Going With The Flow

Bart has played at an extremely high level, so I think it is time to talk about an advanced concept: “Flow”.

Flow is a difficult concept to define. If taken literally it’s difficult to imagine a number of black and white stones undergoing mitosis, increasing their numbers and gracefully sliding to new intersections on a Go board as their Dan-level overlords control everything with telekinetic powers, but I can guess where the author of “flow of the stones” is coming from.

Roughly speaking, “good flow” means everything goes according to plan. You rarely end up in awkward situations and your resources are working at maximum efficiency. Bad flow means you run into problems – you can’t play the move you want to play due to some “injustice”. You reluctantly make a small concession or two. The problems compound, which eventually ends up costing you the game.

Good flow is often a result of good long-term planning. A professional Pool player rarely gets awkward shots because he plans several moves ahead. Even if he can’t forecast the exact position of every ball, he will have a rough approximation of the game-state he is aiming for (or at least the essential features). Similar analogies exist for other games.

Incidentally the Pool analogy is not mine – it is due to Kit Woolsey’s excellent article on Backgammon 😊

Okay, enough with analogies, let’s move onto the actual game.

In the actual game, Bart chose to clear all the cards in columns 1 and 4 – but eventually ran out of things to do. We got the dreaded One Hole No Card (1HNC) scenario.

In the above position we could have turned over cards in columns 7 or 9. Observe that turning over column 7 requires two empty spaces, even though we only spend one. Column 9 also requires two columns – unless we were willing to give up the beautiful run of Diamonds from King to Deuce. Few players would be willing to do that.

This suggests the following principles:

  • If we have 1 empty column then we should turn over something that requires 1 empty column and spends 1 empty column
  • If we have 2 empty columns then we should turn over something that requires 2 empty columns and spends 1 empty column
  • If we have 3 empty columns then we should turn over something that requires 3 empty columns and spends 1 empty column

You don’t need a Ph. D. in math to spot the pattern. But you do need to appreciate this only applies if you have a position of strength. If your game-state is weak then it may be dangerous to make a special effort to avoid 1HNC – you may entail some other strategic risk, such as never seeing any empty columns for the remainder of the game. Yes, we’ve all been there!

When you have a position of strength then it is possible to follow the dot points outlined above. In this case everything flows smoothly. All our empty columns are maximally efficient – if you will – and we never get the 1HNC problem. If you are consistently winning from a position of strength then you are doing something right!

With hindsight it is easy to suggest we should turnover column 7 or 9 in the above position (Score=423). However, turning over column 7 requires we destroy an in-suit build and expose an Ace. Turning over column 9 is a serious alternative – and we don’t have to give up the Diamond run (the important point is to turnover column 9 before shifting the Queen of Diamonds in column 6). We might be afraid that after dumping a King in an empty column there are only have two potential empty columns remaining. For sake of argument, suppose we shift the junk pile in column 9 to column 10. Then we only have columns 4 and 5 as potential “easy spaces”. This may be cutting it a bit thin. True, there is also the hidden possibility of clearing the Diamond Suit when the Ace turns up – this gives us three potential empty spaces instead of two. Even so, it’s a close call and with five unseen cards in columns 1 and 4, Bart had plenty of leeway to justify leaving column 9 alone.

In the above diagram, I would have turned over column 9 – but I would not criticise anyone who chose Bart’s plan. The problem is we do not really have a position of strength, and we had to allow the risk of 1HNC. The point of this post is not to work out if Bart’s play was the absolute best, but rather to get the student thinking about long-term planning. Next time you have 1HNC, it might just be a case of bad planning rather than bad luck. If I had a dollar for every time someone had 1HNC and complained about their bad luck – then I wouldn’t mind having more students!

Incidentally I did not give the exact move sequence for turning over columns 7 or 9. Working out these moves is a useful exercise for the average player, but probably beneath the dignity of IM Bug or IM Bart (they are definitely above average players!)

Until next time, happy Spider Solitaire playing. May all your builds be in-suit and may all your long term plans come to fruition!

2 thoughts on “Going With The Flow

  1. That’s very interesting — thank you! I see your point, and quite possibly I didn’t weigh it enough when making the decision in the game. My intuition was and is that giving up on possible spaces was a more serious problem — but getting better is partly about adjusting intuitions. You do talk a lot about the 1HNC problem, but less about the “can’t get started” problem, though you do mention it in passing as part of your thinking here. Maybe that’s more a beginner or intermediate topic. When I think about applying the “flow” analysis here, I have a strong inclination to put a diamond run starting at jack in a space, and turn over column 7 instead. Because that jack is a space that can be retrieved. However, the cost of that is completely messing up the diamond suit, and another way to “get started” is to observe that a diamond ace has been dealt and remove the diamond suit. So I can also see that as the worst option.

    I went back to look at my write-up for what I actually did propose at that point, and saw a version of the same “flow” thinking: “Now the problem is that if we uncover column d first, we then have an offsuit 45 in column a with only one space, so we won’t be able to move it. We still can uncover column 4 with one space. So I propose to keep going with column a for that reason.” but maybe it’s so trivial it’s not worth mentioning.

    Another way I’m trying to take 1HNC in general is that you are likely creating a situation that looks worse right now, but the benefit is avoiding an even worse situation down the road, and the key is foreseeing how serious that danger is.

    Going to the realm of American NFL football for a parallel, it brings to mind calls by innovative/successful coach Bill Belichick involving going for it on 4th down, which was against the received wisdom of punting and hoping to get the ball back. “Going for it” might be the better play — but if you failed, you would reduce to near zero right then the chance of winning. The common wisdom was appealing because it put off until later finding out whether you would win or not. The networks (and maybe fans) would prefer the “put it off until later” option because it would create a longer period of exciting football — while coaches might prefer to avoid it because it would mean more time for their players to get hurt. But this blog is not about American football, is it…


  2. Let me hop in here with a quick comment before Master Chi-Yuen starts his newest insanity.

    I would like to go forward with Master Chi-Yuen and Esteemed Scholar Bart and, hopefully, someone or two or three someones else.

    I think the mental gynastics here will be good for my lessened intellect.

    To do this I will dust off my trusty AncientExcelCheeterSheeter and use that to keep current. I will attempt, as usual, to do my own “in head” analysis and then post as quickly as possible. If I resort to using AECS for this I will state as such.

    I will also use it to play out the more complicated sequences offered by either Master Chi-Yuen or Esteemed Scholar Bart. Following Complicated Crap authored by others is a problem for the new and improved me.

    Thanks to both my Mentors for their encouraging words.


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