Villain’s Double in Round 1

In this post I will discuss why Villain doubled after dealing the cards in round 1.

The position in round 1 is this:

There is only one way to get two turnovers. The best play is “fg,bf,bc,jc,jb” giving the following position (I used MS Paintbrush instead of explicitly undoing moves in the Spider Solitaire program).

Now let us compute the chances of improving our minimum guaranteed turnovers after turning the card in Column 10. For simplicity assume each of the 13 ranks are equally likely. Let us assume each rank is worth one happy star if it yields a turnover, 0.5 happy stars if you need the correct suit to get the extra turnover and 0 happy stars if no turnovers regardless of suit. Multiple turnovers are possible. For instance, 1.5 happy stars means you always get one extra turnover, with a chance of a second turnover if you were allowed to call the suit, etc.

Note that if the next card in Column 10 were an Ace or Four then we don’t get an extra turnover since we counterfeited the turnover in column 9. It turns out the only good ranks are Three, Nine, Jack and Queen. That’s only 4 happy stars out of a possible 13. Actually, we can increase that to 4 and a half, since a Jack of Spades gives us a double turnover in columns 8 and 10 to go with our turnover in column 9. Given that we only start with two turnovers, it’s about an even chance we get bad cards in both column 9 and column 10.

The other piece of bad news is there are no “atomic columns”. Note that we were forced to pollute column 6 to guarantee our two turnovers in the first place. If we assign the capital letters A and B to columns 9 and 10 respectively, then it’s hard to find decent plans corresponding to the rest of the alphabet. This also means that we need to turnover every card in column 9 or 10, not just the first to get a fighting chance.

In a nutshell, we have difficult short-term problems and long-term problems to deal with. This is why Villain doubled. If I were in Hero’s shoes, I would have passed the double.

Law Of Diminishing Returns

Following an interesting discussion with JM and Alex regarding the plspider program I wanna discuss the Law Of Diminishing Returns (LODR).

When playing with plspider I noticed an interesting phenomenon. The program can often obtain two or three empty columns pretty easily. After all, playing with undo privileges is a massive handicap. But after getting those empty columns the program flounders for a while, not knowing what to do. An expert human player would normally crush a hand once he has three spaces. Plspider will eventually find a winning path, but by that time I have already churned through a number of levels in Toy Blast (I am currently at level 5923).

I think the reason plspider flounders boils down to the LODR: when you have three empty columns the value of further empty columns is very small.

This is based on many years of playing the Royal Game and working out winning strategies, rather than knowledge of the actual code. I should also mention that players are often reminded that getting empty columns is essential strategy (more superficial advice on the internet, hooray!) so it’s not hard to guess why many spider solitaire solvers emphasize the possession of empty columns. The problem is nobody discusses what to do once you get empty columns.

At first sight, the LODR sounds like madness: after all the win condition for Spider Solitaire can be described as “getting ten empty columns”. But suppose that we always declare victory as soon as the game is mathematically won, i.e. there exists a strategy that removes all cards to the foundations regardless of the permutation of unseen cards. Then it is impossible to obtain 10 empty columns, because the game is prematurely terminated. A little-known but useful analogy would be Dead Reckoning in chess composition.

Some examples of mathematically won game states are:

  • Every card face-up in the tableau, 10 cards in the stock, the player has chosen to deal the last row, and a winning move sequence exists for every possible permutation of cards.
  • 7 out of 8 suits moved to the foundations
  • Two spaces and eight runs from Ace to King with mixed suits. Some cards may be face-down.

I haven’t performed any detailed calculations or statistical analyses but my intuition says an expert will typically declare victory with 3 or 4 empty columns. If he has more than 4 spaces then chances are the expert can’t be bothered working out if the game is mathematically won after every turnover.

To illustrate the law of diminishing returns, consider the following game state, which may be familiar to regular readers 😊. While the game is almost certainly won at this point, it is adequate for didactic purposes.

Assuming we merge the three left-most columns into a single run, we have three empty columns. Now, borrowing a phrase from Cracking The Cryptic, let us ask a facetious question: is there any game state that (1) has three empty columns, (2) is reachable if we (temporarily) use at least one empty column, and (3) not reachable if we don’t use any empty columns?

