us miss out altogether. Monkey’s suggestion is much fairer even if it is not based on accepted tradition”.

With nobody able to rebut the Wise Snail’s statement, everybody stews in awkward silence for a few minutes. Finally Bad Idea Bear #1 comes up with a resolution: The Eagle would deal ten random hands and Ninja Monkey would have to win at least one game without rot13(haqb) using his Improved Random Move Algorithm. If the Monkey could achieve this then the new Zodiac is in. Otherwise, the Monkey would have to reluctantly accept the Tiger’s version of events and wait another six years.

Nobody else has anything better to offer, and for once a suggestion from a Bad Idea Bear gets unanimous agreement. At least there is no BIB #2 around to come up with something even worse. So, without further ado Let The Games Begin!

Game 1

Game 2

Game 3

“I thought things had started well,” sighs the Wise Snail, who is Ninja Monkey’s best friend.

Game 4

“Some promising signs there,” sneers the Tiger. “Too bad in the end!”

<<Several hands later>>

“Okay fine”, says the Monkey as he slams the cards onto the ground after conceding the last hand. “Year of the Tiger it is!”

THE END

Monkey Algorithm – In Depth (alternative version)

IM Bartacus and IM Bug had successfully beat the four-suit version of the Royal Game with the help of a few expert friends. Some of the advice was good, some not so good, but eventually they managed to remove all eight suits, albeit with some difficulty.

Meanwhile, Ninja Monkey had tested is new improved algorithm and reported a win rate of 6% inside a sanitised environment with Spider GM overseeing his every move. Now was the time to play with the big boys and see what it was really like.

Unfortunately, the first game did not get off to a good start. No sooner had the game started, Ninja Monkey was immediately ejected from the playing hall.

“What are those things?” says Ninja Monkey.

“Ngrmmph” replies Spider GM with the demeanour of a Scrabble player mega-tilting after picking up way too many consonants against a weak opponent.

“Eeeek!!! Monkey don’t understand Ngrmmph!!!”

“They are among my best and brightest students – but also the rudest” growled Spider GM.

“Tell me about it!”

“Rot13(Svpxyr nf shpx). One day Orange will play at GM strength. The next time Orange will play like a rank beginner and pin the blame on Dark Green whenever something goes wrong. Then everybody starts arguing for the better half of a minute. I don’t remember the last time somebody didn’t end up in detention!”

“This is the position when I got ejected from the playing group”, says Monkey.

“Okay, I see what happened”, says Spider GM. “You correctly calculated the minimum guaranteed evaluation score to be 61. That’s assuming 10 points for a turnover and 1 point for an in-suit build. In the worst case scenario we get six turnovers and one in-suit build guaranteed: even my Dad can do the math.”

Ninja Monkey nods in agreement.

“Now there are several ways to get 61. You can start with id, db, ec, eg or ei”. Any of those moves allows you to get 61, even if you turned over six Kings. Therefore any moveblock starting with the correct first move would score the maximum-minimum-guaranteed-score if you will.”

“Of course we should start with ib” replies Captain Obvious. “If our very first move is an in-suit build then we never lose any guaranteed turnovers.”

“Shifting the Five of Spades is entirely reasonable, since we have three Sixes” replies the Wise Snail, the world’s slowest player and Monkey’s best friend.

“When I ran my algorithm a second time,” says Monkey, “I indeed got the move ec”.

“Note that if we did get six Kings, all these opening moves are equally good,” says Spider GM. “But under normal circumstances, db is clearly bad because we lose a turnover if we expose a Nine. Monkey’s algorithm only considers the worst-case scenario when all cards turned over are bad”.

“Maybe you can think of a way to improve Monkey’s algorithm even further so it doesn’t start with moves like db”, says Captain Obvious.

“True,” replies Spider GM. “Unfortunately, even I have my limits, and I wanna enlist the help of some other friends – who either speak the Monkey’s language, or know something about the Royal Game, or preferably both.”

“The fact I win 6% of the time does mean looking ahead and calculating the consequences of bad cards is more important than getting the opening moves right” says Ninja Monkey.

“I agree you’ve come a long way since you first started Spider Solitaire with your famous random move algorithm”, replies Spider GM.

Spider GM leads his students towards a seedy-looking venue with a sign saying “Crazy House”.

“We call this place Git Hub” says Spider GM.

“Rot13(V jnf ubcvat sbe cbea uho)” moaned the Bad Idea Bears and rot13(Yhpl Gur Fyhg) in perfect unison.

