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

 

Game over, we win!

Continuing from the previous post, the recommended action is

  • Clear the Spade suit
  • Exchange the 6-5-4-3-2-A of Hearts in Column 5 with the 6-5-4-3 of Clubs in Column 6.
  • Dump the 9-8 of Clubs in Column 3 into the empty column
  • Clear the Heart suit, winning back the empty column
  • Shift the Qh-Jd onto the Kh in Column 1, turning over a face-down card in Column 6 (and keeping an empty column)

Note that I went to the extra effort to clear a card in Column 6 rather than Column 5. This is because clearing cards in Column 6 is harder than Column 5 (especially since the Q-J are offsuit). As a general principle it is often wise to save an easy task for later and get the “difficult task” over and done with whenever possible – this helps avoid the embarrassing situation of “One Hole No Card” as alluded to in a previous post.

The resulting position is shown below, with the newly-exposed card redacted.

This is a lock

The astute reader may have noticed I violated the principle of procrastination by removing the Spade suit unnecessarily. This is because the game is in fact mathematically won.

To see this, let us consider all possible face-down cards (which we identified from last week):

  • Queen of Clubs: this can go “underneath” the Jack of Clubs (Jack onto Queen, winning an empty column, Q-J to Column 8, losing an empty column)
  • Queen of Diamonds: this goes onto the King of Clubs
  • Ten of Clubs: this goes onto the Jack of Clubs
  • Ten of Diamonds: this goes onto the Jack of diamonds
  • Ten of Hearts: this goes onto the Jack of Hearts
  • Nine of Diamonds: this goes underneath the 8-7 of Diamonds
  • Seven of Clubs: this goes onto the Eight of Clubs
  • Six of Hearts: we will count this as a “bad card” since the 7 of Diamonds is offsuit (and will counterfeit the Nine of Diamonds). This goes into the empty column
  • Five of Hearts: This is a bad card and goes into the empty column.

Note that the first seven cards are good, and we don’t even require an empty column to achieve the corresponding action. The only possible snag is there are two bad cards and only one empty column. But wait! If we draw both the Five and Six of Hearts then we can immediately place the Five on top of the Six. The net effect is to condense two bad cards into one – hence there is no snag after all.

Finally we also check that there is no issue with one-hole-no-card. Assuming we turnover all cards in Column Six first we will eventually get an empty column in Column Six and then we can choose randomly between shifting the Jh in Column 2 or the 9-8-7 of Hearts in Column 5 into the new empty column. Essentially we are “pretending” that all nine face-down cards are in Column 6.

It turns out the redacted card is the Seven of Clubs. The rest of the face-down cards in Column 6 are: Ten of Diamonds, Queen of Clubs, Queen of Diamonds.

The starting layout is shown below

Summary

This was a difficult game. The first ten cards were average, a minimum of three guaranteed turnovers, but two in-suit builds and no Aces or Kings. I only turned Four cards in round 0, but had an excellent Round 1 with several turnovers thanks to an empty column, but then got a catastrophic middle game with four Kings appearing on the same deal. Just when a loss seemed certain, I managed to find chances by clearing a complete set of Spades. I procrastinated by waiting until both Spade Kings were exposed so then I could decide which was the better King to remove. On the last round, I had three guaranteed turn-overs and realised all hope was not lost. I survived kadoban in the endgame and managed to win. I worked out victory was mathematically certain with only nine face-down cards remaining.

I hope you enjoyed playing through this game as much as I did.

Merry Christmas and Silly New Year!

Spider GM, Ninja Monkey, Ninja Mouse, Bad Idea Bears, all the other animals in the Animal Kingdom, individual playing cards, the two project managers, their team players, and anybody else who appeared in at least one silly story that I have forgotten would like to wish all Spider Solitaire players a merry Christmas and silly new year 😊

Coming soon in 2020 to a place near you: More Of The Same

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.

Monkey wins Man vs Wild

And it’s over! Spider GM played well to win 8 games, but monkey went one better with 9 victories. Most of the games were easy, but there were a few exceptions. Game 3 was just horrible: the final round was 833A5A8jk4 which is close to an instant loss (assuming no lucky suited connector such as a 3 landing on a 4 of the same suit). And that was not the only problem. Both human and monkey “agreed” on every game (i.e. both win or both lose) except game 4. Spider GM never found an empty column since the tactics were all wrong. Even so, 64% by the monkey was not the most convincing of victories. The conclusion is that the monkey’s win rate should have some correlation with an expert playing 4-suit solitaire. In other words, the effects of making random moves and playing at the one-suit level pretty much cancel each other out.

GameSpiderGMMonkey
1win89%
2win 64%
3lose26%
4lose 64%
5win67%
6win72%
7win79%
8win55%
9win62%
10loss36%
points7eight

Of course 10 trials is not a lot of data, and perhaps I need more games to say for sure. Also, lesser players may find similar results, but the threshold should be e.g. 30% not 50%.

Congrats to Monkey for a well-earned win and commiserations to Spider GM.

BTW If anyone knows how to change the word “eight” in the above spreadsheet into a number 8 without the unwanted percentage sign, please let me know 🙂

 

Man vs Wild!!!!!

And now for something completely different:

A human and monkey will do battle against the fickle card gods as they fight for ultimate survival on a virtual reality of 104 playing cards in the double-decker series of MAN VS WILD.

Spider GM and Ninja Monkey have agreed to play 10 “episodes” or pre-set hands of their fave game. Spider GM wins if he can remove all eight suits without 85,78,68,79. Ninja Monkey will pretend all games are played at the 1-suit level and he wins if he achieves a 50% rate or better if the game is repeated 100 times. Whoever wins the most hands will be declared the winner (or a tie is declared if they win an equal number of games). Note that Spider GM and Ninja Monkey are not versing each other, so they can possibly both win or both lose the same hand.

