In this article I wanna take a short break from Steve’s game and take a closer look at individual columns.

I believe that many players tend to focus only on the “uppermost sequence” in every column. For instance, in a column containing three face-down cards followed by K-Q-J-5-4-7-6-5-4-3-2-A (suits irrelevant), players would tend to focus primarily on the 7-6-5-4-3-2-A. This is understandable: if we have an empty column or two chances are we can easily shift the 6-5-4-3-2-A around (but not the 7 unless we have a spare Eight or were willing to spend an empty column).

In the following example, if we only focus on the uppermost sequence of columns 1,4,6 in the following diagram we would ignore the identity of four face-up cards (5s,4d,3d,Qs) and the number of face-down cards.

As a player improves his understanding of the game, he may start wondering why a number of close games tend to fall just short of victory. Is it just rot13(onq yhpx) or is there some deeper cause?

I think a useful guideline is to check for “danger signs” in individual columns. In an earlier post I warned about the dangers of e.g. having two Queens in the same column but no Jacks – because if that column became a junk pile then there is a real risk of having a Queen shortage when Jacks suddenly appearing at the worst possible moment. Whereas if the two Queens were in different columns it is harder for the Luck Gods to conjure up a Queen shortage.

The situation I am talking about is illustrated from another screen-shot from Steve’s book (Winning Spider Solitaire Strategies), but not taken from our current game. If the K of Hearts in column 9 is never shifted, there is always the danger of having too many Jacks appear later on. Note that this problem can’t be eliminated by turning over cards or obtaining empty columns.

Going back to the first diagram, column 3 is unbalanced. There is a Q-J imbalance of 2 and also a K-Q imbalance of 2. Obviously, we expect any column to have an imbalance of at least 1 somewhere (unless it’s a complete run of Ace to King, in mixed suits), so an imbalance of 1 is nothing to really complain about. An imbalance of 2 in a few columns may indicate sub-optimal play somewhere along the line (sometimes it can’t be helped). If a single column contains an imbalance of 3 or greater than you might wanna change your goal from “winning the game” to “publishing a paper”.

In column 4 we have two Queens, but also one Jack. That means if we deal e.g. a Ten in column 4 then there is only a Q-J imbalance of 1, but the K-Q imbalance is still 2. On the other hand, both Queens are the same suit. This means if we are close to completing a suit of Spades then having both Warlpiri Women (*) in the same column can become inconvenient. Generally, we prefer to have identical cards (in both suit and rank) in different columns, if all other things are equal. In column 1 we have the same situation with the 5 of Spades.

(*) There is another less savoury name for the same card that is worth 13 penalty points in a well-known trick-taking card game.

Of course, we are a long way from completing a full suit, but at least we are able to identify the possible seeds of defeat if we do get stuck with a “12-suit” in Spades in a difficult endgame.

Earlier in Steve’s game we had an “inverted sequence” in column 10. The Ten and Nine are in reverse order from what we would normally expect. Obviously, this game state is the result of dealing a row of 10 cards. The inverted sequence is a Good Thing since whenever the Ten of Hearts is shifted, it is always possible to move the Nine of Spades and win a turnover. Of course, this is counterfeited if another Nine of any suit is moved onto the Ten of Hearts.

Needless to say, it’s even better if the 9-0 in column ten is the same suit, but we take what we can get.

Other variants on inverted sequence are possible. For instance, if we had 3-2-A-6-5-4 all the same suit then moving the 6-5-4 guarantees we are able to move the 3-2-A. If they were different suits then we might still be in luck if we had an empty column or two. We could even have 6-7-8, which is only possible after dealing from the stock at least twice.

As an extreme example, if a column contained only A-2 suited then it is never correct to change it to 2-A. If you could win with 2-A, then victory was also possible with A-2. If this doesn’t illustrate the importance of inverted sequences then nothing will.

Summary

In this post I gave a number of possible good and bad situations in individual columns. In high-level play, evaluating a position is much more than counting the number of turnovers, in-suit builds or completed suits. With experience you should be able to tell the difference between e.g. a “good 4 turnovers” and a medium or poor 4 turnovers. Similar comments apply to in-suit builds.

A good player may pay attention to the whole board when it’s time to think about removing a suit or avoiding one-hole-no-card. But a great player is thinking about the whole board before things get critical. Next time you are asked to evaluate a game state, you should be able to recognise the danger signs pertaining to the contents of individual columns.

