Don’t Miss the Forest for the Trees

Having dealt three rows of cards from the stock, I think now is a good time to take stock (badumtish!) before thinking about our next moves. We don’t wanna miss the forest for the trees, if you pardon the terrible cliché.

The game state is deplorable. We have a million cards face-down and very few in-suit builds. Bart correctly points out we don’t even have a run of three cards in-suit anywhere. But at least we have an empty column and a turnover in column 2.

In the opening stages it is easy to approximate the chances of increasing our minimum guaranteed turnovers by assuming each rank from Ace to King occurs with an equal probability of 1/13. But with many cards exposed, this assumption is no longer reliable. We can still apply the usual routines of “computing outs” but we need to be careful.

AceTwoThreeFourFiveSixSevenEightNineTenJackQueenKing
4623644414545

We have a severe excess of various cards (Twos, Fives, Eights) and droughts (Threes and Nines in particular). The good news is once we turn over more cards, these inequalities should even out. But we need to turn over cards first!

We have some “good news” in column Three. Two useless deuces and aces are already used up, so this effectively makes a good junk pile. Basically our shortage of Threes is not as bad as it looks. Most of the buried cards are relatively useless – apart from that Three of Clubs in column Eight. Still, given our poor position, one “inefficiency” could be enough to consign us to a loss. If the Three of Clubs were at the front of column Eight instead of being buried our position would be much better.

Bart talks about “Market Value”. There are two Sevens available for the 6-5 of Clubs so Sevens are expendable. In contrast, there is only the Six of Hearts available for the 5-4 of Diamonds, so Sixes are not expendable. At least we get our hole back. We also have two Jacks that “want” the Queen in column Ten, so Queens are definitely not expendable.

If you have an incredibly good memory, you may recall that we started the game with the intention of listing a number of possible cheevos as a possible bonus. Unfortunately, we will have more than enough difficulty with winning the game, let alone pulling off a cheevo. It seems our most likely cheevo is getting someone other than Bart or George to contribute a meaningful comment, and I wouldn’t wanna bet my Ph. D. thesis on that happening any time soon!

BTW, last time, I yanked the J-T from column 1 in hopes of being able to shift the 7-6-5. My gamble was partially correct – we got our empty column back but the Two of Hearts scotched any dreams of column 1.

In the next week I will answer the question of finding the best play.

Game on (3 April, 2021)

Here is the position from last time:

It turns out we cannot turn over a card without losing the empty column. We can “yank” the J-T in column One onto the Queen (or better still, shift the J-T-9 of Hearts in column Ten onto the Queen of Hearts first, but we cannot shift the off-suit 7-6-5 onto an Eight. As a general rule, one hole is not enough to shift a sequence of three cards if they are all off-suit. Well done to Bart for spotting this.

Note that we exposed the “wrong” Five last week. If it were the Five of Hearts instead of Clubs then we can turnover column 1 without losing the empty column (yank the J-T, swap the Five of Diamonds with the Five of Hearts and then we are good to go).

Bart gives four possible plans:

  • Turn over a card in column h, putting an Eight into the empty column.
  • Move the queen of Hearts directly onto the empty column
  • Move the 5-4 of Diamonds onto the empty column, then dump the Queen of Hearts onto the King
  • Dump the 6-5 of Clubs onto the empty column then build in-suit with 2-A of Diamonds.

There are many variations possible but any reasonable sequence of moves boils down to one of the above four plans. Another key decision is: do we yank the J-T from column One?

Bart prefers the third option, with the Boolean yank_JT flag set to TRUE. His exact move sequence is:

fb,af,jg,aj,fa, de,df,gd

I have a few things to say about this:

  • The move jg is illegal! We should perform jg before af. As so often happens in delicate situations: move order matters!
  • The first move should be fe not fb. This retains an extra in-suit build for no cost.
  • It will be necessary to break an in-suit build in Hearts if we are to turnover column Seven. The last move gd is therefore also illegal.

Still I think Bart has done extremely well to spot both the correct plan and value of yank_JT: even though we can’t turnover column 1 yet, we might be in a good position to do so after the next deal.

It is true that dumping the Queen directly into the empty column has an advantage over dumping the 5-4: we regain the empty column if the next card is a King or a Six. The downside is if nothing good happens then the Queen will be blocking Column 6 with only three Kings unseen. This could be unpleasant, especially with at least three face-down cards in every other column.