Clearly the answer is yes since the supermove “fe” fits the bill.

Now let us ask the same facetious question, but this time we want a game state that is only reachable with the use of TWO spaces BUT NOT ONE.

That’s not so hard. We could for instance swap the 8-7-6-5-4 of Spades in column 1 with 8-7-6-5-4 in column 5. That breaks an in-suit build for no good reason but at least we answered the question 😊

Now we ask what happens with three empty columns. One can show that it’s possible to shift the J-0-9-e-t-c-e-t-e-r-A of mixed suits in Column 6 onto the Queen of Spades in column 8. For sake of argument, I will pretend this is not possible with only two empty columns (proving or disproving this is left as an exercise for the reader!)

But that leaves not much room for improvement if we have four empty columns. If three spaces are sufficient to achieve the super-move “fh” then it’s hard to imagine a single game state that can be reached with four spaces but not three.

Admittedly this is not a rigorous proof of the LODR, but hopefully you get the idea. When you have three spaces it is probably wrong to aim for a fourth space. You should concentrate on columns with more face-down cards rather than less. At the risk of sounding like a broken record, at least this helps avoid one-hole-no-card problems (all other things being equal). Or you might sacrifice turnovers and spend a space or two to remove a suit – or even an “almost suit” of 12 cards instead of 13. Obviously, the correct course of action depends on circumstances, but the underlying theme is you never play for Yet Another Empty Column without thinking.

In summary, I believe extracting maximum value from empty columns is the heart of winning play at Spider Solitaire. If the Spider Solitaire Body Of Knowledge was a thing, then the Law Of Diminishing Returns should be part of it.

Improving the plspider algorithm

The plspider program achieves a very high win rate (with undo!), but takes far too long to find a winning sequence of moves. If I had to improve plspider’s performance I would modify the code to start focusing on complete suits instead of spaces once it has accumulated three spaces. Of course, this is easier said than done if you pardon the terrible cliché, especially considering that I do not have the source code of plspider.

While we’re here I may as well mention that 3 is not a magic number. In some given game states, the LODR kicks in after 2 empty columns. On a really good day, most builds are in-suit after 20 moves and the LODR applies with only 1 empty column. In other games, an expert player might find a good reason to chase 4 spaces. That should be rare, but might depend on which version of Spider Solitaire you are playing  😉

An Interesting Decision in Round 3

In this post, I wanna discuss a very interesting decision taken by Bart in Round 3.

In the diagram below Bart’s last move was “cb” deliberately breaking an in-suit build on the basis it was impossible to turnover any cards. Ergo, he played to maximise the chances of getting back the empty column after dealing the next 10 cards. Before reading on, what do you think of this play?

Although I am not particularly fond of this play, I can see where Bart is coming from. From experience I know that once you achieve some lofty goal such as clearing a space or removing a full suit, the in-suit builds tend to take care of themselves. If you have sacrificed an in-suit build or two for some obscure reason and the card-gods are kind, you essentially win them back without really trying. No doubt Bart has figured out the same from his own experience at the Royal game. The main risk is after dealing 10 fresh cards you can’t do any of the wonderful things you intended because you need an empty column to procure an empty column. Bart calls this the “can’t-get-started problem”. Ironically, Bart did suffer this problem despite his best efforts to avoid it.

Knowing when to break in-suit builds is an essential skill for the improving player. The simplest explanation is “weight of sheer numbers”. Consider the diagram above. Suppose that, for sake of argument, there are 2,000 legal positions you can reach before dealing a new row of cards – but that number goes down to 100 if you add the restriction of never breaking in-suit builds. With a Suit-Break (S) versus No-Suit-Break (N) Ratio (R) of 20:1 it is at least plausible that our optimal play will involve breaking at least one in-suit build. I have discovered a truly marvellous list of many different reasons why breaking suit is sometimes useful, which however, this blog post is not large enough to contain. Fortunately, there is enough room for a picture, which is well known to be worth a thousand words.

However, I think Bart goofed despite his noble intentions. Ideally, I would like to simulate a large number of iterations of this position with an Artificial Intelligence, so I can be reasonably certain Bart’s play did (or did not) cost a sizable chunk of winning chances. Alas, Ninja Monkey only has the status of Artificial Stupidity so I have to rely on heuristics instead.

