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!)

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