“It’s a place for gits, pricks, dorks and old farts playing Bingo,” says Spider GM, “and the occasional unkempt computer nerd(s). A lot of us stay up late at night, against our collective better judgment. When you enter, you have no idea who you might bump into. Could be anybody from around the world …”

Confused looks from everyone else.

“I know it’s complicated but I’m hoping to find some really smart people among the nerds. Hopefully they will have some idea of how to play the Royal Game, or how to communicate with the Monkey to help him improve his win rate”

“Not sure if monkey like this!” squeals the Monkey

“Can’t be worse than those horrible coloured Blobs,” replies Spider GM.

“True,” says Monkey “Always true! Spider GM is always true!”

Ninja Monkey leaps into the air and into the arms of Spider GM. He cradles the monkey and assures everything will be okay …

Spider GM and his students enter the Git Hub. Meanwhile, Rot13(Yhpl Gur Fyhg) is looking rather bored.

The End

One for the Math Geeks (alternative version)

Simon: Seven of Clubs

Julie: Four of Diamonds

Simon: Eight of Spades

Julie: Jack of Clubs

Simon: Three of Diamonds

Webb: That’s Spiderwang!

Audience: (canned laughter)

Julie sighed audibly. This was the 100^th game she had lost in a row. On 57 occasions Simon called a card and it was Spiderwang. On the other 43 occasions, Julie called a losing card and the host declared it was Not Spiderwang. Yes, Julie could rot13(xvpx Fvzba’f nefr) at regular Spider Solitaire and a game with more dependency on luck was required to prevent things becoming boring. But a game show with unexplained rules was taking things too far. Julie had to reluctantly consider the possibility that Simon might be (gasp!) cheating with the cooperation of the host.

Julie discussed her predicament with her trusted group of Very Smart Friends. They eventually agreed on a plan. On the next few episodes her VSF would record the footage, take meticulous notes and work out the pattern. Once the pattern was figured out Julie could at least hope to fight on equal terms.

After burning much midnight oil, a pattern was found. Webb would declare Spiderwang whenever every card of a single suit was named at least once. Webb would declare Not Spiderwang if any single card was named for the third time.

Eventually some Math Ph. D.’s decided to join in the fun. They worked out that if nobody named the same card thrice and the probability of a new card being named was double the probability of a card already named once then Spiderwang should occur after 66.5 cards on average. The median was 67.0. The theoretical minimum was obviously 13 cards, and if e.g. no Kings were named within the first 96 cards we would achieve the maximum of 97 cards. On the last hand, Simon achieved Spiderwang after 60 cards, which corresponded to the 23^rd percentile.

On the next day Julie is pleased when the host announces that Simon is going first. Her group of Very Smart Friends have done the math and with best play she would win her first game after 90 cards.

Julie takes out some pen and paper for round 1. Curiously neither Simon or Webb object to her taking copious notes during the game. Then again, nothing on this game show made much sense to her anyway.

Simon: Jack of Spades

Julie: Four of Diamonds

Simon: Queen of Clubs

Julie: Jack of Spades

Simon: Jack of Spades

Rot13(jung gur shpx) – why would Simon throw away round 1 just like that? Of course, it takes less than three nano-seconds for the host to confirm her worst fears.

Webb: That’s Wangerspy!

Audience: (canned laughter)

THE END

Post-Mortem Analysis – Round 4 (alternative version)

Hester(*) was no stranger to staying up late and battling through miserable positions against her better judgment. But even she would have conceded the current game if tomorrow wasn’t a public holiday – or if an “opponent” were able to send over a Backgammon doubling cube with the “2” face-up at the most inconvenient moment.

Hester vividly recalled her first lesson from Arthur: Arthur drew a large scarlet letter “A” on a whiteboard and explained in no uncertain terms that Aces were not your friends. The colour scarlet signified danger – a fact even Pearl would know. Nothing could be moved onto an Ace. One or two Aces did not seem like much, but she knew from experience having too many of the rot13(saqbref) exposed meant limited options in the middlegame. Although Arthur had repeatedly drummed into her head that Aces were even worse than Kings, Hester had to learn this the hard way – losing 500 games in a row on a Spider Solitaire server that would later be shown to be biased.

Every time Hester exposed an Ace, a little voice at the back of her head would remind her that “A” stands for “AAAAAAAARRRRRGGGHHH!!!!”