Lame attempts at humour aside, my instinct says Bart’s play is suboptimal for two reasons:

  • Assuming we make a routine play such as “bc, fb” in the diagram position we have no less than five (5) clean columns with no face-down cards and a single sequential run of cards: a straight flush in poker lingo or “atomic” in Bart lingo. We don’t have to do anything drastic to have reasonable hopes of getting at least one space on the next deal.
  • Bart’s play does not address what happens after we get back the empty column. The simplest play is “bc, gb,cg”. This gives us a “twelve-suit” in Hearts – every card minus the Ten – in two columns. If the Ten of Hearts appears in the next round we can entertain hopes of clearing the Hearts. Moreover, “bc,gb,cg” exposes a King when no other column is also headed by a King. This may be exactly what we need if any Queens turn up on the next round. We might be able to improve this plan further by tidying up column 8, which contains the K-Q-J of Hearts.

My recommended play from the diagram position would therefore be “bc, e3=i5, h5=i2, gb, cg” with an outside chance of completing the Heart suit. The chances of clearing Hearts on the next round aren’t exactly great, but at least I’ve made a start.

From experience I find that putting all eggs in one basket (e.g. maximising our chances of winning back a space in column 2) is almost never worth it. When 10 fresh cards appear simultaneously instead of sequentially a lot can change. We’ve all had games where we believed Nines were the worst card in the world and no rational sentient being could find a reason to like Nines and then we suddenly changed our mind when all the Eights and Tens appear in a single round. Reminds me of that Dr Seuss character who is suddenly enlightened and thanks Sam I Am for such a splendid meal. If I do get one-hole-no-card then I play on general considerations and let the cards fall where they may: if I cannot turnover a card then perhaps I can settle for freeing a Jack because no other column is headed by a Jack and there are several Tens unseen. Ergo, I still gain some value from a space, even if it is less than one turnover. I might make an exception if the game state were really bad and getting a space in column 2 was the only reasonable game plan (but in this case we are probably headed for defeat anyway). Or perhaps if the game state were really good you can justify going all-out to prevent an unlikely parlay (or “reverse Hail Mary”, pandering to Bart’s love of all things American Football).

Overall, Bart’s decision in round 3 was my only real criticism throughout the game and everything else was played at an extremely high level. Well done team!

Going With The Flow

Bart has played at an extremely high level, so I think it is time to talk about an advanced concept: “Flow”.

Flow is a difficult concept to define. If taken literally it’s difficult to imagine a number of black and white stones undergoing mitosis, increasing their numbers and gracefully sliding to new intersections on a Go board as their Dan-level overlords control everything with telekinetic powers, but I can guess where the author of “flow of the stones” is coming from.

Roughly speaking, “good flow” means everything goes according to plan. You rarely end up in awkward situations and your resources are working at maximum efficiency. Bad flow means you run into problems – you can’t play the move you want to play due to some “injustice”. You reluctantly make a small concession or two. The problems compound, which eventually ends up costing you the game.

Good flow is often a result of good long-term planning. A professional Pool player rarely gets awkward shots because he plans several moves ahead. Even if he can’t forecast the exact position of every ball, he will have a rough approximation of the game-state he is aiming for (or at least the essential features). Similar analogies exist for other games.

Incidentally the Pool analogy is not mine – it is due to Kit Woolsey’s excellent article on Backgammon 😊

Okay, enough with analogies, let’s move onto the actual game.

In the actual game, Bart chose to clear all the cards in columns 1 and 4 – but eventually ran out of things to do. We got the dreaded One Hole No Card (1HNC) scenario.

In the above position we could have turned over cards in columns 7 or 9. Observe that turning over column 7 requires two empty spaces, even though we only spend one. Column 9 also requires two columns – unless we were willing to give up the beautiful run of Diamonds from King to Deuce. Few players would be willing to do that.

This suggests the following principles:

  • If we have 1 empty column then we should turn over something that requires 1 empty column and spends 1 empty column
  • If we have 2 empty columns then we should turn over something that requires 2 empty columns and spends 1 empty column
  • If we have 3 empty columns then we should turn over something that requires 3 empty columns and spends 1 empty column

You don’t need a Ph. D. in math to spot the pattern. But you do need to appreciate this only applies if you have a position of strength. If your game-state is weak then it may be dangerous to make a special effort to avoid 1HNC – you may entail some other strategic risk, such as never seeing any empty columns for the remainder of the game. Yes, we’ve all been there!

