# A new game!

It’s been a while since I’ve done one of these, but with my work year done for 2020 I should have a lot more spare time on my hands for the next few weeks 😊

In this “experiment” I will try a game of Four-Suit Spider sans rot13(haqb) at “random” difficulty. Random means the cards are perfectly shuffled (so for the mathematical cognoscenti among you there are 104! possible hands ignoring equivalence of cards with same rank and suit and each hand occurs with equal probability), and there are no consideration for hands being “rigged”.

To spice things up let us say I need to complete all eight suits AND obtain a score of 1000 or better. In this version of Spider Solitaire, each move costs a point and each complete suit is worth +100. This adds some complexity to the game since I can’t make too many “reversible moves” without thinking.

Before I start the game, I will encourage some audience participation by asking a simple question:

Is this hand better or worse than “average”? In other words, if you had a choice of accepting this hand or choosing a new one what would you do? (assume that you can only take one mulligan). Please let me know in the comments below 😊

# Game on (27 May, 2020)

Here is the position from last week:

We are guaranteed three turnovers and there are several ways to achieve this. It would be difficult even for an expert player to visualise the final state once we get the three (or more) turnovers. Obviously, much will depend on the newly exposed cards, but the following sequences should give a general feel of how the game might play out:

<ja, jc, hc, hc, bd, fb, fi>

<ja, jc, hc, hc, bd, fb, ib, fb>

<ag, ad, jg, jc, hc, hc>

<ag, dj, ed, jg, ag, jc, hc, hc>

Looking beyond the number of turnovers, we see it may be desirable to build in-suit with e.g. the 2-A of Diamonds or 6-7 of Clubs. We might wanna start a junk pile on the King of Clubs so that other columns become easier to deal with later. Or we might wanna start thinking about obtaining an empty column ASAP. And don’t forget the virtues of procrastination – the more flexible the game state the better our chances will be. So there is plenty to think about (assuming you are serious about improving your game!)

I executed the following moves. It is beyond the scope of this blog post to explain every decision in detail:

<ja,jc> Qs

<hc,hg> 4h

<hb> 3s

<da,ba,ha,ed,ea> 7d

Now that we turned over a Seven, it becomes clear to shift the Queen in column f (not column j) to expose an Eight. Of course we can improve this plan slightly by procrastination i.e. dumping the Seven onto the empty column.

<eh> 2c

<fb, fi> Qc

Things have settled down somewhat. We have an empty column, but must use it immediately to turn over a new card. We can do some significant tidying. For instance the J-0-9 in column c can shift onto one of three queens. Even though we can’t immediately turn over column c, it might become available next round. Several other shifts are possible (an exercise for the reader!). In other words, there are several plausible actions to choose from.

What would be your play here?

# Game on!

I am now ready to walk through a complete game of Spider Solitaire.

Without loss of generality, I will assume that every man dog and millipede on the planet has read every post in Edifying Thoughts of a Spider Solitaire Addict and is keen on improving their game. I have already discussed various concepts such as guaranteed turnovers, procrastination, completing suits, Gantt Charts etc. I have also dabbled in a bit of math behind the game and of course I have my journal publication in Parabola.

I will try to beat a single hand of 4-suit Spider, sans 85,78,68,79 and discuss critical or interesting moments of the game. Updates on the game will occur about once per week, and of course I won’t neglect the silly stories involving Monkey and his friends along the way 😊

For now, we will start with a random opening position and try to answer the following questions:

• How many cards are we guaranteed to turn over?
• How many in-suit builds are we guaranteed?
• Assuming we win 10 points per turnover and 1 point per in-suit build, and no 1-point penalty per move what is our Guaranteed Minimum Evaluation Score?
• What would be your opening move?
• Do you think this is a good, bad or average starting hand?

We are guaranteed to turnover 3 cards with correct play, 2 of which are in-suit. Our Guaranteed Minimum Evaluation Score is 32.

Our opening move is a no-brainer. We can shift the Seven of Hearts onto either Eight of Hearts in the first two columns. It’s the best of all possible worlds: we build in-suit and we are turning over a column with only four face-down cards instead of five (recall that our first priority is obtaining an empty column). And we also have two spare Eights.

The fly in the ointment is we only have 3 guaranteed turnovers. In an earlier post I wrote that 4 turnovers should be considered average. At least we have two in-suit builds and no Aces or Kings exposed. In other words, given that we only have three guaranteed turnovers our starting hand is about as good as it gets.

Any odd-numbered card or a Ten will give us at least an extra turnover: hence it is heavy odds-on that we can turn over more than 3 cards. Note that since our first build is in-suit we don’t have to worry about “losing an out” (e.g. Move J onto Q off-suit, expose a K, drop the 70,66,79,77,66). Of course if I was playing on the Blue Screen of Death instead of the Windows version then there would be a fair chance of having exactly three turnovers 😊

Being the self-proclaimed Grand Master of Spider Solitaire, I will estimate our chances of winning this hand are fair.

Till next time, and may all your builds be in-suit 😊