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

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.


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 …)