The Chess Scandal Everyone Is Talking About

With the Sinquefield Cup finally over, I think now is a good time to give my thoughts on the scandal.

Strictly speaking, this doesn’t really belong in a blog that purports to talk about the Spider Solitaire, the whole Spider Solitaire and nothing but the Spider Solitaire, but I believe that Chess and Spider have (at least) one thing in common: strong players always get the raw end of the deal when it comes to cheating accusations. Besides, I have an IM title or better in both disciplines 😊

The basic problem is strong players just “know” when something is off – but good luck expressing the word “know” in language that a layman and understand and a lawyer cannot argue with. I count myself lucky I was able to actually prove that dodgy Spider Solitaire servers do exist.

Here is my opinion on the whole saga – which I have listed in dot point form. I will not attempt to justify these dot points. No doubt every man, dog and millipede on the planet has formed their own opinion on the matter. Googling various facts and coming to your own conclusions is left as the proverbial exercise for the reader.

Niemann is an rot13(nffubyr)
Niemann should never have been invited to play in the first place
Niemann has form when it comes to being an rot13(nffubyr) and cheating
Carlsen has good reason to withdraw, even without evidence of cheating. If cheating is proved then that is icing on the cake if you pardon the terrible cliché!
Carlsen doesn’t owe anyone an apology or explanation. If the tournament organisers wish to defend 2+2=5 (i.e. invite Niemann) that’s not Carlsen’s problem. Maybe Carlsen could have handled things better with hindsight, but his options weren’t great to begin with.

I won’t be surprised if Niemann counts a single victory against Carlsen as “surpassing his Key Expected Results”, even if he rot13(shpxf) up the rest of the tournament in every way possible

FWIW, I have a proposal for solving the cheating problem in chess, called the Useless Task Protocol. This is an attempt to give more “bargaining power” to the experts. Again, I will not attempt to justify the motivation behind this protocol and leave it as an exercise for the reader. If you can see where I am coming from, then chances are you have the right analytical mindset to excel at Spider Solitaire 😊

Useless Task protocol

I wish to propose a new rule for competitive chess:

That’s all there is to it. Just move your king towards the centre and leave your opponent with the “know-what’s-coming-but-can’t-do-much-about-it problem”. It doesn’t matter if you resign, get mated or your opponent starts playing random moves. You could have a dead drawn (or indeed a winning) position and still elect to call opponent for cheating. You can take a punt, knowing the worst that can happen is your game is counted as a loss. You could end up looking like a goose but there is no possible universe where can you get sued for defamation.

If your king can’t (legally) reach the centre, you can still call your opponent if you’re willing to risk heavy penalties for a false alarm. Conversely there is no compulsion to call opponent for cheating if your King is on e4 but you believe your opponent is legit.

I proposed this rule after the cheating scandal involving Nikhil Kamath and Vishy Anand, but nobody took it seriously. I do not claim it’s a perfect solution, but something worth mulling over. The diagram above shows a plausible position that might have arisen if the Useless Task Protocol was being used (I would recommend White should wait for Black’s next move before stopping the clock).

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.

Bart Wright and Schistocerca Americana awarded IM Titles

It’s official: after achieving victory on the Four-Suit version of Spider Solitaire sans rot13(haqb), with one impostor trying to rot13(shpx) things up at every opportunity I have decided to award both Bart Wright and Schistocerca Americana the title of International Master. It’s a bit of a misnomer in that we don’t get to travel all over the world to play in tournaments and prove we can mix it with the best – but I will stick with the IM title because it is considered the next level below GM and both players certainly displayed an extremely high level of skill. The other reason for the IM title is because it allows Spider GM to showcase himself at his brilliant worst. If you would like to guess the punchline before reading on, I have inserted the usual spoiler blocker.

In Chess, all titles are obtained by playing in enough tournaments and getting a sufficiently high score against decent opposition. Players can achieve “norms” in individual tournaments and you need enough norms to prove you didn’t get lucky in a single tournament. Your rating also needs to be sufficiently high. The good news is you don’t lose your title after a dip in your rating (or a string of bad tournaments), so you keep your title for life – save for something incredibly stupid, such as an arbiter finding compromising images of Stockfish recommending the best move on your mobile phone. This is fair enough: if there was no guarantee of keeping your title there would be much less incentive to achieve it in the first place. A GM title implies that your ability/talent is enough to mix it with the world’s best, provided you are willing to put in the time and effort and life doesn’t get in the way. An IM title is pretty much the same thing except “the next level down”. Then you get Federation Master titles and of course you can also add a W-hook (using the Scrabble vernacular) for female players. Hence WGM, WIM and so on.

