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?

7 thoughts on “Game On (31 January 2021)”

1. Bart Wright says:

I agree your play is better than mine in the last situation. We do have 4 atomic items anyway, and by no means is the game won. Putting the 8 of clubs on the nine really does help order things. So I’m with you on that one. And this is one of the key reasons I like contributing here, because I might learn how to improve my game.

I think my concern about retrieving spaces is suited for the fairly common situation where you have the last deal coming, all the cards are exposed and sorted, and likely 4 suits removed, and the biggest obstacle to winning will be the inability to get that first space.

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2. Bart Wright says:

“spiderwing”

This is a little C program I wrote a few years ago to help analyze a Spider position. First you enter the visible cards (and also a-k for any suits you’ve removed), like this for the position — this is where we start the final problem:
3a-k456jqkj896a23q32a-k8jqk7-k57873-9ka-54k8-ja-5

Then when you press “enter” it first gives you the ranks of the remaining cards, and then two numbers needing explanation:

Remaining: A 2 3 4 5 6 7 8 9 T J Q K
22 left. 3 2 0 1 1 3 2 0 2 4 1 2 1
Strangeness is 0.7211 (bumpinesss 18)

I wrote it for a very specific purpose. Like, “Come on, the cards shouldn’t be like that, I was very unlucky!” So my measure of “badness” is “bumpiness”, and it is simply the sum of the differences between the counts of any two adjacent ranks. So if you had “1 1 1 1…” the bumpiness of that piece is 0, and if you had “4 0 1 3…” then it is 7. Then I deal out that number of cards 100,000 times and see what proportion of the deals were less bumpy than mine. That’s the “strangeness”. And a lot of the time I’m not quite as unlucky as I thought.

C code and/or executable available upon request.

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3. Bart Wright says:

As for the next deal… I don’t know how the luck here compares with the other possibilities, but it leaves us in quite a poor position — though esteemed blogger can pull rabbits out of hats and maybe he’s got a brilliant idea.

9s and 8s are locked in position as we have no receiving 10s or 9s. That means our only possible space is in columns 3 or 4. The single four in column 10 lets us get one or the other of them, but not both. Which one to get could depend on looking far ahead to what want to accomplish. But if I use heuristics, I would note that for receiving cards there is only one king, but three 7s we can easily get. So heuristic says to move the 6 of hearts to get the space. Receiving 7s are common/cheap, but receiving kings are rare/expensive.

When I first looked at it I thought I could complete a club suit and retain one space, but now when I look again (after Hanabi with my daughters online) I still see it but think it leaves me with zero spaces. We have only one receiving four, and we need to use it to get a space initially, and the only way to get an ace of clubs to complete a suit is to move the 3 of diamonds in the leftmost column into the space. Completing the suit exposes the 8 of spades in the rightmost column, which is of no great importance — it doesn’t get you your space back. You can (I think) continue to move that spade run onto a queen (the jack in column 2 is right where it started), leaving you with an A-5 run with lots of suit breaks. Maybe you can make something of it next round but not quickly or easily. So I’d like to look for something better than the club suit.

Another suit? There is no 10 of diamonds on the board. The 2 4s of hearts are in difficult-to-access locations. Likewise the only 10 of spades we can see. Nor can we build 9-card runs or better in any of them.

Doing anything with the leftmost column will be very difficult because to get at it you have to move the 3 into your only space before you even get started.

It’s intriguing that although we can only get one space this round, we can leave the 3 other candidate columns atomic. This I think we can do even if we do the heavy lifting to make a long club suit, K to 2 or K to A. The top cards in all those suits have homes elsewhere. So that gives us some likely flexibility at the start of the last round. But we want to wait until near the very end to do that because some of those receiving cards are valuable steppingstones.

