That done, we can move on and face our own humanity: the fact is, we humans have poor intuition and understanding of probabilities. Our story, our history is hundreds of thousands, perhaps millions of years old, yet, statistics, a special branch of mathematics, only goes back a few hundred years at most. And trading is all about probabilities, therefore it is crucial that traders understand what is below intellectually and embrace it emotionally. Doing both, successfully, is step two on any trading journey.

Skipping the above two steps would lead to ruin. Conquering them, on the other hand, will be a giant leap forward on your trading journey.

Visualizing probabilities and the edge

Let’s imagine John and Paul are playing a coin tossing game, the rules of which are as follows:

• If it’s heads, John gives Paul $1, if it’s tails, Paul gives John $1 (see Chart 1).

  The boys toss 1,000 times in each game. (Simply refresh your browser to start a new game.) Notice: any trend is purely random chance, since it’s the result of a random process. (In other words: randomness often doesn’t look random. So next time you see a “trend”, ask yourself what process produced the data series you’re looking at.) Also note: the boys, being smart, would never play this game: they know it would be a complete waste of time. In this game, there can be no edge, and any advantage is, by mathematical necessity, temporary. Also note, while each game starts at 0, it rarely ends at 0. But wherever it ends, it only ends there by random chance. And random chance is not a business plan!

Now let’s look at the second chart and change the rules of the game a bit (enter values in the yellow cells).

• When heads, John gives Paul $1.20.

• When tails, Paul still gives John $1.

  The new rule changes the game fundamentally (see Chart 2): although each run will still be different (and will include setbacks!), the results will, by and large, trend and that trend will be the result of a mathematical necessity.

  In the second game, Paul has an edge. Paul will make money. Yes, with fluctuations, but consistently (enter the amount again or press F5 to start a new game).

Finally, in the third chart, you’ll see the probabilistic outcome of the interplay between two variables. (Imagine the coin is not fair, and tosses are not 50-50 between heads and tails). Enter varying degrees of accuracy (the probability of win or loss) and the win/loss ratio (the average payouts of all wins and losses in the series) in the yellow fields, then press F5 to run 1000 tosses.

As we see, even with the same mathematical edge, each run will be different since data points within the probability space are distributed randomly. This is why two traders who trade with the exact same rules, even the same accuracy and win/loss ratio, are unlikely to end up with the same results.

The above has far-reaching implications for all participants of the world’s financial markets. Welcome to the world of trading!