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:

“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