Rounding the clubs up gets us some very useful “preening” in columns 5, 7, and 9. I don’t see how we can do much in any of the other columns as we have to lose the space early and are then pretty much stuck. But how far do we want to round the clubs up? If we just build K-2, we can likely take it off next time, and in the mean time a nearly complete suit can be priceless for ordering other things as you swap in and out, so there’s a lot to be said for doing that and not taking it off. So now we have a space at the end of play instead of the 3 of diamonds in it and need to do something with it. My plan is to move the QK of spades from column 7 into the space. Kings into spaces are often a bad idea, but we will discover one card, and if it’s good it could help us now, and offer us more flexibility next time. We will still need very good luck to pull this off, and a lucky card under the spade King might be a piece of that. If it’s a 10 for instance it translates to 2 spaces immediately.

Here is the spiderwing output showing remaining ranks (sorry, this looks best with a fixed-pitch font like Courier-New):
Remaining: A 2 3 4 5 6 7 8 9 T J Q K
22 left. 3 2 0 1 1 3 2 0 2 4 1 2 1

And then, finally, do we move the top cards from the other potential spaces to make them atomic, because the exposed card might make us want to play differently.

So, that’s my plan! I put more work into this than I would into an actual Spider position, but didn’t pore over it for hours either.

I await the better plan from esteemed blogger.

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4. Master T I offer my humble apology for confusing you. I shall endeavor to improve quickly.

Going forward I think we can do a club run. It is at the far end of my vision meter and a bit blurry and a perhaps impossible but lets have a go at it.. Move 7H from g to f, cover with the 6H. Move the 2, 1 from e to a. Now move the 5H to f. Then move the 4D to h and cover with the A, 2, 3 from a. Move QC to j then cover with the JC from g. Now the JH from b can go to g allowing the 7H in i to go to b. Finish building clubs (ij,fj,aj)

(gf,cf,ea,ea,eh,ef,hf,jh,af,ah,fh,dj,gj,bg,ib,ij,fj,aj)

All errors in the above string of moves to be blamed on spell check.

After that I see the 7S in i going to j and the 7H from b going to i. Maybe some more fine tuning.

End product is a club run and three atomic columns: b, c, d.

Instead of that we could go for a card in g. I am going weaken the hearts by contaminating f in order to make h atomic.

(gf,cf,hf,jf,dj,gj,df,gd)

I would do a long pause before filling the void to see if any wonderful ideas have miraculously appeared.

Some housekeeping can follow, the most important one being (bd)

Baring a K turnover in g we get at worst a card and four atomics and possibly a card and three atomics and a void.

I am not overly happy with conveying just these two scenarios, I feel there may be better paths. I think I could mull this position over for an hour or three every day for a month. But life calls to me with deadlines and commitments and I need to post this.

So here my rookie status combined with eternal optimism again comes to the fore and I swing for the fences: get a card in g for me.

Master T you are a bad bad man for leading us to such a complicated position. Thank you

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1. In the club run sequence I left out ej before ij. This level of play is a bit above my capacity.

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2. Bart Wright says:

George, I’m glad to see that you and I analyze the basics pretty much the same way. So if we’re both wrong at least we weren’t alone in being wrong and fell for a “common error”. 🙂 Is it really possible that you made a club suit without using a space? I didn’t even think about it, and here is where my instinct for not counting number of moves may get in my way. I just figure a space will be vital and get it, without worrying about the extra move to make it.

Overall it looks like my solution is close to your first solution but I stop short. After I build K-2 of clubs I stop and leave the 3 of diamonds in column a — while you do things in a different order I think your plan works fine if you delay retrieving that ace of clubs to the very end. The only place you could have moved that 3 of diamonds was onto the 4 of diamonds, and instead of that I move the A-3 of spades from column 3 on that card to make a space. Like you in your Plan B, when you do get a space I think putting the QK of spades in that space is the best bet, though the rest of our cards look different at that point.

Although as we know I’m a big fan of nuclear power (making things atomic) I don’t think I’m following your Plan B. On just about any plan you can move the 5 of diamonds onto the 6 of hearts, making h atomic easily.

Like you all this is at the limit of my planning abilities, so I could be wrong, wrong, wrong.

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5. Esteemed Scholar B thank you for your comments.

We await Master T’s wisdom and brilliance.

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