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!

Cheevo, away we go!

We’ve all been there.

Playing Spider Solitaire is no longer fun. Winning is too easy, even at the four-suit level, sans ZeeKee (as George will say) and playing an online server that is known to be biased #yeahright. Not enough frustration in our lives? Do you need more challenges to keep life meaningful?

Enter our old friend, the Cheevo.

Originally used to describe achievements earned through various games on the Xbox360 and other platforms, the C-word has been made universal throughout all kinds of games, including cerebral pursuits that don’t involve the curse of Nintendo Thumb. Cheevos are not the official goal(s) the protagonist is trying to obtain, but are optional extras invented by game fanatics who crave an extra challenge.

For instance, I once beat a very strong chess player without moving my queen off her starting square. My opponent blundered horribly and had to give up the material equivalent of four pawns for no compensation. He immediately resigned – but had he been paying more attention to my queen throughout the game he might have continued playing out of spite, just to wreck my cheevo. Chess fans may recall that Magnus Carlsen pulled off a similar feat against Viswanathan Anand (and also promoting a pawn to a second queen!) Similarly, a poker expert might hope to win first prize in a home game without ever showing down AA in Texas Holdem. And of course, every serious bridge player above the legal drinking age knows the significance of the Seven of Diamonds!

So, what possible cheevos can we have in Spider Solitaire? The short answer is you are only limited by your imagination.

For instance, one cheevo is to remove all eight suits in the last eight moves of the game. I suspect this will be very difficult with four suits sans ZeeKee, even for an expert player. Another cheevo might be some form of multi-tasking, such as improvising a rap song describing your thought processes while simultaneously playing to the best of your ability. What other cheevos can you think of? Remember that you are only limited by your imagination!

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?

Intermezzo

In Microsoft Window’s Spider Solitaire I found an unusual feature/bug: if a player completes a suit he receives a 100-point bonus but is not penalised 1 point for the move. For instance, suppose we have K-Q-J-T-9 of Hearts in one column and 8-7-6-5-4-3-2-A of Hearts in another and our score is 458. If we clear Hearts our score becomes 558, not 557. Another example: suppose we have no completed suits, a score of 400 and our target is to win with 1000+ points. The maximum number of moves we have is 208, not 200.

Note that clearing a suit is automatic, so we don’t have the option of completing the suit but refusing to move it do the foundations. In rare circumstances this option may be desirable, but giving an example is left as the proverbial exercise for the reader.

Here’s another fun question: what is the theoretical minimum number of moves required to beat Spider Solitaire if the cards fall perfectly?

To avoid accidentally revealing spoilers, I will insert the lyrics for one of my favourite anti-smoking songs.

Once a stupid smoker camped by a billabong

Under the influence of L.S.D.

And he sang and he smoked while his mates were drinking alcohol

You’ll come a smoking will kill ya with me

Smoking will kill ya smoking will kill ya

You’ll come a smoking will kill ya with me

And he sang and he smoked while his mates were drinking alcohol

You’ll come a smoking will kill ya with me

Up rode the smoker mounted on his thoroughbred

Down came the troopers one two three

What’s that illegal drug you’ve got in your tucker bag?

You’ll come a smoking will kill ya with me

Smoking will kill ya smoking will kill ya

You’ll come a smoking will kill ya with me

What’s that illegal drug you’ve got in your tucker bag?

You’ll come a smoking will kill ya with me

Rot13(shpx) said the smoker he committed suicide

You’ll never catch me alive said he

And his ghost may be heard as you pass by the riverside

You’ll come a smoking will kill ya with me

Smoking will kill ya smoking will kill ya

You’ll come a smoking will kill ya with me

And his ghost may be heard as you pass by the riverside

You’ll come a smoking will kill ya with me

The simplest viewpoint is to consider in-suit builds because the game is finished if and only if we have exactly 96 in-suit builds.

