*Zero-sum games can enhance a trading strategy. Photo: iStock*

By fxtime*

First let's consider a very simplistic trade model.

Using the 9-10am trading range of the spot cable market (GBPUSD) we can trade the price break out seeking 5+ pips net.

The ticket spread will determine how far the spot mid price must move before your trade opens. A spread of 1.8 pips implies you open a trade 2.3 pips above/below the trade range before entering a trade. The success rate is 90%.

Before you rush off and commit to the trade we must also consider stops...plus deal costs etc.

Cable, EURUSD and USDCAD are interesting FX pairings as they all have the same optimum stop. There is a level of price movement that, should the market move by 45 pips in one direction, then there is a greater probability value that the market will indeed continue further in that direction where as below 45 is what is known as ''noise'' — an area of natural vibration/oscillation that is statistically directionless.

Thus lets go back to the original strategy above.

A 90% success rate sounds great for net 5+ pips profit each day. But using the optimum stop value gives an interesting conundrum. If we measure 10 consecutive trades on a 90% success rate we get the following:

Nine successful trades totalling 9 x 5 pips = 45 pips profit and the optimum stop should of course be 45 pips.

Now we have a zero-sum trade scenario. We know over time that every point/pip profit we make will be totally lost.

Maybe we can consider a means of taking advantage of this zero-sum balance. We know that a break beyond 45 pips implies a continued move in that direction. Therefore a 46-pip move follows that trade direction. Probability implies a further 12-pip minimum move using the same stop value.

Also we know the 9-10am trading range strategy is a price breakout strategy so if the trading range you are measuring is in excess of 45 pips, *do not* enter that trade as empirically the trade is against you. Conversely a trade range below 45 pips is far more favourable.

*Cause and effect. Photo: iStock*

For example, if the trade range was say 30 pips then make your stop that amount. After all a price breakout strategy relies on a single directional trade. Consequently your risk is reduced but the probability of success remains.

Using the original example:

- 90% success on 10 trades is really 9 trades x 5 pips = 45-pip profit
- One bad trade with a 30 pip stop means we are still 15+ pips in profit
- Should the market continue moving beyond the stop and the 45-pip value, then you would expect to earn a further 12 pips
- The result is a 27 pips net profit overall

As a poor student when studying for my degree, I worked in a casino and came across zero-sum strategies as used by casinos. If you look at the roulette table, you can wager on red or black numbers and would expect a 50/50 chance but in truth it isn't because the zero number is green.

American roulette tables are slightly different as they have two green number slots. This is because it introduces skew to a game of chance. They are taking advantage of a mathematical fundamental called The Law of Large Numbers.

Equally card players playing Black Jack etc were often using statistics and counting high value cards used by other players and the ''House'' to establish what other cards were available. However casinos started to use two decks of cards always having in play a 52 rolling supply of playing cards at any given time to eliminate conditional probability card players and introduce a skew in favour of the casino. The element of chance remained static for the player but the element of risk dropped for the casino. This is a zero-sum advantageous game play.

There is a plethora of permutations you can play in forex and mainstream indices using these theorems which consider a three-month timeframe as a reference value and determine how many trades are required to break even only, then introduce skew (really known as a Kurtosis Skew) to the trade to be more beneficial/profitable whilst seeking the worst-case parameter such as a stop maximum level as a reversal point and an individual trade structure in its own right.

As I have no reliable broadband and charting at present due to maintenance work in my area I will post real-time charts later in the week to show the workings of the above. Hopefully, however, this makes some sense?

*Glitz and glamour are not the only tricks used by casinos. Photo: iStock*

— Edited by Martin O'Rourke

**fxtime is an alias*