When you have a position of strength then it is possible to follow the dot points outlined above. In this case everything flows smoothly. All our empty columns are maximally efficient – if you will – and we never get the 1HNC problem. If you are consistently winning from a position of strength then you are doing something right!

With hindsight it is easy to suggest we should turnover column 7 or 9 in the above position (Score=423). However, turning over column 7 requires we destroy an in-suit build and expose an Ace. Turning over column 9 is a serious alternative – and we don’t have to give up the Diamond run (the important point is to turnover column 9 before shifting the Queen of Diamonds in column 6). We might be afraid that after dumping a King in an empty column there are only have two potential empty columns remaining. For sake of argument, suppose we shift the junk pile in column 9 to column 10. Then we only have columns 4 and 5 as potential “easy spaces”. This may be cutting it a bit thin. True, there is also the hidden possibility of clearing the Diamond Suit when the Ace turns up – this gives us three potential empty spaces instead of two. Even so, it’s a close call and with five unseen cards in columns 1 and 4, Bart had plenty of leeway to justify leaving column 9 alone.

In the above diagram, I would have turned over column 9 – but I would not criticise anyone who chose Bart’s plan. The problem is we do not really have a position of strength, and we had to allow the risk of 1HNC. The point of this post is not to work out if Bart’s play was the absolute best, but rather to get the student thinking about long-term planning. Next time you have 1HNC, it might just be a case of bad planning rather than bad luck. If I had a dollar for every time someone had 1HNC and complained about their bad luck – then I wouldn’t mind having more students!

Incidentally I did not give the exact move sequence for turning over columns 7 or 9. Working out these moves is a useful exercise for the average player, but probably beneath the dignity of IM Bug or IM Bart (they are definitely above average players!)

Until next time, happy Spider Solitaire playing. May all your builds be in-suit and may all your long term plans come to fruition!

A Far-Sighted Play

In round 1, Team Good reached the following position. As so often happens, our options increase significantly when we procure an empty column – and so do our opportunities for mistakes.

Although we received a large slice of luck with several good cards in column 5 the game state remains deplorable. Bart chose the obvious “ef,be” to reveal the last face-down card in column 2. The problem is what do we do for an encore?

As I have alluded to several times earlier, we should be wary of the dangers of one-hole-no-card. With a glaring deficiency of Vitamin Q and Lucky Sevens it is not hard to imagine a scenario where we would be unable to turn over any cards even if we did obtain an empty column. In other words, empty columns are worth less than their usual face value in this particular situation. Let us construct a histogram of the cards that are visible so far:

We immediately see the biggest problem: only a solitary Seven is visible (mind the gap in column 8!) and we have no less than seven Eights. But the histogram doesn’t tell the full story. Close analysis of the tableau shows that most the Eights are buried under Kings. Ergo, if several Sevens appear on the next round, then we would be in an awkward spot when the Eights suddenly become essential. We should note that the shortage of Queens isn’t nearly as serious as the shortage of Eights. The difference is 5:1 instead of 7:1 and we still have one king exposed (or two if we allow the possibility of “eg,cg”). Also, if the last card in column 2 was a Seven of any suit, we would be considerably embarrassed after making the obvious play.

Going back to the diagram let us look for other possibilities. We soon notice that it is possible to turnover a card in column 10. This frees two precious Eights, so now we have a home if the next card is a Seven. In fact, we would obtain a double turnover if the next card is any Queen or Seven. Several other cards would yield a single turnover – less ideal, but at least we still get another shot at a double turnover before dealing a new row. Of course, the down-side is we dump a King into an empty column, but as noted above, empty columns are not all they’re cracked up to be.

This illustrates another general principle: when a game is going badly, we should think outside the box (terrible cliché notwithstanding) and look for opportunities to change the flow of the game, rather than letting the winning chances drift from Buckleys to Nada. And yes, the same principle applies to many strategy games, not just Spider Solitaire.

I believe Bart (and Ninja Monkey!) made an error in not turning over column 10. It may not be a serious mistake, but given that our situation is dire, the margin of error isn’t exactly great.

