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

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.

Voting Results Are In! (alternative version)

Red and Green had done it. They had beaten the Royal Game at the highest difficulty level, without undoing any moves, and all this despite the shenanigans by Blue.

But the big winner was social media. With expert live-commentary entertaining all viewers and dissecting every decision, every good, and every bad card in simple language, social media platforms had every right to boast how they had successfully connected blobs all over the world. Red and Green were relative newcomers. It was well-known the game was beatable with expert play, but nobody expected them to achieve awesomeness on the big stage. But achieve awesomeness they did. The post-match interviews were a blast and Green even improvised a rap song in the iambic pentameter at one point, to thunderous applause.

Red: This is gonna be massive.

Green: Thanks to the wonders of technology, the Royal Game would finally take its rightful place among the likes of Chess, Poker, Bridge or even Tetris 99 Battle Royale. Hang on a moment. What is this?

Green watches a video on his mobile phone. A Blue-skinned player has dealt a row of cards and is considering his options. The video alone has three million views and counting, and one didn’t need a Ph. D. to realise this is statistically significant at the α = 0.05 level.

Green: Blue eventually finds a way to remove a complete suit of Hearts, but in the process, she made it mathematically impossible to win regardless of the permutation of unseen cards. Hence the hashtag “#blueboo”.

Red does not share the slightest concern, his eyes fixed firmly on his own mobile phone.

Red: Incredible Game 5. Magnus Carlsen looks horribly passive but he has correctly calculated there is no way for White to improve his position. A well-earned draw with the Black pieces. No way I could escape like that.

Green: There are a large number of #blueboo tweets going viral thanks to the likes of RojoTheGreat123, RojoTheAwesome456 and RojoTheGM789. Hmmm … these look like bot accounts with a profile pic of a Spanish flag.

Red: I never heard of this #blueboo. When did you –

Green: The overarching narrative seems to be anybody with blue skin is inherently bad at Spider Solitaire. Now you and I both know that even if our Blue-skinned team member played poorly, there is no logical reason why all other Blues on this planet would be just as bad –

Red (squirming in his seat): What does it matter? We proved we can wield a mean deck of cards, who cares what the others th–

Green: You don’t understand. Suppose you took the entire population of Blobs, then add an order of magnitude and have every one of them chant “Red Is Sus! Red Is Sus!” How you would feel … wait a minute, you’re not –

Red stands up and glares at Green. Green races towards the exit only to find the doors locked. <sarcasm> How convenient! </sarcasm> Red pulls out a knife and Green can only stew at the injustice of it all. If only the Random Number Generator had yielded an odd number instead of an even. Red would have been voted off instead of Blue and all the good guys would have lived happily ever after. Instead, here he is – cornered by an Angry Red Blob and having approximately three nano-seconds left to live.

The end.

Post-Mortem Analysis – Rounds 0 and 1

Round 0

Not much in the way of tricky decision making. Unless we get a really good round with many turnovers it’s virtually impossible to suggest an egregiously bad line of play without arousing a disproportionate amount of suspicion.

That being said, when no more turnovers were available, Red tried to rot13(shpx) things up by increasing the number of in-suit builds at the expense of “junk-piling” a column with a Queen. Even though Queens were cheap because supply exceeded demand, I believe it is a definite error in the long run.

Red tried to rot13(shpx) things up with “he” before dealing

I’ve played enough games to know that the supply-demand relationship can change drastically. This phenomenon occurs because the rules of the game demand 10 cards to be dealt simultaneously instead of sequentially. This problem is exacerbated when you’re forced to deal two rounds in quick succession. Before we know it there are too many Jacks and Kings in play and the once-hated Queens suddenly become our only hope of salvation. All this trouble just for the sake of one measly extra in-suit build!

Needless to say, IM Bartacus and IM Bug weren’t falling for Red’s shenanigans this early in the piece 😊

Round  1

A fairly good result with three columns containing no face-down cards – thus we have fair chances of getting back at least one empty column on the next deal. We have 10 out of 13 cards in the Diamond suit, but the cards are scattered in various columns and it’s odds-against the Jack, Five and Three appearing soon – therefore now is not the time to think about the Diamond suit, unless we somehow manage to satisfy the proverbial “all other things being equal”.

Decision 19 stands out as a particularly interesting moment when all three Kolourful Kibitzers suggested a different line of play.