Eventually Hester realised that Aces were sometimes useful to complete a suit. How annoying it would be when she followed Arthur’s teachings only to end up with a lovely run from King to Deuce in a single suit – with the missing Ace hopelessly buried under some random pile of rot13(fuvg). The secret was to plan ahead for the right Ace, before it was hopelessly buried under some random pile of rot13(fuvg). If the Ace was covered by only one other card, her options wouldn’t be so limited – and she would avoid the random pile of rot13(fuvg) problem. As Hester’s play improved, she would realise that “A” stands for Awesome. After many further months of self-study, Hester had even surpassed her tutor.

On the next day, Hester received the sad news: Arthur – the club champion in “A” Division, and Roger – her Autistic partner who introduced her to Spider Solitaire, had both passed.

So said Hester, and glanced her sad eyes downward at the scarlet letter. And, after many, many years, a new grave was delved, near an old and sunken one, in that burial-ground beside which King’s Chapel has since been built. It was near that old and sunken grave, yet with a space between, as if the dust of the two sleepers had no right to mingle. Yet one tomb-stone served for both. All around, there were monuments carved with armorial bearings; and on this simple slab of slate – as the curious investigator may still discern, and perplex himself with the purport – there appeared the semblance of an engraved escutcheon. It bore a device, a herald’s wording of which may serve for a motto and brief description of our now concluded legend; so sombre is it, and relieved only by one ever-glowing point of light gloomier than the shadow:

“ON A FIELD, SABLE, THE LETTER A, GULES”

The End.

(*) Surnames have been withheld to maintain confidentiality

Voting Results Are In! (alternative version)

Red and Green had done it. They had beaten the Royal Game at the highest difficulty level, without undoing any moves, and all this despite the shenanigans by Blue.

But the big winner was social media. With expert live-commentary entertaining all viewers and dissecting every decision, every good, and every bad card in simple language, social media platforms had every right to boast how they had successfully connected blobs all over the world. Red and Green were relative newcomers. It was well-known the game was beatable with expert play, but nobody expected them to achieve awesomeness on the big stage. But achieve awesomeness they did. The post-match interviews were a blast and Green even improvised a rap song in the iambic pentameter at one point, to thunderous applause.

Red: This is gonna be massive.

Green: Thanks to the wonders of technology, the Royal Game would finally take its rightful place among the likes of Chess, Poker, Bridge or even Tetris 99 Battle Royale. Hang on a moment. What is this?

Green watches a video on his mobile phone. A Blue-skinned player has dealt a row of cards and is considering his options. The video alone has three million views and counting, and one didn’t need a Ph. D. to realise this is statistically significant at the α = 0.05 level.

Green: Blue eventually finds a way to remove a complete suit of Hearts, but in the process, she made it mathematically impossible to win regardless of the permutation of unseen cards. Hence the hashtag “#blueboo”.

Red does not share the slightest concern, his eyes fixed firmly on his own mobile phone.

Red: Incredible Game 5. Magnus Carlsen looks horribly passive but he has correctly calculated there is no way for White to improve his position. A well-earned draw with the Black pieces. No way I could escape like that.

Green: There are a large number of #blueboo tweets going viral thanks to the likes of RojoTheGreat123, RojoTheAwesome456 and RojoTheGM789. Hmmm … these look like bot accounts with a profile pic of a Spanish flag.

Red: I never heard of this #blueboo. When did you –

Green: The overarching narrative seems to be anybody with blue skin is inherently bad at Spider Solitaire. Now you and I both know that even if our Blue-skinned team member played poorly, there is no logical reason why all other Blues on this planet would be just as bad –

Red (squirming in his seat): What does it matter? We proved we can wield a mean deck of cards, who cares what the others th–

Green: You don’t understand. Suppose you took the entire population of Blobs, then add an order of magnitude and have every one of them chant “Red Is Sus! Red Is Sus!” How you would feel … wait a minute, you’re not –

Red stands up and glares at Green. Green races towards the exit only to find the doors locked. <sarcasm> How convenient! </sarcasm> Red pulls out a knife and Green can only stew at the injustice of it all. If only the Random Number Generator had yielded an odd number instead of an even. Red would have been voted off instead of Blue and all the good guys would have lived happily ever after. Instead, here he is – cornered by an Angry Red Blob and having approximately three nano-seconds left to live.

The end.

I guess that got pretty pathetic (alternative version)

Commentator 1: “Welcome to the biggest event of year in the Animal Kingdom – Shah Mat Spider Solitaire! This is a charity event to help raise funds for animals affected by the Virus That Dare Not Speak Its Name …”

Spider GM waltzes around the tables dealing different hands to ten different players.

