introducing chance in the chessmen

an idea for introducing the element of chance into chess

concept

One of the defining aspects of chess is that there is no element of chance, other than the ephemeral advantage of who draws white and gets the first move. The two sides are perfectly matched.

However, I believe that chess was originally conceived as an exercise to develop military thinking. The board is a field of battle with two armies arrayed against each other. In real battles, unlike chess, there is an element of chance. There are many ways that chance enters into battles, but especially chancy is the composition of the forces on each side. Rarely are they exactly equal. One side might have more foot-soldiers, the other more cavalry. That could translate into chess as varying numbers of pawns and knights.

So I began thinking how to introduce an element of random chance into the recruiting of the armies. The ideal would be a system that would statistically be the same as the standard set. In other words, over a very large number of games the average game would have the same composition as the standard set. But, the odds that any given game would have the standard set would be infinitesimally small.

analysis

I began with a simple analysis of the composition of the standard set. First, there could be only one king and one queen. This is a monarchy after all. Yes, you could have more than one queen, and this often happens from pawn promotions in standard play. However, this would greatly complicate the recruitment  ratios since the all the types of chessmen except king and queen occur in even numbers. Only the king and queen are solitary at the beginning of the game. 

The monarchs have an army of 14 chessmen. There are two each of the three pieces; bishop, knight, and rook, for a total of six pieces. Then there are eight pawns. Reduced to the lowest common denominator, 6 pieces to 8 pawns is a ratio of 3:4 pieces:pawns. The ratio of each different kind of piece to pawns, rook vs pawns for example, is 1:4. The ratio of any piece to any other piece is 1:1. That is, you want an equal chance of getting a bishop vs a knight or a rook. When you recruit a chessman, you want each instance to represent those ratios. There should be four chances of getting a pawn, three chances of getting a piece, and one chance each for a bishop, knight, or rook.

The goal, then, is to have an element of chance in recruiting the army that results in the same ratios as the standard set…on average!

methodology

A classical way of achieving random selection is the rolling of dice. Suppose you have a die with seven faces, which in fact has been developed by the game industry. This can yield the ratios described above. The four numbers 1-4 will be a pawn. The three numbers 5-7 will represent pieces. Five will be a bishop, six a knight, and seven a rook. This yields on average the correct ratios of pieces to pawns, and pieces to each other.

setup

Each player would recruit their army. Roll the die 14 times, with each number deciding which chessman you draw. Ideally you would want more than one die to speed up the process. Because the end result would usually be different from the composition of the standard set you would need several standard chess sets; something like three or four identical Staunton sets. The board would be the standard chess board.

The players would place the pieces as follows. King and Queen go in their usual places. The pawns would be preferentially be placed in the ranks 2 and 7 as usual. If there are fewer than eight pawns then the player can choose where to place them on their usual rank. If there are more than eight, the player then chooses where on the back rank to place the remainder. The player places the pieces as follows: bishops next to the king and queen, then knights, then rooks to the outside. Identical pieces must be distributed as evenly as possible to either side of the King and Queen. In short, the idea is to place the chessmen as nearly like their usual positions as possible. If by rare chance the recruitment resulted in the standard set, these rules would result in placing them in their traditional places.

play

The game would be played by the standard rules. Since I have not had an opportunity to actually test this with real games, I don’t know whether exceptions might occur. Still, thought experiments suggest that the standard rules would suffice and no new rules would be needed. After all, even in a standard game pawn promotions can result in a different composition of chessmen on the board.

tactics and strategy

Some aspects of play would remain unchanged. Control of the center would still be paramount, bishops like diagonals, rooks like ranks and files, knights are at their best advantage near the middle of a cluttered board, etc. Other aspects of the game would be right out the window. Probably none of the standard openings would be of much value. In fact, the opening of every game would depend on the composition and arrangement of the forces.

discussion

I am not a chess scholar and I don’t know whether anything like this has ever been done. I do know that there are several variants of chess using dice, but they are using the conventional chess set and dice with 6 faces. In dice chess, throwing the dice controls how the pieces can move. There are a number of variants on how the dice control the moves. I propose using dice to control the composition of the chessmen themselves, which would then move normally throughout the game.

I believe that dice with seven faces are a relatively recent invention, so this was not a possibility in classical times. I don’t know that anyone has used dice to change the composition of the chess set as I propose here.

I think the resulting games would be very interesting. I have looked at other variants of chess, but chess is inherently so complex that most variants end up simply bewildering the players. I once had a set for three players. The idea was intriguing but I found the games not very much fun. 3D chess is even more of a complication. By contrast, this proposal retains all the traditional elements of chess, and would not necessarily be more complicated.

One possible drawback is that chance will sometimes produce a result that is so lopsided that the game would not be worth playing. You could agree in advance to a convention for deciding when the result is too unequal, and redo the recruitment.  For example, if one player has an advantage of two or more pieces the outcome would not be in much doubt between players of equal ranking. But, after all, if you agree to introduce chance, then play it out. An unlucky player who goes on to win or draw would have bragging rights!

Another way offset unequal recruitment would be to give any back-rank pawns some special rules or privileges, making them a bit more like pieces. Perhaps they could move three squares on their first move, capture forward as well as diagonally, etc. If they were somehow different from other pawns they would need some marker to show their status. For example, you could put checker (draught) pieces underneath them like a pedestal.

Why make the font small?

This was my first post. I wondered why it was so small. I didn’t choose to make it small.