Each move gains at most one in-suit build (e.g. 6 of Hearts onto the 7 of Hearts). Dealing a row of 10 cards can gain at most 10 in-suit builds. We start with zero in-suit builds and can deal from the stock five times. To obtain 96 in-suit builds we require a minimum of 5 deals (worth 50 in-suit builds) plus 46 moves to pull off the Holy Grail of Four-Suit Spider Solitaire. That’s 51 moves in total. Well done if you answered 51 moves.

Assuming we start with 500 points, our final score is 500-51+800 = 1249 points … plus an 8-point rebate for the feature/bug described above. That’s a grand total of 1257.

And what happens to our score if we deal a row of ten cards and automatically remove two or more suits? Even I don’t know the answer to that one 😊

Exercise for the interested reader: get two physical decks of playing cards and deal a hand of Spider Solitaire. Ignore the identity of face-up cards (so if you see an Eight of Hearts, you can pretend it is the Four of Spades or any other card of your choosing), so you are effectively distinguishing only between face-up cards and face-down cards. Remember that you cannot deal a row of ten cards if you have at least one empty column. Play out the hand and verify that victory can indeed be attained in exactly 51 moves.

Game On (31 January 2021)

This is the position from last time:

Bart said he wants to make sure column 2,3,4,8 are atomic (i.e. a single in-suit run of 1 or more cards) to maximise the chances of getting an empty column. Thus one option is 6-5-4-3 of Clubs into column 8 and then A-2 of Spades onto either column 3 or 4. Bart even went so far as to suggest an alternative of putting the 2-A of Spades in column 5 into column 8 instead of one of the in-suit threes! This is to maximise the chances of getting back the empty column with many exposed Threes available.

George suggested we look at column 7. He suggested we can “break” the J-T-9 of Clubs by shifting the Ten of Clubs onto column 6. Then he wants to move the 9-8 of Hearts in Column 9 hoping to work on column 9 in the future. The lowly Schistocerca Americana quickly adds a caveat that we may be hoping for a miracle (as per the well-known ageless cartoon with step two needing to be more explicit).

George’s plan sounds very strange to me. Firstly I think he is trying to achieve too many goals with limited resources – if you’re gonna split the J-T-9 of Clubs, why not go all the way and split K-Q of Spades and shift the Queen of Spades onto column 10 (incidentally we can rebuild the J-T-9 of Clubs)? Then at least we can dump the King of Spades into the empty column and get one turnover. The second issue I have is even if we get a card in column 9, we would have exposed a King and Ace in the process. Ideally I would much rather work on Column 1 (at least we win back an empty column as soon as we reach the Four of Hearts). Unfortunately, this turns out to be impossible.

Bart’s plan looks more sane, but I think he is fighting the wrong battle. We should be aiming to complete entire suits – this sounds more positive than just “trying to maintain the status quo” by keeping at least one empty column. Eventually we will run out of cards from the stock and if we’re unable to clear an entire suit or turnover any cards then having an empty column is about as useless as the Fundamental Theorem of Calculus – admittedly that’s not the best expression to use but we gotta keep this blog clean 😊

A closer look at the game state reveals we now have every card in the Club suit exposed. Ditto for Spades. Therefore we should work on at least one of them. Clubs seems the better suit, so we must work on column 5 (even though it will expose an Ace). I would shift the 2-A of Spades onto one of the in-suit Threes, then dump the 8-7 of Diamonds in column 7 into column 8 and build in-suit with the 9-8 of Clubs. I would also break an in-suit build in Column 2 by shifting the 7-6-5-4-3 onto column 9 since Bart correctly points out the importance of keeping some columns “atomic”. My actual play would therefore be ec,bi,gh,eg which costs six moves since “bi” was a supermove. Assuming we get a good deal on the next round, there is a decent chance of tidying up (e.g. connecting the J-T of Hearts in the middle two columns), even if we don’t clear the Club suit.

As a general principle, when thinking about long term goals (e.g. clearing a suit), don’t be afraid to sacrifice a little e.g. by breaking an in-suit sequence or refusing to turnover a card even though it’s legal.

We deal another round, let’s hope it’s good.

