The Final Problem

In the middlegame or endgame it is often wise to think beyond turning over cards and building in-suit. What would you do in this position?

Note: This isn’t part of our on-going game but I wanted to discuss an interesting concept in the middlegame.

We have one empty column and are about to lose it. We can obtain a new turnover in column j or f, but as usual it is good strategy to look beyond the obvious.

An experienced player might well consider turning over a card in column d. One advantage is if we get this “difficult task” out of the way first then columns j and f will be easier in the future. Alas, we soon hit a snag: there is a double Seven in the first eight cards (T-9-8-7-7-6-5-4). We don’t even get to shift the Ten of Clubs onto the Jack of Spades.

An experienced player would also know too often that the 7-6 offsuit in column e is a problem. On the next row of ten cards, an Eight will appear and it is impossible to recover an empty column precisely because the 7-6 is off-suit. So it may be feasible to compromise by not turning over a new card. For instance we can play (eb) and deal another row, hoping to win back the empty column later. Not terribly exciting but perhaps we can improve it by <eb,ce> getting a run of hearts from Seven to Ace.

Further analysis shows we can in fact do better still with <hb,eh,ce> obtaining two in-suit builds in the red suits. This not only yields good chances to recover a hole in column b or e, but it also gets to work on column h. If the cards fall well, we might be able to turn over a number of face-down cards in that column. There is also a strong possibility of obtaining a run of hearts from Jack to Ace in the future. The basic principle is we suffer a small loss, in exchange for (hopefully) a large gain in the future.

Of course, all this is possible only because the stock is not empty. If the stock were empty then we would have to go all-in, turning over at least one card and saying 70,85,67,75 73,84 even if it entails trashing our position in every way possible. There are no consolation points for a “pretty loss” – a loss is a loss is a loss is a loss.

I in fact chose the plan <hb,eh,ce> in the game and managed to win. Fiddling with rot13(haqb) – after obtaining a clearly winning position😊 – suggests that turning over a card in column j or f would probably have resulted in a loss.

2 thoughts on “The Final Problem

  1. I agree with you on just about everything (harmony in sight), with one move to add ().

    We agree that it is very high priority that columns b and e both be “atomic” before we deal — clearable in a single move. The differences among the other options that all share that property are quite small.

    You compare the options and and think the latter is better. I think it might not be. You’re in a good position here, and there’s a lot to be said for patiently waiting. You might be more concerned with not doing something to make you lose than doing something to help you win. If you stop with eb, then if a 6 comes up in the next deal, you have a place to put it (column e). If you have done ce, then you can’t. You’ve instead opened up another receiving king — but you already had one of those in column j. Of course getting those hearts slightly more sorted out is also good. Not sure which is more important, but I wanted to make the argument for doing less.

    I didn’t see the heart move from column h when I first looked at it, and I agree with you that is better than for opening. Improving column h is a big plus. Once you’ve done that, you have the same choice as above as to whether to continue with or not. Does being closer to that Jack-Ace heart run change things? Maybe slightly.

    I would also recommend . You are right that when your next step there is moving the 9 to the space, that is worse. But you can just move the 32 and then stop. It gives you more options for work in column f next time. This is worth doing whichever choice you make with columns b, c, e, and h — it is independent. Sorting out column d is a longer-term project.

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  2. Hrrumph: It seems I can’t put things in angle brackets or they disappear, I guess being interpreted as HTML commands. So the text becomes largely unreadable (grrrr). Here’s a revised version without the HTML misinterpretation (I hope):

    I agree with you on just about everything (harmony in sight 🙂 ), with one move to add “fd”.

    We agree that it is very high priority that columns b and e both be “atomic” before we deal — clearable in a single move. The differences among the other options that all share that property are quite small.

    You compare the options “eb” and “eb,ce” and think the latter is better. I think it might not be. You’re in a good position here, and there’s a lot to be said for patiently waiting. You might be more concerned with not doing something to make you lose than doing something to help you win. If you stop with eb, then if a 6 comes up in the next deal, you have a place to put it (column e). If you have done ce, then you can’t. You’ve instead opened up another receiving king — but you already had one of those in column j. Of course getting those hearts slightly more sorted out is also good. Not sure which is more important, but I wanted to make the argument for doing less.

    I didn’t see the heart move from column h when I first looked at it, and I agree with you that “hb,eh” is better than “eb” for opening. Improving column h is a big plus. Once you’ve done that, you have the same choice as above as to whether to continue with “ce” or not. Does being closer to that Jack-Ace heart run change things? Maybe slightly.

    I would also recommend “fd”. You are right that when your next step there is moving the 9 to the space, that is worse. But you can just move the 32 and then stop. It gives you more options for work in column f next time. This is worth doing whichever choice you make with columns b, c, e, and h — it is independent. Sorting out column d is a longer-term project.

    Like

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