You may be wondering why I chose to tidy up column One now when I had an earlier opportunity to do so. The reason boils down to the following knowledge bomb from Edifying Thoughts of a Spider Solitaire Addict:

An empty column will never contain face-down cards for the remainder of the game.

Why is this important? Since column 6 will never contain face-down cards for the remainder of the game our chances of recovering an empty column are decent. It is so much easier to win back an empty column if there are no face-down cards to worry about. And once we get the empty column back, we have a reasonable chance to shift the off-suit 7-6-5 onto an Eight.

In summary, my move sequence would be “fe,de,jg,af,aj,fa,gj,de,gd”

We expose a Two of Diamonds and are forced to deal another row.

As usual, we have an interesting decision to make immediately dealing a new row of cards. How would you continue here? Are there any tesuji possibilities, borrowing a term from the game of Go (a.k.a. Baduk)? Or should we simply ask ourselves What Would Captain Obvious Do?

Game on (27 March 2021)

This is the position from last time

The obvious play is fj,fj but Bart recommends to tidy up with eb,eh,eg,je presumably followed by fe,fe turning over a card. In fact there are several reasonable options to choose from, despite the fact we have only one guaranteed turnover. Let us look at the position a bit more closely:

After fj,fj we get an extra turnover if we expose any of the following cards: A4577TJK. Note that I count the Seven twice since that gives two turnovers.

With Bart’s suggestion we get a turnover if we expose any of the following: A47TJK. Note that a Seven is only worth one turn-over since the 6-5 in Column Two is offsuit. This would be a significant price to pay in a game that’s not going so well. Another long-term problem is we are shifting cards off column 5 but there is little chance of clearing the King of Hearts anyway – unless we get something like 8H-7H-6H-5H-4H-3H-2H-AH on the next deal. Good luck with that!

Looking for other options reveals the possibility of working on column One with ab,jg,aj,fj,fj. This allows a turnover if the next card is any of A4577TK and also guarantees the best possible  layout in column 1 even if we get a bad card in column 6. A disadvantage is we commit ourselves to shifting the Jack of Diamonds onto a Queen when we might prefer the Jack of Clubs.

Our main priority is turning over cards and empty columns.  If we get an empty column then in-suit builds will take care of themselves. With several reasonable options to choose from there is no standout play. I chose the simple fj,fj (note that jg,fg,fg is an extra in-suit build but would not result in a turnover if we get a King).

We turn over a Five of Clubs – good thing we kept that Six of Clubs free, and as Texas Holdem players are wont to say – it was suited!

We turn over the Four of Spades, and that’s our first empty column!

Unfortunately we’re not yet in a position to party hard, pretend the game is Backgammon instead of Spider Solitaire, whip out a doubling cube and look for someone willing to bet against us winning with at least one cheevo to boot. We’ve still got some work to do.

I know it sounds trite but with great power comes great responsibility. Our empty column means there are a great many possibilities to consider, and therefore more chances of choosing a sub-optimal line of play.

How would you continue?

Game on (20 March 2021)

This is the position from last week.

Bart suggests we move the Ace of Hearts to column 4, split an in-suit build by shifting the Ten of Hearts onto the Jack of Clubs, then take the turnover in column 6. Our notation would be gd,gh,fh,fh.

The reason for splitting the J-T of Hearts is to focus all our efforts into getting a free space in column 6. However I don’t like the idea of dumping so much junk into column 8. I would rather have the junk in column 10 since that already has two Kings.

Bart’s play would only gain if the next card in column 6 was a Jack. Then even if we did obtain an empty column there is a good chance we are forced to give it back anyway. That’s a lot of ifs and buts for the cost of one in-suit build and junk in the wrong column.

Still there is not much difference between the plays and our position is rather poor in any case.

Bart also briefly mentions other plays which are clearly inferior, e.g. Jack of Clubs onto Queen of Spades, forfeiting a turnover for no reason.

With nobody else suggesting a spectacular brilliancy that everybody has missed, I’m going for the simple gd,gj, turning over a card in column 7 and intending to turnover column 6 if nothing better turns up.

We get the Queen of Hearts.

This raises an interesting point. We have three “excess Kings” (i.e. unaccompanied by a Queen) in column 4,9,10. This suggests Queens may be difficult to extract in future rounds. Clearly the Queen was not the best card (no extra turnover!), but it does give us some options.

We could continue with the original plan of turning over column 6. Are there any other options to consider? Remember that the most obvious move is not always the best! How would you play here?

