In this article I wanna take a short break from Steve’s game and take a closer look at individual columns.
I believe that many players tend to focus only on the “uppermost sequence” in every column. For instance, in a column containing three face-down cards followed by K-Q-J-5-4-7-6-5-4-3-2-A (suits irrelevant), players would tend to focus primarily on the 7-6-5-4-3-2-A. This is understandable: if we have an empty column or two chances are we can easily shift the 6-5-4-3-2-A around (but not the 7 unless we have a spare Eight or were willing to spend an empty column).
In the following example, if we only focus on the uppermost sequence of columns 1,4,6 in the following diagram we would ignore the identity of four face-up cards (5s,4d,3d,Qs) and the number of face-down cards.
As a player improves his understanding of the game, he may start wondering why a number of close games tend to fall just short of victory. Is it just rot13(onq yhpx) or is there some deeper cause?
I think a useful guideline is to check for “danger signs” in individual columns. In an earlier post I warned about the dangers of e.g. having two Queens in the same column but no Jacks – because if that column became a junk pile then there is a real risk of having a Queen shortage when Jacks suddenly appearing at the worst possible moment. Whereas if the two Queens were in different columns it is harder for the Luck Gods to conjure up a Queen shortage.
The situation I am talking about is illustrated from another screen-shot from Steve’s book (Winning Spider Solitaire Strategies), but not taken from our current game. If the K of Hearts in column 9 is never shifted, there is always the danger of having too many Jacks appear later on. Note that this problem can’t be eliminated by turning over cards or obtaining empty columns.
Going back to the first diagram, column 3 is unbalanced. There is a Q-J imbalance of 2 and also a K-Q imbalance of 2. Obviously, we expect any column to have an imbalance of at least 1 somewhere (unless it’s a complete run of Ace to King, in mixed suits), so an imbalance of 1 is nothing to really complain about. An imbalance of 2 in a few columns may indicate sub-optimal play somewhere along the line (sometimes it can’t be helped). If a single column contains an imbalance of 3 or greater than you might wanna change your goal from “winning the game” to “publishing a paper”.
In column 4 we have two Queens, but also one Jack. That means if we deal e.g. a Ten in column 4 then there is only a Q-J imbalance of 1, but the K-Q imbalance is still 2. On the other hand, both Queens are the same suit. This means if we are close to completing a suit of Spades then having both Warlpiri Women (*) in the same column can become inconvenient. Generally, we prefer to have identical cards (in both suit and rank) in different columns, if all other things are equal. In column 1 we have the same situation with the 5 of Spades.
(*) There is another less savoury name for the same card that is worth 13 penalty points in a well-known trick-taking card game.
Of course, we are a long way from completing a full suit, but at least we are able to identify the possible seeds of defeat if we do get stuck with a “12-suit” in Spades in a difficult endgame.
Earlier in Steve’s game we had an “inverted sequence” in column 10. The Ten and Nine are in reverse order from what we would normally expect. Obviously, this game state is the result of dealing a row of 10 cards. The inverted sequence is a Good Thing since whenever the Ten of Hearts is shifted, it is always possible to move the Nine of Spades and win a turnover. Of course, this is counterfeited if another Nine of any suit is moved onto the Ten of Hearts.
Needless to say, it’s even better if the 9-0 in column ten is the same suit, but we take what we can get.
Other variants on inverted sequence are possible. For instance, if we had 3-2-A-6-5-4 all the same suit then moving the 6-5-4 guarantees we are able to move the 3-2-A. If they were different suits then we might still be in luck if we had an empty column or two. We could even have 6-7-8, which is only possible after dealing from the stock at least twice.
As an extreme example, if a column contained only A-2 suited then it is never correct to change it to 2-A. If you could win with 2-A, then victory was also possible with A-2. If this doesn’t illustrate the importance of inverted sequences then nothing will.
In this post I gave a number of possible good and bad situations in individual columns. In high-level play, evaluating a position is much more than counting the number of turnovers, in-suit builds or completed suits. With experience you should be able to tell the difference between e.g. a “good 4 turnovers” and a medium or poor 4 turnovers. Similar comments apply to in-suit builds.
A good player may pay attention to the whole board when it’s time to think about removing a suit or avoiding one-hole-no-card. But a great player is thinking about the whole board before things get critical. Next time you are asked to evaluate a game state, you should be able to recognise the danger signs pertaining to the contents of individual columns.