On each hand, Spider GM will record his result (win or loss) as well as the rank of every card in the initial game state. Then he will feed Ninja Monkey the same hand and Spider GM will record Monkey’s win rate. Spider GM will also give a subjective assessment as either “convincing” (easy win or loss) or “marginal”.

NOTE: if Spider GM cannot win a hand without 85,78,68,79, then he will try to win a hand with 85,78,68,79. This is necessary otherwise Ninja Monkey won’t be able to play the same hand. It is tacitly assumed this will in fact be possible. If it is not possible then we will cross that bridge when we come to it, if you excuse the cliché!

Let the games begin!!! (cue theme music for Man vs Wild)

Continued …

The Cadillac of Solitaire

The reader may be familiar with Klondike and Freecell. In Klondike, exposed cards are always ordered. For instance, if an exposed Seven of Hearts is covered by another exposed card, the latter must be one of the two black Sixes. This means the number of legal game states is much smaller than a game with “random rules”. The “non-trivial” part of Klondike of course comes from the face-down cards. Freecell is a famous game because it should almost always be won with perfect play. With all cards exposed, any initial game state can (in theory) be analysed to a certain win or certain loss before making a single move. The “non-trivial” part of Freecell comes from the fact exposed cards are not necessarily in order. For instance, the Seven of Hearts can be covered by any other card, not just the black Sixes.

As you might have guessed, Spider Solitaire combines the non-trivial aspects of both Klondike and Freecell. With half the cards face-down there is no question of certain victory or defeat at the start. The fact that exposed cards are not necessarily in sequential order yields several orders of magnitude of extra possible game states, and hence much greater scope for interesting strategy.

Oh, did I mention that Spider is played with two decks instead of one?

Local vs Global

The last point I wish to discuss is the concept of local vs global. If you have played board games like Die Siedler von Catan or Agricola, you probably know that the early rounds of a game have “small-scale plans”, but the middle game is where “deep strategizing” and “maximum tension” occurs. The endgame is where the tension ceases, presumably because everybody knows one player has a decisive advantage and it is basically impossible to lose, except by tanking. The ideal curve is shown below (disclaimer: I only got ‘C’ in Year 10 art).

Note that the peak is not centred, but is closer to the end than the beginning. Although I am not the world’s greatest expert on Board Games in general, I think the most successful games tend to obey this curve. Obviously if you play Catan 100 times, not every game will have the ideal curve: for instance, one game might be easily won by Player 3 thanks to some lucky rolls at the start. But most of the games will be “fair” and everyone feels they started with a decent chance to win.

In my experience, I think Spider Solitaire has a reasonable time-tension curve. In the beginning the player is concerned with short-term plans such as exposing as many face-down cards as possible. In the middle game, the tension increases because there are a large number of cards in play, and the player is usually aiming to clear a complete suit or two. Spider only allows complete suits (instead of single cards in Klondike or Freecell) to be moved to the foundations and it is rarely possible to achieve this with short-term planning alone. Assuming the player is successful, the tension decreases because the player is practically certain of victory. Technically one can still search for the very best moves, but by this stage the player is probably playing on auto-pilot.

So there you have it. Hopefully my first blog post gives you some idea of why I consider Spider to be the Cadillac of Solitaire. Okay, this entire post probably didn’t make much sense because I haven’t even explained the rules … I should probably start with that on my next post 😊

Toodle pip and piddle too, ciao 😊

My first meaningful post, hooray! :)

Why Spider Solitaire?

Welcome to my blog on Spider Solitaire.

In an age dominated by Netflix, Fortnite, Randy Rainbow songs, internet memes, griping about the NBN, checking Twitter feeds every 5 minutes, Tetris99 (okay, even I have to admit the concept is kinda cool) and what-not, it seems Spider Solitaire (indeed most abstract mathematical games in general) is becoming a lost art. If you’ve never heard of the game you’re not alone. I’ve even come across one dude at work who didn’t even know what Sudoku was one year after it became a thing. But I digress.

Like most armchair critics, I consider myself to be pretty good at Spider Solitaire. But I also have some concrete data: I can win about half the time on four-suit level without undoing moves. I know very few people who have claimed (let alone proved) to be expert at Spider Solitaire. Certainly one can google basic strategies easily enough, but I find most of it to be superficial. For instance, Joe Bloggs might show a complete game from start to finish, but the game turned out to be ridiculously easy. Jane Citizen might say that empty columns are better than smoking, it’s always better to build sequences in the same suit and bears defecate in the woods. But that fails the Duh Test since every man, dog and millipede on the planet could have figured that out by themselves. I believe Spider Solitaire is a lot deeper than the trash advice I found on the internet. Hence this blog was born.

Okay, so what is Spider Solitaire?

You have made it to the final table of the World Series of Spider Solitaire. You look at the left-most column. The Seven of Hearts, then the Deuce of Clubs, followed by five face-down cards. After studying the rest of the layout you announce that you are all-in! The audience gasps with horror: is this guy on tilt? Unperturbed, you shift the Seven and Deuce out of the way and expose the hidden cards one by one. The last card gives you a straight flush in diamonds, which you immediately move onto the foundations. You take a large bite of your last Oreo. Crunch. Victory is mathematically certain and the rest is a formality. You take home an $8 million pay cheque and a gold bracelet and the good guys live happily ever after … or something like that.

Okay that’s probably not the most accurate description of how the game is played, but I do believe Spider is the Cadillac of Solitaire games.

Spider, the Cadillac of Solitaire Games (with apologies to Doyle “Texas Dolly” Brunson)

To be continued …