Game on (13 March 2021)

This is the position from last time:

An obvious option is to build in-suit with 2-A of clubs in column 3, but that is only one turnover as well as exposing another ace. A closer look reveals we can obtain two turnovers in columns 6 and 2 which is clearly far superior.

It is possible to combine both plans with cg,fg,fi but I would rather avoid that. If we played fc,fi and turned over a Deuce we would still get the turnover in column 3 anyway. So fc,fi it is.

We get Eight of Clubs and Five of Spades as our turnovers. Obviously we turnover another card instead of building in-suit and exposing a King. Unfortunately we get another Ace. We then do some tidying up before dealing a new row.

Not the greatest start to a game of Spider Solitaire, but the only bright spot is Colorful Sisters is now following my blog (unfortunately a cheevo only occurs if they contribute something meaningful in the comments section). Going back to more important matters – how would you continue here?

Game on (3 March 2021)

Recall we asked the following questions:

  • Suppose you were legally required to turn over all three four possible cards simultaneously. What would be your play?
  • Suppose after making your first move you were able to call the next card (both rank and suit). What would be your top three choices?

To answer the first question: the obvious moves are to build in-suit with the Q-J-T of Hearts and then put that on one of the Kings, followed by an off-suit J-T. The problem is that if we turn over a new Queen then we lose a turnover since our off-suit J-T cannot play onto the Q.

At this stage, it might occur to you that one can play the Q of Hearts onto a King, then add the J of SPADES and an off-suit Ten. Finally we can build in-suit with the J-T of Hearts. The difference is we only build in-suit once, but we get an extra turnover if any Queen appears. It’s not at all clear whether sacrificing a turnover like this is worthwhile, but the main point I wish to make is such a possibility exists – and you will find many more examples in your journey to Spider Solitaire mastery 😊

As for the second question, Bart correctly identified that Queen is the only rank that gains two turnovers. The best suit is clearly Spades, ensuring both turnovers are in-suit. Bart then wants the Queen of Hearts, but I prefer the Queen of Clubs since that means one of our extra turn-overs are in-suit. Bart then has Queen of Clubs as third choice, which I would agree with given he has already committed to the wrong Queen for 2nd choice 😊

Bart chose the QH because Hearts is closest to completion and exposing more Hearts will further that goal, even if some cards are duplicated (since we might need the “other” queen later). At this early stage, I don’t like committing to the “suit nearest to completion”. There are plenty more cards to come, and we might find e.g. the 9-8-7-6-5-4 of Diamonds turns up and suddenly we wish we focussed on Diamonds from the beginning. Of course if we do manage to land the Bart’s Quickie cheevo I am happy to be proven wrong.

In other words, let’s just focus on maximum turn-overs, in-suit builds and empty columns and once we have more cards in play it will become obvious which suit is closest to completion.

Well that’s enough pontification on the opening position for now. Let’s make some moves.

(eg = KH, ce = AC, ie = KD, ae=7D, fa=7C)

Well that was disappointing. We drew two Kings and an Ace, and only obtained one turnover more than our guaranteed minimum. Looks like Trevor’s Quickie isn’t happening any time soon. ☹ Note that I eschewed the Q-J of Hearts in-suit build for reasons described earlier.

So here we are, like it or not. At least the Kind of Diamonds landed on another King. How would you continue here? (HINT: consider all reasonable options before committing to a line of play).

Game on (28 Feb 2021)

As promised, here is the new game. Recall that I have decided on the following cheevos

  • Cocky: if the game is going well, deal the last 20 cards as a single unit and still manage to win.
  • Auto-complete*: Deal an in-suit ace onto an existing run of King through Deuce, thus completing a suit.
  • Trevor’s Quickie*: Get an empty column in 6(5) moves for columns 1-4 (5-10)
  • Bart’s Quickie*: remove a suit before third deal
  • Nigiri: remove suits in pairs (as suggested by Bart)

There is to be no Mulligan, even if the hand rot13(fhpxf). Here is what the Card Gods have given us:

By this stage, the question of counting guaranteed turnovers and finding the best move is too easy so I will instead ask the following questions:

  • Suppose you were legally required to turn over all three possible cards simultaneously. What would be your play?
  • Suppose after making your first move you were able to call the next card (both rank and suit). What would be your top three choices?

The cheevos are in!

