Game on (26 Feb)

Time to continue our sample game.

We have reached the following position after drawing the last row of cards.

The following histogram paints a grim picture: we have a severe shortage of Tens. However there are some bright spots:

• We are guaranteed an empty column and at least three turnovers (columns 1,8,9) which is quite surprising given the deplorable state of the game.
• When we turn over more cards, the histogram is likely to improve. For instance, we are much more likely to expose a Ten rather than a Nine or Jack.
• Apart from the shortage of Tens, there is no other problem (okay maybe a minor shortage of Sevens).

At this point we should be paying attention to removing complete suits. Even when the game state seems deplorable you never know … perhaps all cards of a suit are scattered all over the place, yet one can guarantee a complete suit with the right sequence of moves involving only face-up cards.

Indeed it turns out a suit of Spades can be completed. Clubs and Diamonds are immediately discounted because the 7 of Clubs and 10 of Diamonds are not visible. All Hearts are visible, but extracting the sole Six and Jack in columns 2 and 4 is gonna be a problem.

We therefore conclude the game is far from lost. There are many options to consider. It is beyond the scope of this post to go through them all, but the main points are these:

• We should think in terms of move-sequences instead of individual moves. In theory, it doesn’t make sense to play a move (or sequence of moves) unless only the last move of the sequence exposes one or more cards. Otherwise we are reducing our options for no reason. In practice there may be valid exceptions (a common example is performing “reversible moves” when you are only concerned with winning, regardless of number of moves). But this is a good guiding principle for improving players
• We want to turn over a card in column 1 or 8.
• We want to obtain an empty column (column 9) or at least keep the option of doing so
• We want to clear the Spade suit, or at least keep the option of doing so
• We want to maintain as much flexibility as possible (recall the virtues of procrastination!). This may imply e.g. we don’t actually clear the Spade suit.

We can also go through the usual motions of calculating good and bad cards. For instance a Ten is good because we have easy access to the J of diamonds in Column 2. But for this post I wanna emphasize the importance of long-term planning.

What would you do here?