This article falls in two classes. For one thing I want to discuss possible ways of modeling the a priori uncertainty that exists in war. On the other hand, I want to show some ways to incorporate these ideas in interesting chess variants.

One feature of war that I've never seen modeled is the uncertainty about how effective new weapons will be. Or old techniques in new situations. Let me give a few examples from the American Civil War.

ACW Gunpowder Boat

On the night of 23 Dec 1864, the Union Navy exploded a boat loaded with 30 tons of gunpowder 300 yards from the Confederate Fort Fisher. There were some expectations that the Confederate works would be destroyed. They withdrew their own fleet 12 miles. Admiral David Porter commanding wrote, "My calculations are that the explosion will wind up Fort Fisher and the works along the beach, and we can open fire with the vessels without damage." In fact, it was barely noticed by the Confederates.

The Commander, Col W. Lamb, wrote in his diary "A blockader got aground near the fort, set fire to herself, and blew up."

The ability of river boats to run past shore batteries was another unknown The first time it was tried an all volunteer crew took the CARONDELET past batteries near Island No. 10. They made elaborate precautions of extra shielding for the ironclad. They waited for a dark night. Although they were fired on by all the Confederate guns, only two shots lodged, and those were harmless. By 1864 it was almost a routine operation.

Those examples both involved new technology. Here's an example of an old tech nique, used in new circumstances. After the fact we know that frontal attacks were most unlikely to succeed. If I were modeling Pickett's charge, I could not give it more than 1/10 chance of success. Less would be more accurate. Would a good wargamer try that attack with such a small chance of success? I doubt it. Would Lee have tried it if he had really known the odds? Again I doubt it. The conclusion is that Lee didn't know the odds. Yet wargamers always know the odds. The Combat Results Table tells them.

Translation?

Now suppose a wargame designer represents the true odds in a game. In the first case, the Union player would not even try the gunpowder ship. In the second he will staft running batteries sooner and more often. In the third case, Lee would not try the charge.

Suppose on the other hand the designer represents the estimated odds. Then the Union would use a bunch of gunpowder ships. They might never run a battery. Pickett would succeed often enough to make it worthwile.

Now consider one simple device for making the odds really unknown. When the feat is attempted the first time, a die roll will determine which of several odds tables will be used to determine the event. That same odds table will be used throughout the rest of the game. There are two things "wrong" with this. First the odds will sometimes, at least, not be the correct historic odds. Secondly, it becomes very hard for the designer to control play balance.

Dilemma

This is truly a dilemma. A simulation can be accurate except as to uncertainty, or it can be accurate in uncertainty but not otherwise. The two criteria are exclusive. No wonder, I've never seen a game incorporating uncertainty about capabilities.

The way out of this dilemma is to incorporate unknown capabilities into an abstract "period" game rather than into a historical simulation game. Most of the abstract games represent the modern period. The period is indeed a good candidate for exploring uncertainty, because each war has introduced new types of weapons. I will give a very abstract set of games below.

Several quite distinct ways of introducing unknown capabilities are available.

One dimension is whether the final capabilities are known or not, at the start.

As a second dimension, there may be no "learning sequence" of intermediate capabilities, a known learning sequence, or an unknown learning sequence. (if the final state is known, and there is no learning sequence, then that is the usual case of a fixed rule.)

Thirdly, the rules may be discovered only by directly trying new things, or some provision for research may be made. If there is research, the results may be private, or may leak out.

Examples Using Chess

Now let me illustrate some of the possibilities, using chess. Chess is quite an elegant game. It is deep with variation, but has simple rules. It achieves these both by sacrificing realism. The abstractmess makes it a suitable game for modifying to explore the effects of unknown capabilities.

The first example uses a known set of intermediates, to a known final capacity. However, whether a certain move is possible may be unknown. The king and pawns have their ordinary moves. The queen at all times moves as a combination of rook and bishop. At the start there are no known moves for the rook, bishop, or knight. On any turn a player may move a rook or bishop up to as many spaces as it is known to be capable of. Or it may try to move one space more. After the player announces the try as his turn, he rolls a die. If the result is 1, 2, or 3 the move succeeds, and moves of that distance for that piece becomes known as possible. Otherwise the piece does not move.

The knights learn in the sequence: FL, FR, BL, BR, LF, RF, LB, RB. Here FL means Forward 2 and Left, etc., with B for Backwards. It is illegal for the king to move where he might be captured. It is necessary to capture the king to win. This version has only direct trial as a way to learning.

Here is a variant with an unknown intermediate sequence, but known final capability. Lay out a separate diagram showing the 8 possible moves of a knight and 7 possible moves in each of 4 directions for the bishop and rook. Also lay out for the pawn five positions labled (a) one move forward, (b) two moves forward from start line, (c) capture to left, (d) capture to the right, and (e) promotion to any piece on 8th rank. Capture includes en passant capture.

The king has usual known moves, and the queen is at all times the combination of bishop and rook. The pawns, knights, bishops, and rooks start with no known moves. Once a move is made by one piece of a give type, the move is known possible. Any legal move can be tried. Roll the die as before. If successful, move the piece and place a marker on the chart showing that the move is known.

The charts should be oriented by forward backward rather than white side and black side. On his turn a player may designate two moves on the chart, draw cards from an ordinary deck, look at each one and place them successively on the designated spots. No move is made on the turn on which this is done. Any time later that the move chosen is tried all cards on the position are turned up. If any card is from a red suit, the move succeeds and becomes known as possible.

As before, the king may not move to where he might be taken. The opponent's king must be captured to win. Stalement is possible. In this version I have also intoduced research as a separate activity, with the information private.

For a final chess variant exploring uncertain capabilities, I offer the followinq which has an unknown intermediate sequence to an unknown final state. Again lay out chart patterns for rook, bishop, knight and pawn. Augment the usual rook pattern by 4 spaces one move diagonal. Augment the usual bishop pattern by 4 spaces one move orthogonal and the same for the knight. Augment the pawn pattern by two spaces calling for (f) move backwards one space, and (q) promotion to the move of a king on occupying the 8th rank. The additional possibilities are added because some of the regular ones will become impossible Make a large number of markers labled 1 through 6. Place one marked 4 on each chart position. This number indicates the current probability (in sixths) of success if the move is attempted.

The procedure is the same as before for moving a piece. But now whenever a trial is successful, replace the marker with another one number lower. When the marker reaches 6, the move is known possible. When the marker reaches 0, the move is known impossible.

A slight translation of these patterns of uncertainty will be needed for the de signer interested in applying these concepts to a more modern warqame. The uncertainty can be in the Combat Results Table, the strengths, or the movement factors of certain types of units. In order to have a balanced game, the players should have symmetric opportunities.