Fortunately, the last card in column 2 turned out to be the Three of Spades. We get our empty column back, but any Seven is no longer worth a double-turnover.

NOTE: My main concern with critiquing the play before the end of the hand is that players can receive “undeserved hints” for subsequent rounds, but I believe we have made enough progress for this concern to be rendered moot.

Monkey Algorithm – In Depth

Let us take a closer look at Ninja Monkey’s algorithm. We know it can get about 6% win rate on random four-suit deals without undoing moves – and that’s nothing to sneeze at when many players have difficulty with the 4-suit version. Not to mention that I am unaware of any research into designing a Spider Solitaire AI that plays without rot13(haqb). The heart of the monkey algorithm is as follows:

This represents “what to do with the current game state”. The basic idea is if any column is headed by a face-down card then we can count it as a turnover – but we don’t know the rank or suit of that card. If we call that card X then nothing can move onto X and X cannot move anywhere (not even an empty column). Let’s look at an example:

Let’s say we executed the moveblock “id,ah,fh” but without turning over any cards. The game state would look like this:

Disclaimer: I only got ‘C’ in Year 10 Art

Without loss of generality, let us assume we score 10 points for turning over a card and 1 point for building in-suit. Our score would be 31 regardless of the identity of newly-turned cards.

Clearly, “id,ah,fh” is not the best possible moveblock for several reasons. For starters, we can play only “id” and examine the new card in column 9. Then we still retain the option of playing “ah,fh” if the new card is useless – or we may find something better than “ah,fh”. This is why the statement “execute best moveblock found” comes with the caveat “first turn over only”.

Now let us consider only the three lowest-numbered cards in columns 1,6,8 in the original position. Clearly we can guarantee two turnovers with ah,fh. But suppose we knew the card under the Two of Spades is the Three of Clubs. Then we can get two turnovers plus an in-suit build with fa,fh. Obviously, that would be cheating since we aren’t entitled to this information. This explains why the statement “guess a move block” comes with the caveat “no turnovers”.

The rest of the algorithm should be fairly self-explanatory.

The observant reader will have noticed it is not necessary to begin with an in-suit build to achieve the worst-case scenario. Going back to our hypothetical moveblock of “id,ah,fh”, we would get the exact same position with, e.g. “ah, id, fh”. If we only had two guesses “id,ah,fh” and “ah,id,fh”  they would have the same evaluation score. We all know we should begin with the in-suit build, but my algorithm would effectively decide by tossing a coin.

Assuming we make enough guesses, we should eventually stumble upon a score of 61 with six turnovers and one in-suit build. One such moveblock would be “ec,hc,ac,fc,id,db”. If that was the final best_moveblock_found then we would execute the move “ec”.

In this case, our algorithm actually found a decent opening move – with three Sixes available, it’s hard to imagine “ec” being a significant blunder even though an in-suit build was available with “id”. Of course the algorithm could equally well have come up with “db,ib,eg,hg,ag,fg” and start with “db”. This would cost a turnover if the next card was a Nine.

Of course, it should be possible to modify this algorithm to avoid the latter scenario given sufficient effort, but I would rather gain some experience with collaborating with other software developers via GitHub. As mentioned previously the current state of my project is a bare-bones AI with plenty of room for improvement and my Spider Solitaire project gives me a perfect excuse to do so.

Post-Mortem Analysis – Round 5

Link to Round 5 is here

Link to PMA Round 4 is here

This is a critical point of the hand. At the risk of sounding like a broken record, a lot can change when 10 cards are dealt simultaneously instead of sequentially. Moreover, once the stock is empty the effects of a bad draw can be catastrophic, or we could come up golden and reach a position where it’s virtually impossible to lose (unless all three blobs were impostors) – or it could be somewhere in between.

In this case, we got an excellent draw. The main point in these situations is not to panic at the sheer number of cards in the tableau. Careful analysis shows we can indeed remove one full deck of cards (including the Diamonds that have already been removed) regardless of the permutation of unseen cards. It’s not necessarily the best course of action, but at least we have a fallback if analysis reveals nothing better.