New deal: 3d,Jh,6h,Qc,2d,8h,7h,5d,7h,4d

How would you continue?

Something different

In a previous post, I’ve had (legitimate) complaints about someone not being able to see images clearly.

It’s easy enough when I’m typing in the comfort of my own home, with my own PC that is yay wide and yay high (insert corresponding hand motions here). But my readers could be reading on mobile phone. The other issue is suits of the same colour can be hard to distinguish.

I’ve seen poker cards with four different colours, so Clubs become green instead of black and Diamonds are blue instead of red. I am not aware of something similar in Spider Solitaire programs (online or otherwise). Perhaps this is a chance for one of my readers to teach me something instead of the other way round!

Absent the possibility of four-colour suits, the next-best option is for me to transcribe a text version of the current game state – which you no doubt will have noticed in my previous post. Transcribing images seems to be the Done Thing in Puzzling Stack Exchange, which I have also contributed to.

Another problem I noticed over the years is if I type a string of numbers separated by hyphens then some devices may treat it as a phone number. This was back in the day when I was liberally using ASCII to encode rude words. But if I use commas instead of hyphens then things are OK. Similar considerations may apply to move sequences such as <ab,bd,gb> where each letter corresponds to one of the ten columns in Spider Solitaire.

TLDR version: the noble Spider GM is aware that he has goofed and is trying to make every effort to un-goof in future posts. Let me know if you have any other thoughts.

Game on (24 Jan 2021)

This is the position from last time

First of all, a big thank you to anyone who took the time to analyse this game state.

My preferred play is to get three empty columns, then take a card in column 3.

I won’t claim this is the best play and/or attempt to analyse this position to the N-th degree, but I will make a few general observations:

  • Getting a partial run of Clubs is not worth it. It costs two empty columns and exposes an Ace of Hearts (Aces are often undesirable since nothing can be played onto an Ace).
  • We also should pay attention to column 8, since once we exhaust the “easy” cards in column 3 we might be in an embarrassing predicament of not being able to expose any cards despite having at least one empty column. However, we can turn one card in column 3 and still have the option of taking a card in column 8. So may as well start with the easy option and reassess later.
  • Note that turning over a card in column 8 would cost two empty columns – but would not be a terrible play. For one thing, it allows us to build a partial run of Hearts from King to Eight. Also, the Nine of Spades may take care of the Eight of Clubs in column 5.

Since we are playing for a score of 1000+, we should think about careful move orders. My preferred play is: bi,di,di,fh,fe,fc,bd,gf,bg,dg,bg ,cb,cd.

 Note that the 9-J-T-8 of mixed suits in column 2 is particularly awkward. Clever attempts to expose a card ASAP (thus gaining more information) before taking our three empty columns do not work – as far as I can see.

We turn the 8 of Diamonds. This means we’re definitely taking the Nine of Spades in column 8. We then get two more Threes, which at least means we’re closer to using the cards in column 5 if we need ‘em.

Thanks to our foresight, we avoid the one-hole-no-card problem alluded to earlier. If we get empty columns then there are plenty of easy turnovers in column 8 to go around. We get the SEVEN OF SPADES …. Hallelujah! This is such a good card, I’m taking a screenshot 😊

Unfortunately we get another Three of Spades. This leads to an interesting problem.

We got a glut of Threes in the last few cards. Suddenly we want to shift the King of Hearts in column 1 to an empty column – and immediately get it back with the Four of Hearts. But this is not possible.

The main point I wish to make is three empty columns ain’t a licence to claim immediate victory. I learnt this lesson many times over at https://www.free-spider-solitaire.com/. Perhaps it was possible to anticipate the problem in column 1 with more judicious play. I probably would have been more careful – except I already committed to winning with a score of 1000+ ☹ If this game is lost then at least I can blame my mobile phone’s random number generator.

Anyways, let us continue. The Seven of Spades gives us back an empty column in column 4 and we have to take another card in Column 8.

We cleared all cards in column 8, but now we have to use up the empty column. How would you continue?