This was a well-played game by Steve. There were no major inaccuracies and he overcame a difficult start. He kept himself in the game and only after dealing the final 10 cards he had a good position for the first time. And he duly converted. Of course I would bet my Ph. D. thesis to a brick that Steve cherry-picked that game out of over 300+ games to demonstrate it’s possible to win even with a bad start. It is highly likely a fair percentage of Steve’s victories were walkovers after a good start.

There were a few inaccuracies like not realising he can get another in-suit build at no cost, or missing the fact some column had a 5 missing (easy to do when you have a sequence like 8-7-6-4-3-2-A). But there is no individual play that screams “ThIs GuY cAnNoT pOsSiBlY bE a GM”. If I had to give a single pointer for Steve to improve his game even further, I would choose the concept of “good and bad shape in individual columns”.

Steve has a good feel for the game. He can anticipate the Job 38:11 problem several moves in advance, and either he will find a way around the problem or at least avoid acting surprised when it does hit. He does not explicitly mention “one-hole-no-card” – but that’s merely one of many ways of explaining a concept that Steve is no doubt familiar with.

Steve was unable to get close to removing a suit before the last round – but not for lack of trying. The card gods decreed there would be no reasonable prospect of doing so before the last round – and then Steve showed his skill when it mattered most:  he found a plan that guaranteed the removal of a complete suit. It was relatively straightforward to verify removing the suit was not a trap, and victory was a mere formality.

The process of finding the correct plan at the start of round 5 is not trivial, and admittedly I glossed over that. Steve gives plenty of examples of finding a good plan in complex positions in other chapters of his book. I recommend you get the book (if you haven’t already done so) and study his thought processes for the examples given by him.

As for Steve’s book, my main criticism is that his notation for moves is very unwieldy. Yes, I get that he is trying to explain important concepts like “breaks, doors, locks, delaying, etc” but I am pretty sure there is a way to get his message across without resorting to clumsy notation. Apart from that, the entire book is an extremely useful resource for someone who is serious about improving their game.

Overall Strength

Overall, I would say Steve is GM strength, or close to it. Unfortunately it’s difficult for me to judge properly unless I had access to the moves in all of the 306 games he played.

I will only give the general plans and avoid giving exact move sequences. Verifying this is all legit is left as the proverbial exercise for the reader.

As a general rule, being able to visualise long move sequences is an essential ingredient to playing well at Spider Solitaire. If you struggle with this, I recommend you play with “pseudo-undo” i.e. undo is allowed provided you don’t gain information you’re not entitled to by turning over a card or dealing from the stock (note that removing a suit does not gain information). If you pardon the terrible cliché, practice makes perfect!

Another useful tip is this sort of situation is to start with the following question: “Can I remove a suit if I were willing to trash my board in every way possible?” If the answer is yes, then a more careful analysis will often yield a way to remove a suit without trashing up the board so badly. Of course, there are cases where prematurely removing a suit does cause the loss of a winnable game – but if you’re able to find a move sequence that completes a suit, then you should be good enough to work out if removing a suit is desirable.

• Clear columns 2, 3
• Extract the C4:Kc
• Expose the C0:7h

• Clear columns 7,10
• Order column 8

• Tidy up

• More tidying up

By this stage even my Ninja Monkey friend is claiming the game is won.

• Clear the Spades

The rest of the game is just a formality so the moves are omitted. The identity of the remaining face-down cards are available in the screen-dump below:

And that brings us to the end of the game. Well played Steve!

Here is the start of round 5 after Steve deals the last ten cards from the stock.

In some sense, the last round is the “simplest” to calculate. Since the stock is empty, there are no more possible surprises associated with 10 new cards appearing simultaneously rather than sequentially. Most of the time, an empty stock implies the winning chances are either very very good or very very bad. Whereas, in previous rounds we have to make do with general considerations and “fuzzy evaluations” such as “we have good winning chances but not enough to justify sending over a Backgammon doubling cube with the ‘2’ face up”.

Of course, one can argue the last round is “hardest” to calculate since there are so many cards. To play the last round well you will need a LOT of calculation. Steve correctly points out the ability to calculate is a necessary (but not sufficient!) condition to achieving a high win rate at the Royal Game.

Another peculiarity of the last round is that most of the time at least one full suit will be visible (or it has already been moved to the foundations). For instance, every card in Hearts can be found in column 1, 5 or 8. Obviously we wanna work out if we can guarantee removing at least one suit. Most of the time, once you are able to clear any complete suit, everything else will collapse.

In the next post I will discuss how Steve proceeds from here. You may wish to analyse this game state for yourself and come to your own conclusions. If you do so then I recommend you give only a “general plan” rather than specific moves. Also, stop as soon as you turn over any face-down card. Your answer would look something like the following: (this is a template only and does not apply to the current hand).

(1) obtain two empty columns (2) Tidy up so we have a complete Heart suit missing only the King (3) Dump the K of Spades into an empty column (4) Win back another empty column (5) Complete Hearts (6) burn all empty columns to turnover a card in column 8.

Continuing our game. Steve’s only possible turnover is in column 2, albeit at the cost of splitting Aces.

In some cases it may be wise to spurn a turnover “for the greater good”, but not today. There is a fair chance of two turnovers, and the alternatives ain’t so attractive anyway.

Steve is able to turn both face-down cards in Column 2. They are the Eight of Clubs and Two of Diamonds. The good news is he has recovered the empty column.