All three blobs wanted to “delay” this decision by not turning over any cards – and I believe IM Bartacus and IM Bug chose the wrong plan. They ended up in the following situation:

If we ignore the fact the newly turned over card in column 2 is a K of Spades, then we have three suits removed and two guaranteed turnovers. Now let’s look at Blue’s suggestion: “id,ai,ai,hi,hf,ha,ei,ea,gi,gj (h12=i8)” leading to this position:

This is much better. We can play fe,df,jd,jh,ie,fi,cg,cb,ci,(e7=h7),bi,ei,be,(b1=h6) to reach this position with four suits removed and also two guaranteed turnovers

No wait – in the actual game we get three suits removed and THREE turnovers. We weren’t allowed to count the fact the newly turned over card is a King of Spades (giving a home for the Queen in column 7) but we can count the fact we turned over something in column 2. This means Blue’s suggestion was not clearly superior to the actual continuation, and the team had every right to believe Blue was the impostor. Rot13(SHPX SHPX SHPX SHPX SHPX SHPX SHPX SHPX SHPX!!!!!).

Blue thought he was being clever, by using the Queen of Hearts in column 8 instead of column 6 (indeed using the Q in column 6 would be egregiously bad) but this turned out to be a miscalculation. To be more specific, the actual game continuation achieved one more guaranteed turnover at the expense of one more suit – and this is a good trade-off because the biggest danger of losing this game is if the next 2 or 3 cards are bad. There is little danger of losing because we removed too few suits.

In case you didn’t follow all of the above the TLDR version is rot13(Fcvqre TZ shpxrq hc).

In the endgame, Blue insisted on clearing the mess in column 8 early to avoid column 8 becoming a problem later. This is a good general principle:

KNOWLEDGE BOMB: From a position of strength, it is often wise to identify a “difficult task” and get it out of the way before it becomes a problem later (remember the dangers of one-hole-no-card).

The situation Blue wanted to avoid was this one:

This image is from the back cover of Steve N Brown’s excellent book “Spider Solitaire Winning Strategies”. When I saw this image, I immediately recognised it for what it was – most probably thanks to playing far too many games on a Spider Solitaire server that I am convinced is biased. If Steve played on that server, I would bet my Ph. D. thesis he would not have written the words “this game could have been won if only a little more care had been taken”.

Unfortunately for Blue, this knowledge bomb turned out to be unnecessary – the simple plan of turning over everything outside Column 8 was sufficient, even if the impostor were allowed to call the remaining face-down cards in column 8. My calculations say that ten columns in the tableau is just barely enough to get the job done (and I fully trust IM Bartacus and IM Bug are more than capable of reaching the same conclusion) and the actual cards were nowhere near the worst-case scenario. With winning reduced to a mere formality, Blue had no chance to redeem himself. He tried to inject a little humour by rapping in the Iambic pentameter but it was all in vain.

In summary, a great game with both Team Good and the Impostor having legitimate chances to win until the very end. IM Bartacus and IM Bug navigated most of the traps but let a few bad ones through, and the position looked desperate at one stage. But we managed to pull everything through in the end – until Blue had an absolute brain-fart, miscalculating a critical decision at the start of round 5 and giving IM Bartacus a good reason to believe Blue was the impostor. IM Bug tried to salvage the situation by explaining that “1 impostor” was written in red font and therefore the impostor should be Red. But my Random Number Generator app would have none of that and Blue was declared the impostor anyway on the tie-break. In the end, honours were shared with Team Good winning 100VP out of a possible 200.

Post-Mortem Analysis – Round 3

A short but highly eventful round. The card gods saw fit to give us Three Turnovers. The card gods also saw fit to give us the Three of Diamonds, enabling us to remove the Diamond suit. Unfortunately, they also threw in that nasty logical disjunction operator instead of the logical conjunction that Spider players and mathematicians so dearly love. To put it in layman’s terms, we were able to take three turnovers or remove diamonds, but not both.

The interesting part of this round was Red suggesting we not remove Diamonds and keep flexibility, thus effectively backtracking on what he said the previous round. As I mentioned earlier, a lot can change after 10 cards are dealt simultaneously instead of sequentially. And indeed, all the signs are pointing to the Diamond suit: we received the Three of Diamonds and plenty of Jacks. Hence the Queen of Diamonds in Column 4 is suddenly a good card. Also, we are nowhere near completing any other suit and the number of cards is dangerously high, so there is little chance we could progress without removing Diamonds.

