The Ultimate Game of Strategy
Chapter 2
Through the looking glass

System play in a game of roulette may not immediately strike you as having much to do with business strategy, but, at an abstract level there are many useful conclusions that can be drawn. This becomes apparent if the game of roulette and business strategy are examined in the context of Game Theory.

Game Theory differentiates between two different types of game. A zero sum game and a non zero sum game. Zero sum games are those games where the winners win what the losers lose, such that total winnings of all winning players, minus the total losses of all losing players, equals zero. Hence the description as a zero sum game.

Non zero sum games, on the other hand, are games where winnings do not add up to the same value as the losses. At the end of the game, there could be more money won than is lost, or, more money lost than is won. Winnings minus losses do not come to a zero sum.

Roulette is a typical zero sum game because the players win from the house or lose to it. At the end of every roulette session, if you were to sum the winnings and losses of all players together it will equal the amount won or lost by the house. Though, almost invariably, it is the house that wins because they have that edge: the percentage in their favour due to the zero slot.

There is, however, a different way of looking at a game of roulette that can turn it into a non zero sum game. That is to consider the players to be playing against each other and the amount going to the house being an overhead charge, paid to the house for providing the playing facilities.

With this paradigm shift, the players can be seen as playing against each other (for the total they bet minus the amount taken by the house). The practical certainty that the house always wins make this a realistic way to view the game, so, making the game between the players a non zero sum game (because there are will be more losses than winnings for the players: a negative non zero sum game).

Looked at in this way, the game can be likened to a competitive game of chance with an overhead charged on turnover. However, as we have seen, winning and losing is not determined solely by chance because the strategy used by the players will have a direct bearing on how much the house takes as an overhead: a single bet strategy loses less to the house than a system. This will ensure that some players will lose more than others according to the way they play.

This can be seen by looking at the relative costs per day of the holidays: according to whether they played the seven sequence system or the all in one bet system. The all in one bet system players are getting their holidays cheaper than those who play the sequence of seven system. They are faring much better than the sytem players in the game.