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.

3 thoughts on “Don’t Miss the Forest for the Trees

  1. Well… given all the hints it sure looks like you want to clear out column h.

    That was my alternative strategy I looked at in my last answer to what to do in this position, and I rejected it. However, I realize I perhaps took it one step too far. I first described how to get a single turnover, but assuming bad luck, went on to how to get a second turnover and the ugly situation that resulted. Instead, perhaps it is better to just go for that single turnover and assume it is something good.

    So, fb, fc to create the space.
    ie, hi, hj, hf, he to uncover the card.
    The best card here is a 9, which as you note is quite likely, and if we get one we can move it to one of the 10s and also immediately win the space back. If the next card is another 9 we have a home for that too. That free 3 is likely to come in handy, likely for clearing column a or g. I can certainly see the possibility of an engine roaring to life here that could send us on the path to victory…

    For instance, uncovering a second 9 would let us expose the king in column i, which could then take the queen from column j, allowing us to move another 7, perhaps to expose pile a. With 4 good cards from column h and 4 good ones from column a, there’s a lot of opportunity to turn our luck around. We’ve also removed suit breaks from columns i and j.

    If I was using “undo” and did not find good enough cards in pile b, it would certainly be worth undoing and trying to dig in column h instead.

    However, if the argument is that the column h plan is better given what we know at the time without information from “Undo”, I don’t see it yet. If 9s came up in column b, we’d also be able to get things rolling. Perhaps my comments about “market value” are correct as far as they go, but are also timid and wimpy and don’t allow for the sort of BIG transformation we need to win this one. Maybe you can see that with deeper analysis than I can do. Such a result “feels reasonable”, and would motivate your “forest for the trees” comment.

    In bridge, sometimes, for instance, one play might get you 2 tricks for certain, and another play gets you a single trick 90% of the time but 3 tricks 10% of the time. If you need three tricks, the second play is the better one. Maybe the good cards that can come up in column h are good enough to win, but even the best cards from column b are not enough to win. If so, a sketch of why that is would be interesting

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    1. Hi Bart, well done for using the hints and spotting the option of clearing column h. Of course this doesn’t imply it’s the best move – otherwise you could just meta-game it and argue that Spider GM wouldn’t bother posting this if there was only a single trivial option 🙂

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