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

 

Easy Difficulty

Continuing my experimentation with Microsoft Spider Solitaire, I decided to try five hands on Expert difficulty level.

Recall that Expert is the easiest possible setting when you play with 4 suits. We therefore expect Expert hands will be easier than random hands.

Indeed when I tried playing Five hands at Expert level I crushed it. I won the first four hands and probably should have won the fifth, but for a lapse in concentration.

Getting trips (or even quads) when dealing a row of 10 cards occurred very rarely, and I had a healthy number of turnovers in round 0. Once I removed two complete suits the game was pretty much in the bag.

However, I should emphasize that removing two suits most definitely does not guarantee victory for Grandmaster level. And don’t get me started on Rogue Solitaire.

Recall that in a previous post, I ran the Gauranteed Minimum Evaluation Score on hands of various difficulty. Ninja Monkey said that he could win 4 Experts hands out of 50, but zilch on Master and Nada on Grandmaster.

I haven’t experimented with what various difficulty levels look like with fewer than 4 suits. Perhaps that’s some material for a future post 😊

Personally I like the idea of giving players the option of choosing a difficulty level as well as number of suits, and Spider Solitaire lends itself to this type of choose-your-difficulty. In contrast, the same cannot be said of games like Klondike or Freecell (one-suit is perhaps too easy even for a newbie)

Until next time, happy Spider Solitaire playing.

Choose Your Difficulty

The classic Microsoft Spider Solitaire software gives a Four-suit expert player a choose between Expert, Master, Grandmaster or Random hand.

With the pandemic not going away any time soon, I thought now is a good time to play three more hands of Spider Solitaire on my PC, choosing difficulty levels of Expert, Master and Grandmaster (while also honing my writing skills!). I easily won an Expert hand, but bombed the Master hand. I briefly entertained some miracle hopes on the Grandmaster hand, but quickly came crashing down to earth if you excuse the terrible cliché.

Ninja Monkey’s Guaranteed Minimum Evaluation Score algorithm yields a win rate of 4/50 on the Expert but 0/50 on the Master and Grandmaster hands.

Here is the Grandmaster board:

Round 0 looks promising with 4 turnovers (the average should be a tad under 4). Moreover, two of these turnovers are suited – but problems appear later.

After a promising initial deal it’s trips galore in almost every round. This reeks of a cold deck – if you’ve ever played late-night poker with some dodgy folk in the neighbourhood then you’ll know what I’m talking about. Then again, I did ask for Grandmaster difficulty.

In contrast three of a kind never occurred in any round of the Expert hand.

It is not clear if arranging three of a kind on nearly every round is an effective way to make the game harder (maybe the permutation of face-down cards in the tableau is also relevant) but it does suggest Microsoft is trying. In defence of Microsoft, they explicitly made it clear that the player will face a difficult challenge to win without boop. In fact I have no problem with the game being “rigged” if the player knows in advance the cards are not properly shuffled (in math terms we say a properly shuffled deck has 104! possible permutations of starting hands, ignoring equivalence of identical cards, and each permutation is equally likely). A player who chooses Grandmaster difficulty can’t say he wasn’t warned!

I will not discuss the strategy in detail. Rather I wanna discuss how easy it is for Microsoft to construct “easy” or “difficult” hands.

There are several ways one might go about constructing a difficult hand:

  • “Crowdsourcing”: give each hand a unique identifier (like a hash). If only e.g. 10% of players can win even with the help of boop, then chances are the game is difficult. If a good percentage of Microsoft employees like to slack off in their spare time this shouldn’t be too hard 😊
  • Design an evaluation function e.g. number of guaranteed turnovers for Round 0, or number of guaranteed turnovers if we pretend we start with the 10 cards in Round 3 instead of Round 0. The main difficulty is finding a good evaluation function.
  • Design an AI to play the game with or without boop. The main difficulty is designing a good AI is not trivial.

It is not clear which method Microsoft uses (my best guess is crowdsourding), but I agree they succeeded in arranging matters so that Grandmaster is harder than Expert (Master is perhaps equally hard as Grandmaster but I only have a sample size of three games, so I won’t jump to conclusions any time soon!)