Estimating the difficulty of a Spider Solitaire hand

We now consider the following question: Given a Spider Solitaire hand, how can we determine the probability of a human expert winning without 85,78,68,79?

Clearly, we have to determine the identity of every face-down card (barring pathological cases where the hand is so bad you can mathematically prove certain defeat without knowing all the cards). The good news is this should almost always be possible given enough patience (and skill).

The bad news is estimating the difficulty of a hand is far from trivial.

I know that the first 10 cards dealt is a poor indicator of winning chances. Yes, most players will get a warm fuzzy feeling if the opening hand gives six guaranteed minimum turnovers and three in-suit builds – but Spider Solitaire is a marathon not a sprint (terrible cliché I know) and there is plenty of opportunity for a good start to sour, or conversely, to recover from a poor start. Other features like “four Queens in the third deal” or (heaven forbid) “all odd cards in the fourth deal” are likewise unreliable indicators – we usually have to consider the whole board. The only exception is if there are no two adjacent cards on the final row of 10 cards (e.g.  A44A7499KJ) – in which case the game is automatically lost unless you get a lucky in-suit build (e.g. the Jack falls onto a Queen of the same suit).

Here is the starting hand of the game I played many months ago and finished last week (a minus sign indicates a face-down card and rows from the stock are dealt starting from the left). Can you think of any “features” that would indicate whether the game should be easier or harder than normal? Let me know in the comments below!

(To be continued …)

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