A closer look at Choose Your Difficulty

In Microsoft Spider Solitaire a player can choose 1/2/4 suits and a difficulty level. A player can gain Experience Points by winning games of Spider Solitaire, and after gaining enough XP he can level up. After sufficient levelling up, the player might even win some percentage of Microsoft shares or dot com stock options … uhhh just kidding 😉

The XP gained is shown in the table below.

Experience Points Table

The first thing to notice is not all combinations of “suit count” and difficulty are legit. For instance there is no Grandmaster hand at the 1-suit level and the minimum difficulty for 4-suit level is Expert. A random deal presumably means the deck is properly shuffled (in math terms all 104! hands occur with equal probability if we ignore the equivalence of cards of the same rank and suit), and the player is explicitly warned that such deals may be unsolvable. Any deal other than random is guaranteed to be solvable with sufficient luck or the use of boop.

Obviously it is difficult to measure the true worth of how hard a game really is. For instance if we played 1-suit then should beating an Easy and Medium hand be worth the same as beating a Hard? At least  increasing the number of suits or difficulty level results in increasing the XP gained, which is what we expect. So far so good.

However, I noted the XP gained for a random deal is equal to the XP gained for the lowest permissible difficulty level for the same number of suits, and this makes little sense.

For sake of argument 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 level (although I know that many folk will dispute that claim!) so the above example should really have e.g. 301 = 100+100+100+1 hands instead of 400. Essentially Random is equivalent to “Random but guaranteed winnable”. Therefore the same reasoning says a Random hand should be worth less than a Grandmaster hand.  Perhaps a Random deal should be worth the same as a Master deal, Maybe a little more or little less. But it certainly should be worth more than Expert. Of course, similar considerations apply to the 1-suit or 2-suit levels.

Perhaps some dude who is much, much smarter than I am can write a Ph. D. on the true worth of XP for a given difficulty level and number of suits. Another Doctor of Spider Solitaire anyone??? 😊

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