Red suggested “hb, he, hf, hg, fh, eh, ef” which I didn’t like because burning the 4 of Hearts costs some flexibility if we need to work on column 9 – not to mention column 2 becomes harder to work on. If we did burn the 4 of Hearts we could at least try to get “compensation” by lining up the 7-6-5 of Spades (as per Blue’s suggestion) and turning over Column 1. Admittedly, but the difference is small and hard for even a GM to argue convincingly. All things considered, the three blobs were well behaved that round.

A difficult decision … hard to criticise the impostor here

Voting Results Are In!

Schistocerca Americana (a.k.a. IM Bug) has voted RED
Bart Wright (a.k.a. IM Bartacus) has voted BLUE

Random Number Generator (tie-breaker) has BLUE

Blue was Ejected.

Blue was not the impostor.

(Red was the Impostor)

Oh well. Random Number Generators can be fickle beasts. At the start I kinda wanted Red not to be the impostor because of the usual association “red-means-danger” but the RNG decreed otherwise, and who am I to argue with the RNG? So no bonus 100VP for the team. But Bart and Bug got their IM titles and that’s the main thing right?

In the next few posts, I will discuss some key moments in the game and dissect where the players and blobs went right or wrong.

Bart Wright and Schistocerca Americana awarded IM Titles

It’s official: after achieving victory on the Four-Suit version of Spider Solitaire sans rot13(haqb), with one impostor trying to rot13(shpx) things up at every opportunity I have decided to award both Bart Wright and Schistocerca Americana the title of International Master. It’s a bit of a misnomer in that we don’t get to travel all over the world to play in tournaments and prove we can mix it with the best – but I will stick with the IM title because it is considered the next level below GM and both players certainly displayed an extremely high level of skill. The other reason for the IM title is because it allows Spider GM to showcase himself at his brilliant worst. If you would like to guess the punchline before reading on, I have inserted the usual spoiler blocker.

In Chess, all titles are obtained by playing in enough tournaments and getting a sufficiently high score against decent opposition. Players can achieve “norms” in individual tournaments and you need enough norms to prove you didn’t get lucky in a single tournament. Your rating also needs to be sufficiently high. The good news is you don’t lose your title after a dip in your rating (or a string of bad tournaments), so you keep your title for life – save for something incredibly stupid, such as an arbiter finding compromising images of Stockfish recommending the best move on your mobile phone. This is fair enough: if there was no guarantee of keeping your title there would be much less incentive to achieve it in the first place. A GM title implies that your ability/talent is enough to mix it with the world’s best, provided you are willing to put in the time and effort and life doesn’t get in the way. An IM title is pretty much the same thing except “the next level down”. Then you get Federation Master titles and of course you can also add a W-hook (using the Scrabble vernacular) for female players. Hence WGM, WIM and so on.

Unfortunately, IM Schistocerca Americana is a bit of a mouthful even for somebody who recently composed a work-related rap song to the tune of Million Voices by Otto Knows. Therefore, he gets the indignity of being renamed IM Bug. And Bart Wright suffers an even worse fate:

Who Is The Impostor?

And it’s all over bar the voting. Bart and Bug have achieved 100 glorious VP for removing all eight suits and have a free swing at another 100 glorious VP is they can guess the impostor. There is no penalty for ejecting the wrong blob.

During the endgame Bart has already voted BLUE and has indicated “nothing will convince him to change his mind” (or words to that effect). Schistocerca Americana (or anybody else who happens to join in the last minute) has not yet voted.

If anybody has enjoyed reading the last few blog posts but doesn’t wish to vote for Red/Blue/Green there is also the “skip vote” option 😊

In case of a tie (e.g. SA votes Red/Green and nobody else joins at the last minute ) a Random Number Generator will be used as tiebreaker. The “skip vote” option is not counted for ties (or even outright wins), so if 50% vote BLUE and 50% vote SKIP then BLUE is still ejected.

Among Us Lite – Round 5

Link to previous round can be found here

Previous Moves

Round 5 initial position:

Ts9s8s7s6s5s4s3s2sAsJs/xxxx9c8s7c6c5d4h3d2hAs7s/xxxxxTc2cAh6s9s/xxKdQd3s/Qs6d/Ts4dQhJhTh9h8h7h6h5h4h3hKc/Ac5s/xxxxKcQhJhTh9h8d7c6h5c4c3c2cAcKhQcJcTd9d7d/KhQcjcTc9c8cKsQs2h/4c2s

Stock = 0, Suits removed = 1

Checksum: 11 + 14 + 10 + 5 + 2 + 13 + 2 + 23 + 9 + 2 + 0 + (1*13) = 104

Red: I propose we simply clear Spades with “id, ai, ai”, study the resulting position for a few more days, then choose the best way to remove suits and/or turnover our next card. If we still can’t decide where the next turnover is, there is always the option of clearing Hearts next.

