Chiralkine counting can be used as the basis for a new kind of game.

The chiralkine game was invented to explore how the financial system causes inequality, even though it works on the principle of balance and equations. The system can be gamed, but why, and what needs to be changed to prevent this? Experimenting by playing the game with different rules and tokens reveals the unexpected answer. Try it and discover that nothing is the root of the problem.

The financial system is used to solve the double co-incidence of wants problem inherent in barter. It is much more efficient to exchange goods and services into and out of money than to find someone willing to exchange what they have to offer for what you have to offer.

Each good or service in an economy is in the state mine, not yours to its owner and not mine, yours to everyone else. In the course of a cycle exchange, each participant exchanges what they are offering for what they want. The state of what they are offering switches from mine, not yours to not mine, yours, and the state of what they want from not mine, yours to mine, not yours.

A financial system has three states: balance (0), credit (+1) and debt (-1).  Two people initiating a cycle of exchange each start out at balance (0). When one person “sells” what they have to offer to another, the buyer, who wants this, the seller goes to state of credit (+1) and the buyer goes to a state of debt (-1). The seller can return to a state of balance (0) by buying what they want. Independently, the buyer can return to a state of balance by selling what they have to offer. The system is asymmetric in that the buyer is obligated to return to a state of balance (0), but the seller is not.

There are six states in a chiralkine system, each of which can be represented by a token.

Only three of the six tokens are needed to represent the states in a financial system: balance (0), credit (+1) and debt (-1). 

Offers and wants can be represented by two sets of cards, which can be dealt out to the players, but in such a way that no player at the start holds an offer and want card for the same good or service. When a good or service is purchased by a player who holds a want card, the offer card held by the seller can be handed to the purchaser. The process can continue until all the offer and want cards have been united, at which time all the offers and wants have been cleared.

A financial system works on the principle of balance and equations.

1 = 1

+1 – 1 = 0

The order in which +1 and -1 mutually negate does not matter:

+1 – 1 = 0 = -1 +1

In general the difference between two objects that are the same (1 and 1 or 0 and 0) is 0.

So the rules of the game in a financial system are:

0 is turned by +1 into +1                                            0 is turned by -1 into -1

+1 is turned by -1 into 0                                             -1 is turned by +1 into 0

Only the +1 and -1 tokens need to be played, because playing the 0 token has no effect:

+1 is turned by 0 into +1                                            -1 is turned by 0 into -1.

It is extremely easy to game this system by hoarding credit tokens (money), which drives down selling prices for those in debt, or (as a government) by creating credit (+1) and debt (-1) without having anything to sell (postponed taxation), which drives up prices by flooding the economy with money.

The chiralkine game was invented by thinking about what would happen if the order in which +1 and -1 mutually negate matters, such that one of a pair of opposite 0s is obtained when -1 negates +1 and the other of the pair is obtained when +1 negates -1.

+1 is turned by -1 into +0

-1 is turned by +1 into -0.

However, the other rules are left unchanged, consistent with the principle of balance and equations:

+0 is turned by +1 into +1                                          +0 is turned by -1 into -1

-0 is turned by +1 into +1                                           -0 is turned by -1 into -1

+1 is turned by +0 into +1                                          -1 is turned by +0 into -1

+1 is turned by -0 into +1                                           -1 is turned by -0 into -1.

One way to play the game is by playing tokens in token spaces laid out as a grid, for example 8 x 8 on a game board.

In order to play the game, the following meanings are tethered to the tokens:

The object of the game is to be the first of the players to form a path from one edge of the grid to an opposite edge.

The game can start out as shown below, with all token spaces populated by Not Mine, Not Yours tokens.

Each player’s move is in two parts: one on behalf of the player and one on behalf of the player’s opponent. This is performed by placing one of each kind of a player’s tokens on the game board. An example of the result of Player 1 placing tokens is shown below.

Player 2 now places two tokens, one on the token placed by Player 1, which turns it into a green token with a white centre, meaning that all players can pass though this token space. The result is shown below, together with the paths that can now be used by Player 1 and Player 2. Player 2 has exploited the rules to gain an advantage over Player 1.

The game continues until one player has achieved a path from one edge of the game board to the opposite edge.

The players are able to game the rules, because the token they place on their opponent’s behalf acts in the interests of both players when placed on their opponent’s opposite token.

It is possible for others to play another, different game at the same time, the object of which is to hunt and capture a Mine, Yours token and switch it to a Not Mine, Not Yours token. All the other tokens in this hunter’s game are hidden from sight. The hunters have no idea where the next Mine, Yours token is going to appear. The players in the main game do not know how long the Mine, Yours token will remain.  In effect the two games are coupled together in a hidden way, which adds interest to both games.

The rules governing how the tokens are played can be “gamed”, but not as much as those governing the financial system.

To prevent the system being gamed, the rules must be tightened further, so that the tokens in each token space follow a cycle through all six chiralkine states.

The game must start out with the token spaces populated with equal numbers of Mine, Yours and Not Mine, Not Yours tokens. With this condition, a system can be constructed that treats buyer and seller symmetrically. Exchange can be controlled in a cycle, such that neither buyer nor seller can return to a state of “balance” without both satisfying mirror opposite obligations of selling to and buying from a third party. The “price” that must be paid for achieving this symmetry is the loss of the principle of balance and equations: nothing.