The bad news is – yes you guessed it – this brings the familiar one-hole-no-card. Steve elects to shift the C8:4s into the empty column. Not a great choice, but I’m not seeing anything significantly better. Personally I would be loath to expose another Ace. I would prefer to move “jg”, maintaining the status quo and hoping to make progress after the next round.

This situation (one-hole-no-card) does happen more than we would like to admit. Usually what happens is an empty column gives us at least many different options to choose from and each option will be worth “some fraction of a turnover”. For sake of argument, suppose that we have a free and open source Spider Solitaire engine called StockSpider, and that StockSpider evaluates every turnover is worth an equity of +1.0. Building in-suit is worth +0.2 (on average), exposing an Ace is worth -0.2, having an atomic column is worth +0.1 and so on. Given so many options, sheer numbers dictates that we should be able to get some value from our empty column despite no turnover. Maybe some minor achievements here and there will add up to +0.5 or +0.6. Basically, one-hole-no-card isn’t necessarily the end of the world as we know it.

The observant reader will have noticed Steve failed to build in-suit with ed before wasting the empty column. Presumably Steve wants to get as much junk off column 4, since that is clearly where our most likely source of turnovers is coming from. However, it was actually possible to play “e3=d1” before burning the hole (an exercise for the reader). This allows us to have our anti-smoking song and sing it too: we build in-suit without adding more junk to column 4.

The other point is that at this late stage of the game we should (ideally) be thinking about removing a complete suit rather than our next turnover. Unfortunately, we’re in a bit of a fix and I don’t see anything spectacular here. One bright spot is that with so few cards unseen, there is a decent chance of drawing the cards we need. For instance, we might draw X5X5XX53X3, where X represents any card, take our empty columns and win the game. A little bit of wishful thinking never hurt anybody!

Continuing from last time, we reached a critical position and I asked the reader how best to proceed:

It turns out we can remove the diamond suit. Steve points out the following

• Move: ca, ga, fh, fd, af, a4=f6, a9=c0, da, a2=d1, dg, df, af, ga, hf, aj, a3=c8, c2=e2, jc,
• Move: ag, ag, ha, hg (clear diamonds)

The result is shown below (I have pretended the Diamonds were not moved to the foundations for clarity). We can then proceed with a turnover in column 1.

Bart found pretty much the same sequence (not the exact moves, but clears Diamonds and turns over column 1). I will not present Bart’s exact move sequence.

Unfortunately, Steve did not play this. He writes that “either I did not see the plan or I did not like the after-play”. It’s obviously impossible to reverse engineer his thought processes, not to mention that Steve had to record the moves for over 300 games, so it’s not really practical to record the reasoning behind every move of every game (just recording moves is already a significant effort). But judging from his actual choice, I’m guessing Steve didn’t see the plan.

Steve instead turns over column 9. This exposes three Aces and forfeits the Diamond suit. Not to mention burning both empty columns just for one turnover. The only advantage of this plan is it gets a difficult task out of the way (turning column 9) while it’s still possible. Personally, I would be extremely reluctant to expose three aces and knock back a full suit of Diamonds. I would need several good excuses to justify that, and this isn’t even close.

The exact move sequence is not important and I leave it as the proverbial exercise for the reader to verify this position is reachable from the previous game state.

At least Steve draws a good card (the Two of Spades) getting back “one hole + one turnover”. The next card in column 1 would have been much worse (to avoid spoilers, I will not reveal what that card was), and Steve’s post-mortem analysis says the “superior play” would have actually cost him the game in practice.

Steve is able to extract all face-down cards in column 9. There are (in order), 9h, 2h, 2c. The exact move sequence is trivial and not given here.

To summarise, Steve has managed to extract three face-down Twos in a single column, that was buried by random junk including three “unmatched Aces”. A lucky break if there ever was one, but I believe Steve has demonstrated enough skill (his book contains several examples, not just the profiled game) to earn some good luck!

Steve mentions he now has a full set of Spades – and I won’t expect a player of his calibre to muck up a simple exercise in card counting. Unfortunately, it’s not possible to extract Spades. One reason (possibly not the only reason) is because of the duplicate Queens and Fives in the same column which I alluded to earlier.

Hearts are missing only the Nine. Clubs and Diamonds are only missing the Five. Unfortunately it’s not even possible to “almost-complete” (let alone complete) a suit. So it looks like more short-term planning for now and hope for the best. True, our chances of turning over more than two cards are not great (or four cards if we’re willing to split the Aces in column 2 – generally very desirable in Blackjack but not so much in Spider Solitaire).

The only bright spot for Steve is this game has no “antagonist” and no Backgammon doubling cube.

• Move: cf, ch → 5d
• Move: ea, ge, fi, gi, f1=h1, if, cg → 6d

What a difference a card makes! From experience, I find that if I “hang in tough for long enough” (this really should be the lyrics of some song but my general knowledge of pop music is atrocious), then drawing just a single “joker” (i.e. the best possible card) will provide the good guys with a real fighting chance. And Steve has done exactly that.

This is the first time Steve had two empty columns. Technically, Steve also had two empty columns at an earlier stage – if he was willing to perform some reversible moves (but he chose not to). In any case the empty columns were worth little more than “one turnover one option” where option basically means you get to answer a multiple choice question but there are no correct answers because all of them equally rot13(fhpx).

This is also the first time we can realistically think about long term planning. Unlike last time, we can extract real value from two empty columns. We get several in-suit builds for free and every chance of pulling things around after a difficult start.

How would you continue here? This is a critical point of the hand so I recommend you take your time on this one.