Evaluating a Start Position

We now consider the following question: How can we evaluate a starting position? That is, if you are given an initial game state with 10 exposed cards how do we determine if the chances of winning are good, average or poor? Can we quantify our winning chances as a percentage (e.g. 58%)?

NOTE: evaluating a start position is useful since most Spider Solitaire implementations allow the player to abandon a game without counting it as a loss. But if you are serious about improving your game, I strongly recommend you never abandon games with a poor initial state.

A first thought may be to look for “features” of a game state. For instance suppose we are watching some top quality chess at an unhealthy time of the day. We might notice that

• White has an extra pawn
• The position is an endgame: both sides want to activate their king without fear of suddenly being mated.
• Black’s rook and king are more active than their opposite numbers
• Both sides have vulnerable pawns

Bear in mind we are only identifying individual features at this early stage. Eventually we may wish to formulate an overall assessment by combining these features somehow, but that comes later.

QUESTION: What are plausible features to use in an opening game state in Spider Solitaire?

Avid readers of this blog (yes you!) would immediately identify “guaranteed turnovers” as a possible feature. In the above diagram you should be able to quickly identify 5 turnovers. Of course every man, dog and millipede on the planet knows that building in-suit is even more desirable. In this case we have Q-J in spades and 2-3 in clubs. Therefore we have 2 guaranteed suited turnovers (and hence 3 off-suit turnovers).

Finally we can look at rank multiplicity. All players know that having too much of one rank can be a problem, especially when the adjacent rank is in short supply. You don’t need a Ph. D. in economics to work out things are less than ideal when the Spider Solitaire gods have supplied five Jacks on the opening deal and there is little demand for them. For simplicity let us define the rank multiplicity as the count of the most frequent rank. For instance the above diagram has a rank multiplicity of 2 since we have two Threes/Deuces and no rank appears more than twice. In summary:

• We have 5 guaranteed turnovers
• We have 2 guaranteed suited turnovers
• The rank multiplicity is 2.

There may be other features to consider, but we’ll keep things simple for now.

 Are these values good, bad, or average? It turns out one can use simulation to answer this question. For instance if I had nothing better to do, I could play 10 million games of Spider and compute the number of guaranteed turnovers should be 3.97 on average.

Of course the lazy solution is to write a computer program to do the simulation for me. The program can simply deal 10 cards, do the relevant calculations and then abandon the game. An even lazier solution is to copy the results from Steve Brown’s excellent book Spider Solitaire Winning Strategies. He got the following results:

Looking at these graphs, I would immediately dismiss rank multiplicity as a useful feature (the entry for 5 is non-zero but is too small to be visible). After all more than 90% of games will have a value of 2 or 3! It is true that one can tweak rank multiplicity somehow (e.g. giving more weight to Aces and Kings which are the bugbears of most players), but I wanted to keep things simple for the time being. The important point is these quantities are easily obtained via simulation.

Suited turnovers is nice, but I think it’s more important to have many turnovers at the start of the game. In other words, quantity is more important than quality. In the above example, we have 5 guaranteed turnovers and 2 suited, both of which are above average. Hence if given a choice, I would take this position over a random position.

If you are a beginner, I would estimate that:

• If you start with exactly 4 guaranteed turnovers, your chances of winning are average
• If more (less) than 4 then your chances are above (below) average.

Of course if you lose every game at the 4-suit level then this rule only works when you have exactly 4 turnovers! So perhaps this rule is better suited to the 2 suit level, if you excuse the lousy pun. As you gain more experience, you would be able to tweak these guidelines. For instance, you might think that two suited turnovers is worth an extra non-suited turnover, etc.

That’s it for now. Happy Spider playing, and may all your builds be in-suit 😊