Game on (11 Mar)

Game 11 Mar

I decided to expose a card in Column 8.

As usual it is good technique to procrastinate. The basic idea is to avoid as many non-reversible moves as much as possible, unless we really we can’t help it. This means, we must shift the 9-8-7 in column 9 to obtain the empty column and we must shift the Q-J in column 3 to expose the only visible 10 of spades etc. The resulting position is shown below:

Note that I still haven’t removed the Spade suit, but I have arranged matters that the Spade suit can be removed in two easy moves, even without an empty column. Again this is an example of procrastination. Note that only one 3 of Spades is visible – hence removing the Spade suit entails exposing an Ace of clubs, which is always undesirable. If we can expose the other 3 of Spades before removing the Spade suit, then we can avoid exposing the A of clubs.

We have reached a critical moment of the game. We have no more cards in the stock and still have to expose 17 more cards. Luckily most of the unseen cards are good (as we saw from last week).

At this stage, we should be thinking in terms of “actions” instead of individual moves. Let us say that an action is a sequence of 1 or more moves such that only the last move exposes one or more cards (either by dealing from the stock or exposing a card). Note that if this requirement is not met then we are reducing our options for no gain.

For instance, suppose we complete the Spade suit by merging the KQJ09 + 87654 + 32A in three separate columns and then ask ourselves what is our next step? This would reduce our options for no reason. Yes, it is almost always good to remove a suit and clear an empty column, and yes it does make the resulting position easier to visualise but a serious player should develop the habit of thinking in terms of actions, not individual moves.

Another example: if we moved the 5 of Clubs in column 8 onto the Six of Clubs in column 2, then shift the 32A of Spades in column 6 to Column 4 without examining the newly turned card in column 8 then we are again reducing our options for no reason.

A useful corollary is that if we win, then there will be exactly 17 actions left. We need 16 actions to expose 16 facedown cards and then one final action to win the game. Similarly, winning from any starting position always requires exactly 50 actions. This is assuming no pathological scenarios arise, such as exposing two cards in one move when a complete suit is removed from the tableau (but we can always pretend that complete suits are not removed automatically and the player must spend a move to remove it).

If we lose this game, then there will be less than 17 actions (unless we get a most unlikely “cheevo” of exposing all cards and still managing to lose). Of course, the last action will be “resigning” almost always because the stock is empty and no sequence of legal moves exposes a new card.

Here are some more examples of actions and non-actions:

• Move the 5 of Clubs onto column 2, exposing a new card. This is the simplest example of an action, consisting of only one move.
• Move the 8 of Diamonds in column 1 onto the 9 of Spades in column 9. This is also an action (but we lose the option of removing the Spade suit).
• Do both of the above moves. This is not an action because only the last move should expose a card.
• Move the 432 of Clubs in Column 5 to Column 8. This move is safe since it is reversible. But it is not an action since it fails to expose a new card.
• Remove the Spade suit (columns 4,6,9) then move the 5 of Clubs in column 8 into column 2. This is an action, but violates the procrastination principle.
• Swap the 5-4 of Spades in Column 4 with the 5 of Hearts in Column 7 (this is legal despite the lack of an empty column), then remove the Spade suit, using columns 6,7,9. This is an action, but I would rather expose the K of Hearts than the A of diamonds.
• Remove the Spade suit, then shift the 8 of Diamonds in Column 1 to the empty column in Column 9. This is a somewhat unusual action (why burn the empty column prematurely?) but I won’t say it’s a terrible play.

This list is probably too long already, but this does illustrate the principle of looking beyond the obvious. There are many possibilities to consider, and the most obvious is not necessarily the best.

What would be your action here?