Commentator 1: “On board 1 we have the eagle. Widely known as the best animal in Poker, she can also play a mean game of Spider Solitaire.”

Commentator 2: “Board 2 is the lion who also knows the game.”

A large crowd gathers as the commentators introduce all the players. Spider GM has the routine task of simultaneously monitoring 10 boards and making sure no illegal moves are played. But he is not complaining. However, all eyes are on the player at Board 10. Conspicuous by his presence, one doesn’t have to be named Captain Obvious to spot the strange-looking player.

Commentator 1: “Not the most exciting of tasks for the Spider GM. But he understands it’s all for a noble cause – wait a minute, who is this Big Shiny Red Question Mark?”

Commentator 2: “Very little is known about BSRQM. His name is N. Kamath, co-founder of some stock brokerage most folk wouldn’t give a rot13(fuvg) about. His Spider Solitaire rating is 800 something … compared to the Eagle who is 2400 something”

The spectators exchange confused glances with one another. They are well familiar with the usual riff-raff animal types from Phil Hellmuth’s Play Poker Like the Pros. But not one spectator has heard of N. Kamath.

Rick Astley (guest commentator): “You know the rules – and so do I. Each player has 30 minutes to win as many games as possible. There is no penalty for losing a game. You cannot move any cards until Spider GM appears at your table. You can resign the current game and start a new hand whenever you want. Undo is not allowed.

Commentator 1: “The name sounds familiar – Kamath used to play Chess …”

Commentator 1 pauses. He suddenly realises this is a charity event after all and nobody is supposed to mention the C word that is rhyming slang for Paul Keating.

With all players seated at their tables and ready to play, the formalities have concluded and the games can begin.

As predicted, the Eagle is the first to win a hand. The Lion does the same soon after. Most of the players perform to expectations. But there are some sharp-eyed members in the audience. Big Shiny Red Question Mark has this weird habit of glancing to his left every now and again – but never when Spider GM has appeared at his table.

The time limit is almost over, and the commentators’ voices reach a crescendo (as one does in the pointy end of horse races).

Commentator 2: “We’re into the home stretch, last five minutes … hey rot13(jung gur shpx)? Big Shiny Red Question Mark is about to win a hand!”

Commentator 1: “I don’t believe it – two suits removed, three empty columns. There is no way he can lose from here. Only two face down cards. Plenty of time on the clock … and”

Commentators 1 and 2 (simultaneously): “Big Shiny Red Question Mark Resigns The Game!!!! Unbelievable!!! Rot13(haorshpxvatyvrinoyr!!!). What is this madness???”

n the post-game interview BSRQM explains there were no useful moves detected – therefore he had to resign. He squirms in his seat while the press continue to ask uncomfortable questions. Thankfully the absolute train-wreck of a post mortem doesn’t last long and everyone can head home. BSRQM is never heard from again and everyone lives happily ever after.

THE MORAL OF THE STORY: Cheats never prosper.

THE END

Game On (13 June 2021, Alternative Version)

“I think I have discovered the secret of playing well at Four Suit Spider Solitaire,” says the Cat. “I can win about 99% of the time.”

“How is that possible?” asks the Wise Snail. “Our best player is the Eagle, but she can only win about half the time”

“Well, there are many secrets to winning about 99% of the time,” replies the Cat. “The first secret I will like to talk about is minimum guaranteed turnovers. Expert opinion says on average you should have just under 4 guaranteed turnovers if the cards are dealt randomly. But I think it should be significantly higher.”

“How do you make it higher?” asks the Elephant.

“Let me show you,” replies the Cat. The Cat quickly deals another hand. The initial state is shown below:

“Yes. This is a good example,” says the Cat. “Observe that we start with two Jacks and one Queen. Ignoring the other cards for now, most experts will say this is worth one turnover – either the Jack of Hearts or Jack of Spades can move to the Queen in column Three. Most players will choose the Jack of Hearts for obvious reasons.”

“So far so good,” says the Lion.

“Now I want everyone to close their eyes,” says the Cat. “The Wise Snail will count to fifty and then everyone can open their eyes again.”

“Now I have two turnovers: I have superimposed both the Jack of Hearts and the Jack of Spades onto column 3 revealing two cards in columns 7 and 9.”

“This is revolutionary!” says the Dumb Bunny. “I wonder why nobody has ever thought of this before. I like it!”

