Intermediate: Memory in Stratego

Memory is an important component of Stratego.

Key elements to be remembered
(Thanks to The Prof's Stratego.com forum post)
 * 1) Opponent's pieces that have been revealed
 * 2) Opponent's pieces that have moved
 * 3) One's own pieces that have moved or been revealed.
 * 4) Opponent's pieces about which you have suspicions.
 * 5) One's pieces you have used to bluff your opponent.
 * 6) The initial location of opponent's pieces (since this reveals info when neighboring pieces become known)

Board Memory and Chunking
Thanks to player HiltonChess's post on Stratego.com's forum (and Chapter 9 of his book at strategotips.com)

Board memory  is the ability to remember all moved and unmoved pieces on the board, as well as the identities of any pieces which have been discovered. Board memory is of the utmost importance to Stratego strategy, as we have seen in the previous chapters.

When playing Stratego, it is of the utmost importance that you remember every piece the opponent has moved, and the identities of your opponent’s pieces. It is also important to remember which pieces  you  have moved, so that you have an understanding of what your opponent knows.

Each player begins with forty pieces, so that makes for up to potentially eighty pieces of information. How is a player supposed to remember all this?

Adrianus Dingeman de Groot (1914-2006) was a Dutch psychologist and chess master, and his studies on chess players—conducted in the 40s, 50s, and 60s—showed that a master chess player is---

able to reconstruct from memory an entire chess position he has seen for the very first time in just a matter of seconds, whereas an amateur player is entirely incapable of doing so.

However, there was one caveat: the chess positions being committed to memory had to be one from real games (or at least “normal-looking” positions), not random ones.

When the pieces were scrambled in an entirely random fashion, the strong chess players did no better than the weaker ones in reconstructing the positions from memory.

Thus, de Groot established his theory of “chunking.” His idea was that chess players group pieces they see into “chunks” of information. So instead of remembering where all thirty-two chess pieces were at any one time, the professional chess players only had to remember about five to seven “core” groups of pieces.

This fits with what we believe today about the human working memory, namely, that it is able to hold between five and nine pieces of information at any one time (see “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information,” by George A. Miller).

In the same way, it is possible in Stratego to group pieces into different formations and thus to remember which ones have moved. For instance, consider the following position:

The pieces that have moved are marked here. If you simply tried to remember every single piece here and whether or not it had moved, you would be in trouble: there are thirty-six Red pieces on the board and thirty-six Blue pieces, so that would make for a total of seventy-two pieces of information.

This is far beyond the working memory capacity of most humans. Of course, it might be possible to remember only the individual pieces that have moved. This would result in thirteen pieces of information—which is difficult, but not entirely impossible to remember.

However, after a few additional pieces were moved (and the number of moved pieces rose to, say, twenty), someone pursuing this strategy for keeping track of the pieces would have an impossible task.

With chunking, however, it is easily possible to remember which pieces have moved.

View the board again, this time in the following way:

Looking at the board this way, there are only three pieces of information to remember: the cluster on the Left Flank, the cluster in the Center, and the cluster on the Right Flank. Two of these shapes are rectangles (a very easy shape to remember), so only the constellation in the Center is “difficult.”

Even then, however, practically anyone could remember which pieces have moved. It is also helpful for the players to note that they do not have to remember which enemy pieces that have wandered past the fourth or seventh ranks, respectively.

The Blue pieces on a6, b6, a5, and b5 have obviously been moved—otherwise, they would not be where they are.

Thus, the key to having a good board memory is to be good at chunking—the process of grouping the pieces into easy-to-remember shapes.

Obviously, the more games of Stratego you play, the better you will get at remembering various patterns, since you will have seen them before.

However, it would be helpful to immediately build your pattern base by quickly examining three of the most basic shapes.

Red has an  untouched flank. In order to remember eight pieces of information here, the only thing necessary is to remember that Red has not moved any pieces on his Left Flank.

Red has advanced in a square formation. All four of his pieces towards the middle have moved, and none in the back has moved. This is another easy way to remember eight pieces of information at once.

Blue should also keep in mind that he doesn't have to remember which Red pieces have moved above the fourth rank, too: if a Red piece is above the fourth rank, it has obviously been moved.

Red has a flag formation on the Left Flank. Although only Red knows whether or not there is actually a flag on a1, chances are that his pieces on a1, a2, and b1 will be left unmoved for some time in order to avoid revealing further information.

Both sides only need to remember that Red is keeping a flag formation in the bottom corner and that all of his other pieces on the Left Flank have been moved, thus condensing several pieces of information down into one manageable chunk.

With practice, chunking will become natural. Soon, you will be able to keep track of all the moved and unmoved pieces on the board without a tremendous amount of effort.

With this ability, you will be able to conquer weaker foes quickly, and will be able to hold your own with the Stratego masters.

TheProf's additional comment on memory
Chunking is indeed a useful memory technique. But instead of trying to remember pieces that have moved, I have found it to be easier, and thus more effective, to simply remember bomb-free spaces or regions. Anytime a piece moves from one square to another, it means that neither of those squares can contain a bomb. Thus, any piece found on one of those squares, for the remainder of the game, must have moved at some point. The nice things are that you therefore do not need to track unknown pieces in order to know if they have moved or not, and the chunks that you are remembering are stationary regions which can expand but don’t move, and they usually form nice rectangular shapes. For example, during the game I might tell myself things like, "First two rows are clean on left half of board" or "no bombs three rows deep in right two columns" and I try to visualize the shapes as more squares are added to them. So for keeping track of what has moved, I recommend chunking bomb-free regions as opposed to groups of pieces.