Unfortunately, IM Schistocerca Americana is a bit of a mouthful even for somebody who recently composed a work-related rap song to the tune of Million Voices by Otto Knows. Therefore, he gets the indignity of being renamed IM Bug. And Bart Wright suffers an even worse fate:

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

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

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.” 😊

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

Artificial Stupidity in Chess

You may remember some time ago I discussed an algorithm for Spider Solitaire that is not very good: it simply outputs random moves. It turns out somebody did a much better job in the game of chess. Some dude designed no less than 30 Artificial Stupidities and organised a Tournament of Fools, and published a number of papers in SIGBOVIK. Ideas for weird algorithms include color preference (e.g. White prefers to play pieces onto light squares), random moves, blindfold algorithms (simulating a novice trying to play blindfold), algorithms based on mathematical constants like π and e, single player (pretending opponent will pass) and linear interpolation between Stockfish and some other lousy algorithm (e.g. choose Stockfish’s best move with probability p, lousy move with probability 1-p. But my favourite algorithm was the Mechanical 68,79,82,75 that proved a forced win for Black after 1 d2-d4?? a7xd4!! checkmate 🙂

You can watch all the fun in the video below:

I’m not sure if these ideas will be applicable to Spider Solitaire. Color Preference is easy since we can prefer to move red cards or black cards, and single-player is even easier given the nature of the game, but I am not aware of any equivalent of Stockfish. Mathematical constants should be easy but probably not very interesting. It may be possible to simulate a blindfold (human) player who struggles to remember every card, but I’m, not sure how to do that yet. And I don’t know of a (sensible) variant of Spider Solitaire where all the red cards are replaced with chess pieces. Since Western chess has Black vs White, it may be more appropriate to use Xiangqi, which has Red vs Black pieces. Perhaps something to think about for next time.

Thanks to my good friend Tristrom Cooke for the heads up.

Evaluating a Start Position

We now consider the following question: How can we evaluate a starting position? That is, if you are given an initial game state with 10 exposed cards how do we determine if the chances of winning are good, average or poor? Can we quantify our winning chances as a percentage (e.g. 58%)?

NOTE: evaluating a start position is useful since most Spider Solitaire implementations allow the player to abandon a game without counting it as a loss. But if you are serious about improving your game, I strongly recommend you never abandon games with a poor initial state.

A first thought may be to look for “features” of a game state. For instance suppose we are watching some top quality chess at an unhealthy time of the day. We might notice that

White has an extra pawn
The position is an endgame: both sides want to activate their king without fear of suddenly being mated.
Black’s rook and king are more active than their opposite numbers
Both sides have vulnerable pawns

Bear in mind we are only identifying individual features at this early stage. Eventually we may wish to formulate an overall assessment by combining these features somehow, but that comes later.

QUESTION: What are plausible features to use in an opening game state in Spider Solitaire?

How would you evaluate this starting position?

Avid readers of this blog (yes you!) would immediately identify “guaranteed turnovers” as a possible feature. In the above diagram you should be able to quickly identify 5 turnovers. Of course every man, dog and millipede on the planet knows that building in-suit is even more desirable. In this case we have Q-J in spades and 2-3 in clubs. Therefore we have 2 guaranteed suited turnovers (and hence 3 off-suit turnovers).

Finally we can look at rank multiplicity. All players know that having too much of one rank can be a problem, especially when the adjacent rank is in short supply. You don’t need a Ph. D. in economics to work out things are less than ideal when the Spider Solitaire gods have supplied five Jacks on the opening deal and there is little demand for them. For simplicity let us define the rank multiplicity as the count of the most frequent rank. For instance the above diagram has a rank multiplicity of 2 since we have two Threes/Deuces and no rank appears more than twice. In summary:

We have 5 guaranteed turnovers
We have 2 guaranteed suited turnovers
The rank multiplicity is 2.

There may be other features to consider, but we’ll keep things simple for now.

Are these values good, bad, or average? It turns out one can use simulation to answer this question. For instance if I had nothing better to do, I could play 10 million games of Spider and compute the number of guaranteed turnovers should be 3.97 on average.

Of course the lazy solution is to write a computer program to do the simulation for me. The program can simply deal 10 cards, do the relevant calculations and then abandon the game. An even lazier solution is to copy the results from Steve Brown’s excellent book Spider Solitaire Winning Strategies. He got the following results:

Looking at these graphs, I would immediately dismiss rank multiplicity as a useful feature (the entry for 5 is non-zero but is too small to be visible). After all more than 90% of games will have a value of 2 or 3! It is true that one can tweak rank multiplicity somehow (e.g. giving more weight to Aces and Kings which are the bugbears of most players), but I wanted to keep things simple for the time being. The important point is these quantities are easily obtained via simulation.

Suited turnovers is nice, but I think it’s more important to have many turnovers at the start of the game. In other words, quantity is more important than quality. In the above example, we have 5 guaranteed turnovers and 2 suited, both of which are above average. Hence if given a choice, I would take this position over a random position.

If you are a beginner, I would estimate that:

If you start with exactly 4 guaranteed turnovers, your chances of winning are average
If more (less) than 4 then your chances are above (below) average.

Of course if you lose every game at the 4-suit level then this rule only works when you have exactly 4 turnovers! So perhaps this rule is better suited to the 2 suit level, if you excuse the lousy pun. As you gain more experience, you would be able to tweak these guidelines. For instance, you might think that two suited turnovers is worth an extra non-suited turnover, etc.

That’s it for now. Happy Spider playing, and may all your builds be in-suit 😊