Firstly, many thanks to George and Bart for their thoughts about cheevos. Also, thanks to Chefverse for liking my cheevo post. There is no indication of whether he she or ze actually knows Spider Solitaire or whether he she or ze just likes my engaging writing style 😊 But I’ll take it regardless!

George suggested dealing all cards before making a single move. He claims he succeeded on the first try with two suits sans Zeekee followed by twenty losses in a row. I experimented with this and it does not look feasible.

Bart suggested suits should ideally be removed in pairs. If we ignore cheevos then most wins at the four-suit level occur with the first four suits removed being one of each suit. It would be rare to have e.g. DHDCHSCS with all red cards removed by the fifth triumphant C major chord (assuming we play the Microsoft Windows version). Rarer still would be something like CCHHSSDD, which is the sort of pairing Bart is talking about. Bart also mentioned the possibility of removing a complete suit before the third deal. Both of these are reasonable cheevos.

Bart also mentioned a potential problem with late cheevos: if you have to struggle for half the game before being in a position to even attempt the cheevo then the fun coefficient is not as high as it should be.

Ergo, I think it will be more fun to specify multiple cheevos, in order to increase the chances that we should be in a position to attempt at least one of ‘em. To be more specific let us assume a win is worth 10 happy stars and each additional cheevo is worth less than 10 – and we try to maximise our expected number of happy stars. Since my suggested cheevos are inherently superior to anyone else’s mine will be worth three and Bart’s are only worth 1 bwahhahahahahahah😉

Note that some of these cheevos do not require winning the game. These are marked with an asterisk (*).

  • Cocky: if the game is going well, deal the last 20 cards as a single unit and still manage to win.
  • Auto-complete*: Deal an in-suit ace onto an existing run of King through Deuce, thus completing a suit.
  • Trevor’s Quickie*: Get an empty column in 6(5) moves for columns 1-4 (5-10)
  • Bart’s Quickie*: remove a suit before third deal
  • Nigiri: remove suits in pairs (as suggested by Bart)

Fun fact: Nigiri refers to a protocol for deciding colours in the game of Baduk. It is based on arranging stones in pairs and having one player guess whether the number of stones is odd or even.

As an additional incentive to encourage more interaction on my blog, anyone who contributes at least one meaningful comment before the game ends – win or lose – is worth 1 happy star (except of course Bart and George). So in theory we could win well over 10 happy stars, but remember contributions must be meaningful!

NOTE: We will not be concerned with the number of moves. Hopefully this will simplify the decision making, since I anticipate that keeping track of multiple cheevos will not be trivial. As we gain experience with cheevos, hopefully we can increase the complexity!

The game will begin tomorrow. I will start a new game on Windows 10 and there will be no mulligan if the starting position rot13(fhpxf).

Good luck!

Game Off (13 February 2021)

Here is the game state from last time

We were in the unhappy position of not being able to turn over any cards despite having one empty column (or more precisely the ability to procure one). At least there is the option of removing clubs.

George suggested the following moves: (dj, fj, ed, ge, ae, ag, aj, jc, jg, jf,)

We can improve that slightly: the Two of Hearts can be placed in column 6 instead of column 5. This allows to built in-suit with the 43 of Diamonds. George is hoping to reveal more cards in column 10 which is a reasonable plan.

Bart gives some detailed analysis but doesn’t offer a precise sequence of moves. He suggests something completely different to George: first it is not necessary to remove the Club suit now, since if we deal the “other” King or Ace of that suit then things might improve. He also wants to shift the Jack of Hearts in column 2 to the KQ of Spades. Since there are four Tens unseen, it is highly advantageous to free the 98 of Spades in preparation of the last round.

I actually want to focus on the left-most column because we have all the Hearts exposed. If we can reach the Four of Hearts from under the King then we will have an excellent chance to clear Hearts. Therefore we don’t need to expose any more cards since we already have what we need (I’m hoping that once we clear Hearts and Clubs, the face-down cards will take care of themselves). Yes, this has the disadvantage of exposing an extra Ace, but I’m willing to take the risk.

My preferred sequence is: dj, fj, gd, ad, eg ae, aj, af, da <deal>

Note that the clever gd saves a move because we want to build in-suit with 32 of Hearts. If the third move was the more obvious gf, we would need an extra move! Now surely this attention to detail deserves to win the game, or there would be no justice…

Before going through the usual routine of computing guaranteed turnovers, in-suit builds, empty columns, removing full suits, making coffee etc, a careful examination of the board state reveals a rather unpleasant message saying that we have lost the game. This one is particularly rude since we didn’t even get a chance to examine what the last ten cards were!

