Estimating the difficulty of a Spider Solitaire hand (continued)

Continuing from last week, our task was to evaluate the probability of winning the following starting layout.

I find the best indicator of probability of winning is “playing the hand out”, either manually or getting one of my animal friends to do it, such as Ninja Monkey.

For instance, I might attempt to win the game without boop but during the course of play I have a chronic shortage of Nines and lose badly. I would then examine the starting layout and say to myself “okay, now I understand why I got a shortage of Nines.” The point I am making is that it’s much easier to identify potential problems after playing the hand out. Conversely, I might be able to clear two suits before dealing the second row of cards and guess the game is extremely easy.

In our example above, we can check there are three guaranteed turnovers at the start. The middle row from the stock has four kings, but I still managed to win without boop. However, during the mid-game I estimated a loss was almost certain. For this reason, I would estimate the game to be “maximum difficulty” or close to it. Unfortunately, this assessment is hard to convert into a number.

Fortunately, Ninja Monkey can help me out here. He can simply simulate his improved strategy. Essentially his strategy involves optimising the guaranteed minimum evaluation score given the information provided by face-up cards – and it is good enough to win random deals some of the time (i.e. not ridiculously close to zero). Ninja Monkey’s assessment may not be accurate (his strategy still has serious flaws) but at least we get a “quantitative” estimate (probability of winning) rather than some qualitative 83,72,73,84.

It turns out Ninja Monkey could win 2 trials out of 50. To be honest, I was expecting zero wins from 50 attempts (of course the win rate should be non-zero given enough attempts since I did manage to win).

I believe a player should be awarded a Doctor of Spider Solitaire if he can beat a hand without boop even though Ninja Monkey estimates a win rate of 0/50 with his guaranteed minimum evaluation score algorithm

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