Summary of round 3 can be found here

Initial Position:

8c4d/7h6h5h4h3h2hAh7h/xxxx8hKc8h3s/0dAs/6s5s4sQs/xxx6dKsJc0c9c8c7c/xxxx3h2cAcJs0s9h8s4h/xxxKhQhJh0s9s8s6s5h4c3s2dAsAh/xxxKsQhJd0c9c8d7d6c5c4c3c2c2s/5s4s7c

Checksum: (2 + 8 + 8 + 2 + 4 + 10 + 12 + 16 + 16 + 3) + 1*10 + 1*13 = 104

Monkey Recommends: cg,fe,bc,bc,ig,ie,dg,he, deal

Actual play (date = 5/Feb, score = 459): ???

Spider GM comments: Bart has kindly requested I shorten the Monkey’s sequences if he repeats the same position with redundant moves. I have done this manually for the time being, but hopefully I can fix up my GitHub code soon …

IM Bart/IM Bug, please confirm you are happy with this final position.

Moves can be found here

Not much to write about unfortunately. We got a terrible distribution with five Sixes, five Eights and zero Sevens. Not to mention zero turnovers. At least we got a few in-suit builds.

Bart mentioned that only 5% of distributions would be worse than what we actually have. I would be interested in how he actually measured that. Did he choose to focus on Sixes, Sevens and Eights before the hand or during the hand? Is he measuring the worst differential between any two consecutive ranks or three consecutive ranks? Is he applying the cryptographic Keccak-256 hash function to our game state and looking for any series of 81 digits that form a valid Sudoku? I brought up similar issues in an earlier post.

The other problem worth mentioning is four Kings are already in play. Change them to all Queens and our prospects will be much better (even though we still don’t get a turnover). The only bright spot is it is illegal for the computer to send over a very inconvenient Backgammon doubling cube centred on ‘2’.

Moves can be found here.

This was a decent round. We got 12 turnovers, most of which are in-suit. In Monkey-speak our evaluation is 128 points, assuming turnovers are worth 10, in-suit builds are worth 1, and Spider GM hasn’t forgotten how to count. On the minus side, every column has at least one face-down card and we’ve all had our fair share of demoralising losses where no empty column was obtained for the entire game. Still, I think it’s too early to worry about that yet.

There were no complicated decisions to make and I would expect any half-decent player (such as my famous brother Terence Tao who introduced me to the game many years ago) to reach the same game state – ignoring some minor variation such as flipping a coin on the last turnover.

I expect future rounds will pose some more interesting decisions – as well as further insights into the strengths and weaknesses of Ninja Monkey’s algorithm 😊 Obviously I was never expecting miracles from NM, but having gained some experience with GitHub and Python’s tkinter package, I’m not in a position to complain. At least I have some idea for further improving the algorithm. Whether I actually get enough time to implement this is another story. But we digress.

With IM Bug is returning to the fold in about one week’s time, this promises to be more exciting than the current rot13(fuvgfgbez) involving Novak Djokovic and Australia. 😉 Game on!

After reading the comments on my previous post it is apparent that IM Bug will be busy for the first half of January but is happy to play Tomato Sauce once the game gets under way. So I will probably go with that. The game will begin at the start of the new year, give or take a few.

I anticipate there may be some teething problems with the “Ninja Monkey format”, so I am intending to play a game with IM Bartacus only but I will take things slowly until the (possible) teething problems are sorted out. For instance, I might ask IM Bartacus for the best move even for trivial decisions, or I might have longer breaks between individual posts. Not to mention the pandemic situation in South Australia might also have some impact on my blogging schedule. In any case, that would also mean giving IM Bug less catching up to do once he is ready to join the party.

An alternative idea I had was to start a game with 20 face-up cards instead of 10 (i.e. we are forced to deal 10 cards from the very start). This will ensure the initial decisions will (probably) be much more interesting. However, the main focus of that game will be teething problems with the Ninja Monkey format. I intend to abort the game on 14^th of January (approx.) regardless of how well or badly the game is going. Once IM Bug is ready then I can start a proper game.

I’m expecting the first option is the way to go, unless both IM’s really like the second. The previous Among-Us shenanigans have taught me the simplest option(s) should often be given more respect than what I normally give.

Let me know what you think. Comments from new readers eager to show off their own Mad Spider Solitaire Skillz are especially welcome 😊

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” 😊

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!