All the students nod in agreement with their eyes wide shut. The Cat continues to move some cards around. Meanwhile the song I’m A Believer by Neil Diamond can be heard in the distance. Yes, The Singing Monkeys don’t have the best voices but my students are used to that by now.

At last, the Wise Snail reaches fifty and everyone can open their eyes.

“Cat is sus,” says Purple. “As far as I can tell, there are only eleven cards exposed. The Cat has made a solitary move: Jack of Hearts from column 7 to column 3, revealing the other Queen of Hearts.”

“Yes, it appears I have only made a single move,” replies the Cat. “But I also know that column 9 contains King of Diamonds beneath the Jack of Spades. Column 7 starts with Jack of Hearts, Queen of Hearts, Two of Diamonds, Seven of Clubs. Moreover, it is possible to get an empty column – ”

“But how would you know all this?” asks Orange. “You must have cheated!”

“And remember,” yells the rot13(fzneg nff), “the first rule of Spider Solitaire Club is you do not play with undo. The second rule of Spider Solitaire Club is you DO … NOT … play with undo!”

Purple immediately calls a meeting. A plurality vote is held and all twelve colours from Among Us decide that Cat is indeed sus.

“Sorry I’m late – hey rot13(jung gur shpx?)” I say. It takes me less than three nano-seconds to observe the Elephant has grabbed the Cat with his trunk and is about to hurl the poor thing in the direction of The Singing Monkeys. It doesn’t take long for my students to explain what happened.

“I know I normally don’t play with undo,” I state matter-of-factly. “But I wish to remind you that playing with undo was absolutely necessary for me to publish my paper on Spider Solitaire. And without this paper, I wouldn’t be maintaining this blog – which you are all part of.”

It’s a process, but I am able to eventually convince the Elephant to release the poor Cat. Also, in future when I am late nobody is allowed to give impromptu lessons during my absence.

Nobody ever hears from the Cat again. On the very next day, an unpleasant rumour starts spreading: the cat has somehow been poisoned. Unable to confirm any details, I can only assert that she is simultaneously dead and alive.

The End

Game on (25 April 2021, Alternative version)

Once upon a time, there lived a dude named Abraham Maslow. He kept to himself and had few friends. He brushed his teeth three times a day and only drank orange juice and water. His grades weren’t brilliant – then again he wasn’t terrible either. But like most folk at University, he found the lectures were boring. He was okay with Statistics, but would frequently ask himself why he signed up for Commerce and Law subjects. And the less said about Psychology the better. He would much rather spend time playing good ol’ Spider Solitaire.

During his early years he fantasised about obtaining long suited runs of cards and clearing entire suits before the third round of the stock was even dealt. But over time Maslow realised such wild dreams were only for mediocre players who never progressed beyond the Two-Suited version of the game.

There were no really good books on how to achieve awesomeness at Spider Solitaire so Maslow had to work everything out by himself. After much self-study he developed a “Hierarchy of Wants” for the aspiring Spider Solitaire player. At long last, Maslow found he could beat Four-Suit Spider Solitaire about 40% of the time without rot13(haqb).

Maslow’s theory suggested players often made two types of errors. Type I errors involved a player only focussing on stuff at the bottom of the pyramid. This often resulted in a player having no idea how to convert an empty column plus a handful of in-suit builds into victory. Maybe the game state rot13(fhpxrq) so badly in other respects so as to render the initial gains worthless. A Type II error occurred when a player laid too much emphasis on grand plans and triumphant C-major chords whenever a complete suit was removed (at least in the Microsoft Windows version). In other words, a winning player should be building on a solid foundation (hence the pyramid) before he starts thinking about the grand plans and triumphant C-major chords.

Typical flow charts for players committing Type I (top) and Type II (bottom) errors

Finally, Maslow realised that once the player obtained a decent win rate at the Four-Suit level sans rot13(haqb) he or she could attain further self-fulfillment with the attainment of cheevos, as described in a previous post.

Maslow gave the following example of Hierarchy-of-Wants in action. Maslow noted that the game-state allowed only one guaranteed turnover, and there is a desperate want for empty columns. There are few in-suit builds and only one run of three suited cards (in column 3). Therefore, the player should ignore the fact that the entire Heart Suit is visible except for the Four.

Maslow gives an example in his famous 1943 paper

After the usual cycle of constant revisions and rejections, Maslow was finally able to publish what was to become his famous paper “The Psychology of Achieving Awesomeness at Spider Solitaire”. And everybody lived happily ever after.