Green: Yikes, this is too complex even for me. I like the idea of not turning over a card and minimising the chance of rot13(shpxvat hc) by trying to do too much in one day. “id, ai, ai” it is.

Blue: I wanna start thinking about Spades, Hearts and Clubs. Therefore “id,ai,ai,hi,hf,ha,ei,ea,gi,gj (h12=i8)”, study the resulting position for a few days then choose whether to clear Hearts or turnover a card. Of course If Bart/Bug insist on a turnover today then I won’t stop them.

Actual play (Decision 35, 22 Nov): id,ai,ai, if,bf,bj, eh,ei,bg,bh, (b2=f1), bc, gh, ca,ca,ga,cd,gc,ha,fe,ig,df,fi,fh,ah,af,cd,bc → King of Spades

Green: I’m voting “ca”. The missing cards are AA2334556788JJ. We can’t claim a lock but one or two more good cards should see us home. At least this decision is relatively straightforward.

Red: I prefer “ba” working on a column with only three face-down cards. The alternative “ca” duplicates Tens in columns 3 and 6 so the usual advantages of not shifting a King to an empty column doesn’t apply. Removing the Clubs costs an empty column – that’s too suspicious even by my standards … uhhh just kidding 😊

Blue: I like “ca”. We have plenty of empties, so our main concern is avoiding “one-hole-no-card” traps – and the best way to achieve that is to focus on columns with the most face-down cards.

Actual play (Decision 36, 25 Nov): ca → Four of Spades (Bart + Bug + Blue/Green)

Actual play (Decision 37): fi, cf → Eight of Clubs (Trivial)

Actual play (Decision 38): ca → Ace of Diamonds (Trivial)

Green: Be careful, with only one empty column the obvious “ch” would be embarrassing if we turned over an Eight. Better to sacrifice an in-suit build with “gb, he, ce” so we are well placed if the next card is a Seven or Eight.

Blue: Another alternative is “gb, (d2=h1), cd” which doesn’t lose an in-suit build. We can afford to bury the Q of diamonds since a Jack wouldn’t embarrass anybody – except the impostor.

Red: rot13(OYHR VF FHF). We are very close to completing the second Spade suit so we don’t want the 3 of Spades buried under an off-suit 2-A. I support Green’s “gb, he, ce”

Actual play (Decision 39, Nov 27): gb,he,ce → Five of Clubs (Green + Red + Bart + Bug)

Actual play (decision 40): ic, ei, ce (trivial) → Three of Clubs

Blue: Everything is lookin’ really great/except for one thing that I really hate/we might not be able to navigate/ to the face-down cards in column Eight/sort it out before it is too late/My final plan is now ready to state – “cf, ha, hc, (e1=h4), (c4=h9) he”

Green: I like Blue’s plan a lot, although his rapping in the iambic pentameter leaves much to be desired. The missing cards are A235678JJ. The flexibility in Column 10 means either Two or Five is a good card. I don’t see any way to lose even if Red were allowed to call the next three cards.

Red: Green is waffling too much and “ce,bc” looks simplest. Either we revert to Blue’s plan or we can remove the Club suit using the Four of Clubs in Column 10. That’s four in the corner. Four in the spotlight, losing its religion. Note that we were lucky because the last two cards gave us exactly what we need to complete clubs without shifting that pile of rot13(fuvg) in Column 8.

Actual play (decision 41): dc,jd,cj,ec,je,df (no card)

Green: Bart’s intentions are clear. Turn over all cards in columns 2&4 then trust that the game is won even if the impostor were allowed to call the remaining cards. I vote “be,bg,bi” regardless of what the next three cards are.

Red: I also vote “be,bg,bi”, but if we have N guaranteed empty columns regardless of unseen cards then we also turnover min(2,N-1) cards in column 4.

Blue: Interesting that Bart refused to turn over a card even though we were criticised for the same on Decision 35. In any case, let’s get this rot13(fuvg) over and done with. I also vote the same as Red.

Actual play (Decision 41b, 29 Nov): irrelevant

The final Moves

We have no trouble turning over the last cards in columns 2 & 4.