In the end, we turned over only bad cards in the tableau, achieving only 2 turnovers instead of a guaranteed minimum of 3. But it’s not all doom and gloom if you pardon the terrible cliché. Clubs and Hearts are starting to look promising. It would have been nice if we could “swap the ladies” in columns 8 and 9 but this turned out to be not quite possible.

KNOWLEDGE BOMB: in the latter stages of the game, it’s often wise to think about “how can I progress after getting the next turnover or empty column” rather than “how can I maximise the chances of getting my next turnover or empty column”. In the context of our current game, I would be happy to accept a Backgammon doubling cube centred at 2, despite turning over only 2 cards in Round 3.

After reading the comments, I got the feeling the readers may have cottoned on to the fact Red is the impostor. What should Red’s game plan be? Should he start playing innocent and hope the game will rot13(shpx) itself up by natural causes?  Or is it necessary to sneak just one more bad decision through? I guess a true impostor would have already memorised the official blockchain of suggestions and start thinking about how to convincingly pin the blame on Blue or Green. But as the purpose of this blog is to help improve the reader’s skill at Spider Solitaire I have mainly focussed on that – so the Among Us component plays second fiddle if you pardon the terrible cliché!

Before dealing a new row, the team decided to add the move “cb”. Technically this should not have been allowed but I was willing to let it slide. But it is a good sign that my readers are paying attention to “the little details” since this is exactly what is needed to improve to IM level or beyond.

And the less said about that Spider-GM joke, the better 😊

Final position of Round 3



Post-Mortem Analysis – Round 2

Link to round 2 is here

Link to PMA Rounds 0 & 1 is here

I believe the team made a significant error on the very first decision. What usually happens is the most interesting decision of a round occurs immediately after dealing ten new cards. Subsequent decisions are usually easier because much of the important analysis has already been taken care of.

Red suggested “ge,gd,if,ie,ie”. I don’t like this option on two counts: first, we expose the Ace of Diamonds. Secondly, we lose the important Seven of Spades in Column 8, together with several in-suit builds such as K-Q of Clubs. This would later turn out to be important.

“Hang on”, you say. “Doesn’t the alternative play expose the Ace of Clubs in Column 5?”. To which I reply, “yes, but not all Aces are equal. We anticipate it is difficult to avoid exposing the Ace of Clubs. After all, an empty column is an empty column – so if we don’t take it now, there’s a good chance we’ll be taking it later. Whereas if we found an excuse to not turn over Column 9 then there’s a decent chance the Ace of Diamonds stays buried for some time”.

I like Blue’s option of “hd,fj,fj,ha,hj,(d1=h3), hf”. That results in the following position before turning over column 8.

Game State after Blue’s option

By not messing with the low cards in Column 9 we retain much more flexibility with other low cards in columns 2,3,5. True, having a King in column 6 rot13(fhpxf) after we worked so hard for that empty column, but the worst-case scenario says we still have atomic runs in columns 5 and 7. That’s plenty as far as our chances of winning back an empty column are concerned.

The other problem with Red’s play is that by not sorting out column 8, we risk “one-hole-no-card”. Note that there are very few columns that can be turned over at the cost of only one column – and therefore a strong chance we will run out of things to do once all cards in column 9 are face-up. And sure enough, this is exactly what Red had intended all along:

We have an empty column after “ed”. If we could ask an innocent child to extend his hand and hold the Six of Hearts for a few seconds then everything is happy and we can turnover a card in column 8.  Unfortunately, someone would probably accuse us of cheating – this sort of “injustice” is typical when your position is not flexible enough to withstand bad cards.

Red was also entertaining thoughts of almost-completing the Diamond suit but the team managed to avoid that trap, correctly diagnosing it was not worth chasing the Diamonds when the likely reward is exposing a relatively useless Queen. So Red did not get everything going his way. Still, the game was very close in the end, so Red only needed to sneak a few bad ones past the team to achieve his nefarious ends.