As far as I know, there are three fundamentally different scenarios where the “No More Moves” message occurs:

  • We deal 10 cards and they be like ten odd numbers (counting J/K as 11/13) or ten evens. Unless we get lucky with at least one card falling in-suit then there are literally no legal moves.
  • Our position is hopeless, but we still have some legal (but irrelevant) moves. We know the game is mathematically lost but OCD compels us to make as many in-suit builds as possible. At least the No More Moves message doesn’t come as a surprise.
  • The game is actually not over. I’ve had this happen but can’t remember if Microsoft Windows was the culprit. The game state does look pretty bad, but with some clever manouevering one can actually make progress despite the lack of an empty column. Essentially you are playing the Tower of Hanoi without any free spaces, but you have the right “stepping stones” that achieve the same effect as an empty column. But it is difficult for the software to detect this.

A fun exercise for the reader: recall that we didn’t even get to see what the last 10 cards were. Can you compute all the possible game states given the screen dump above? For instance, we know no column can contain an exposed Two of any suit, otherwise we could shift an Ace in column 1 or 10, and the message would not have appeared. If you’re really obsessed with improving your game, try playing out this position with two physical decks of playing cards and see if we had good winning chances or not.

For ease of reference here is the position before the fateful last round (the Score should be 447 but I had to undo after dealing the last round, since I wasn’t expecting this to happen).

Game On/Short Story (7 Feb 2021)

“Oh I love trash!”, sings Oscar The Grouch. He is especially proud of the ever-growing stacks of cards in columns 1, 5, 9 and 10.

“But what is so good about the ever-growing stacks of cards in columns one, five, nine and ten?” asks Grover.

“Well,” replies Big Bird. “The more cards you have in those columns, the less you have in others. So it is easier to get spaces in columns 2,3,4 or 8. “This is why Oscar likes his trash piles”.

“That is true,” replies Grover. “But we did not get a good deal. We can not get more than one empty column.”

“But I want to know what’s the best move!” cries Elmo, who is clearly impatient with the discussion about how best to proceed.

Count Von Count walks in, together with a couple of human guest stars – today they happen to be Bart and George.

“Before we can work out the best move,” begins Count von Count, “we need to count the cards!”

Count von Count gets all the children to name the cards, starting from the left-most column and working towards the right. As the kids eagerly announce the rank of each card, Bart draws a tally mark next to the corresponding symbol.

“King! … Queen! … Jack! … Six! … Five! … Four! … King! … Queen! … Jack! … Ten! … Nine! …”

It takes a while, but Bart eventually ends up with the image below. Meanwhile, the others are busy contemplating whether it’s possible to remove a complete set of Clubs.

“We can do it!” shout the Bad Idea Bears. “We can remove a complete set of clubs!”

“Not so fast,” says George. “That would cost us our only empty column.”

“Besides,” adds Bart, “You ain’t welcome here, you’re from the wrong crowd.”

“Awwww” groan the Bad Idea Bears. They reluctantly leave the playing hall.

 It seems a better plan is to partially complete the Club suit and wait for better opportunities. If for instance we find the other Ace of Clubs, then we need not shift the Three in column 1. Or if we expose the second Club King then we could look forward to a new card more useful than the Eight of Spades.

“We should turn over a card in column 7,” says Big Bird.

“I agree,” says Count von Count. “There are four Tens unseen and that would give us two empty columns.

“Yes,” says Spider GM. “It is more important to take the card in column 7 than to remove the Club suit. Now it’s just a matter of working out the detailed sequence of moves.”

Spider GM is pleased that all his students are contributing to the discussion.

“Don’t forget,” says Count von Count, “that we are aiming to win this game with a score of 1000 or better. I believe we have played 143 moves so far.”

“Finally!” cries Elmo, as we start to move some cards around.

We reach the following position and are about to reveal what will probably be the most important card in the history of Four-Suit Spider Solitaire. If it’s a Ten then we’re in business.

And the final card in column 7 is … the Two of Hearts. It’s not the best card – then again it certainly isn’t the worst.

We now reach an all-too-familiar endgame scenario. We can easily get back a space in column 7, but we can’t turn over a new card. Fortunately there are still 10 cards in the stock, else it would be game over. How would you continue?