It is trivially easy to turn over all the cards in column 8 and the impostor has conceded “defeat” 😊

Among Us Lite – Round 4 Summary

Final position of Round 4

We’ve managed to clean up the Spade suit and are only one Jack away from shifting it onto the foundations. Hearts aren’t too shabby either. We have also turned over every face-down card in columns 1 and 10. On the minus side, we still 15 face-down cards in the tableau – and only one deal left. The game is not totally hopeless, but we would need some luck right now. I should point out Bart and Bug have done well to reach this position. For obvious reasons, I can’t discuss the specifics of where they went right or wrong at every non-trivial decision.

The other important issue of course is this one:

It is possible that neither Bug or Bart has any clue what’s going on. It’s also possible that both readers have every clue who the impostor is, but are not letting on – hoping to make my job tougher (it’s hard enough playing the role of all three Kolourfull Kibitzers). Or the truth may be somewhere in between. We shall find out in due course!

Among Us Lite – Round 4

Link to previous round can be found here

Previous Moves

Round 4 initial position:

x4s3s2sAsAc/xxxxxQs6h5h4h3hJh/xxxxxTc2cAh6s5s4h6c/xxKdQdJcTh9h8h9d/Ts9s8s7s6s7h/Ts4dQh/Qc8s7c/xxxxKcQhJhTh9h8d7c6h5c4c3c2cAcKh/KhQcJcTc9c8cKs/xxxxTdQs

Stock = 10, Suits removed = 1

Checksum: 6 + 11 + 12 + 9 + 6 + 3 + 3 + 18 + 7 + 6 + 10 + (1*13) = 104

Green: We can take two empty columns but can’t quite force another suit onto the foundations. I vote “bf,be,bi”

Red: I prefer “ji,bf,jf”. But I agree there is no need to take empty columns now.

Blue: I really want to sacrifice an empty column to tidy up that rot13(fuvg) in column 8 but can’t make it work. I vote “bf,ji,dj,df,id”.

Actual Play (Decision 28, 13 Nov): bf,be,bi → 9 of Clubs

Blue: I vote “jh, jf”, guaranteeing two turnovers.

Red: I can improve Blue’s plan with “jh,fh,jh”. We sacrifice an in-suit build but “take out insurance” if the next card is a King.

Green: It’s desperate either way but I vote “jh, dj, df, ef, ed, (d2=g1), je”, playing to complete the Heart suit. I will concede that sacrificing a turnover is not exactly pleasant.

Actual Play (Decision 29, 15 Nov): jh,dj,gb,df,ef,ed,cb,cd,je →  5 of Diamonds (Bart + SA)

Actual play (Decision 30, 17 Nov): jc → 2 of Hearts (Trivial)

Actual play (Decision 31, Nov 17): jf → A of Spades (Trivial)

Blue: Finally, some luck with the unseen cards in the tableau. I vote “dc,af,ad”. We are only one card away from completing the Spades.

Green: I can improve that to “cb,db,af,ad”. For those unfamiliar with Nathaniel Hawthorne, the scarlet letter ‘A’ is initially a symbol of shame but it ends up representing something else entirely. In our case, the Ace of Hearts in column 3 is precisely what we need to complete a suit of Hearts. “A” stands for Awesome!

Red:  Nineteenth Century romance novels aside, the obvious “jf” is entirely plausible. If we draw the Jack of Spades then we can still clear the Spade suit. Therefore, no need to expose Yet Another One Of Those Horrible Things in column 1. “A” stands for AAAAAARRRRRGGGGHHHH!!!!!!

Actual play (Decision 32, Nov 17): cb,db,af,ad → 3 of Diamonds (Green + Bug + Bart)

Green: Could be worse – at least we get one more turnover.  I vote “ab, ja” and pray.

Blue: We can tidy up somewhat. Better to play “ab, ha, gh, dh, ja”. We might need the option of turning over cards in column 4.

Red: Blue meant to say “ab, ha, gh, dh, jg” – which I agree with. Forget the Hearts for now – even if we can clear that suit, our reward would be exposing two Aces in columns 3 and 8. Our game plan must be “Spades or Bust”.

Actual play (Decision 33, Nov 19): ab,da,ed,he,gh,fb,dh,bg,jb → 4 of Clubs

And that’s the final turnover for this round.

Normally we have an opportunity for last-minute tidying up before dealing the next ten cards. But I’m not seeing anything – even “neutral options” are unavailable. The only legal move that doesn’t lose an in-suit build is “ac”, which is clearly ridiculous given the Spade suit situation.

Red: Deal

Blue: The

Green: Cards

Actual play (Decision 34, 21 Nov): Deal the cards.

Coming soon to a place near u: Round 4 wrap summary, followed by round 5.