In summary Round 2 was a great success – for the impostor. The sharp-eyed reader may have noticed Red pointed out the problem after the damage had already been done (Red was hoping when he tries to rectify the situation after the damage is done, it only makes things worse, and it makes him look like a good guy 😊) And having an excess of even-numbered cards certainly didn’t help Team Good!

KNOWLEDGE BOMB: if you ever find yourself in a situation where you can’t turn over any cards despite having one or more empty columns, there is a fair chance you failed to extract maximum value from a position of strength. Use the zee-key (after the game is over, obviously) to find out where you could have played more strongly.

Six point rating scale (continued)

Last week we had the task of evaluating other players:

I gave an example video of someone beating 4-suit Spider without rot13(haqb).

Here are the results from a six-point scale of One-Bone-Bonne-Bonnet-Bullet-rot13(ohyyfuvg). Or for the linguistically-non-cunning among you, there is also One-Two-Three-Four-Five-Six.

 Schistocerca AmericanaScholar Bart
DifficultyBullet (5)Bullet (5)
SkillBullet (5)Bullet (5)
PresentationBonne (3)Bonne (3)
OverallBonnet (4)Bullet (5)

I agree the players are at beginner level. Certainly enough elementary errors to justify Bullet (5). But I guess it could be worse. For instance, Joe Bloggs might upload a vid claiming he won without rot13(haqb), but in actual fact he uses rot13(haqb) frequently. Maybe JB uploaded the wrong vid by mistake, or it was One Of Those Days His Brain Went Psycho And Farted. In any case, I’ve seen plenty of fonumental muck-ups that would make Andy Griffiths’ Bum proud.

To borrow a phrase from Schistocerca Americana … I digress 😊

This is the reason Bart and Americana avoid giving a rating of rot13(ohyyfuvg) (6) for skill – and I agree.

I also agree the presentation level is average. I am certainly not a professional you-tuber so I’m not gonna be too critical. I have a number of decent videos (unrelated to the Royal Game) but happyharvey0 probably has some skill set that I don’t possess. Bonne (3) it is.

Bart and Americana agreed on everything, except for overall score. Americana points out happyharvey0 is probably a much better player six years later. He may certainly well be, but I’ve seen my fair share of Chess and Scrabble players who simply refuse to improve no matter how long they play. It is quite possible that happyharvey0 was aiming to beat hardest difficulty in record time, and therefore mundane matters such as spending bone – uh, I mean two – more seconds looking for in-suit builds instead of off-suit builds is beneath his dignity!

Schistocerca Americana gave another vid:

His ratings are difficulty = bullet (5) , skill = bonnet (4), presentation = bonne (3), overall = bonnet (4).

The skill level is similar, and this player doesn’t have the excuse of trying to beat the hardest level difficulty in record time. I won’t go through every suboptimal play in excruciating detail but the main points are:

  • When you reach a “trivially winning endgame” you should be playing moves quickly and confidently. If you see an in-suit build, just take it without thinking. As long as you maintain at least one empty column to prevent nasty accidents, you can hardly go wrong.
  • In the opening stages a good player should be able to immediately count minimum guaranteed turnovers and in-suit builds, as though it were second nature (as a chess analogy, if you give an experienced player a certain game state, he she or it can immediately deduce which side has a material advantage, what pieces are under attack, whose King is in greater danger etc). A good Spider Solitaire player should be able to whiz through the opening moves without hesitation and without obvious errors.
  • I assume if Joe Bloggs has to stumble his way through the opening and endgame, there is no way he can play a decent middlegame. Therefore, I did not examine the middlegame with my usual scrutiny.

In hindsight, I probably should have stated this is to be an objective evaluation, and there is no need to apologise if you find the player is Awesome in other respects, such as speaking Indonesian, playing a decent game of Zuma Deluxe, or having more subscribers than the Grand Master himself!

I agree that it’s hard to find good videos of someone playing a decent game of Spider Solitaire Four-Suit. Perhaps it’s up to Bart, Americana and I to start a new club of “Generation Sans-Z” players.

Bad puns aside, may all your builds be in-suit and all your long-term plans come to fruition! On second thoughts, if all your builds were in-suit you could probably win without any long-term planning. Whatevs 😊

This week’s homework

If you didn’t get the Andy Griffiths’ Bum reference, do a google search. If you are already familiar with the reference then lucky you – no homework before the next blog post 😊