The coin tossing game

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

  1. If it’s heads, John gives Paul $1.

  2. If it’s tails, Paul gives John $1.

The game starts. See the results of the game below. The boys toss 1,000 times in each game. Simply refresh your browser to start a new game.

(It’s easy to see that in this “game”, the accuracy is 0.5 i.e. 50%, since each coin flip has an exact 50% chance of being either heads or tails, and the win/loss ratio is exactly 1, since for both heads and tails, the payout is the same. Consequently, any results will be random, and any temporary advantage will be a result of sheer luck. In other words, not something you can build a career on. It’s also easy to see the boys would never choose to play this game: it’s a complete waste of time.)

Also notice that some of the random runs will produce data series that trend. We can calls these pseudo trends, since there is no cause or reason behind these “trending” runs since the underlying data is nothing but a random (i.e. unpredictable) data series. This also means, next time you see a “trend”, however good-looking, do not automatically assume there is a reason, i.e. anything predictable behind it. It could be random and, therefore, meaningless.

Now let’s change the rules of the game a bit:

This changes the results fundamentally: although each run will be different, the results will tend to trend upwards. And the trend is a trend not by random chance but the result of a mathematical reality. In the second game, Paul has an edge. Although he will still not know if the next toss is heads or tails, not even if the next 10 tosses are heads or tails, but nonetheless, he has nothing to worry about, since he has a statistical advantage, an “edge”.

This mathematical reality you can also see by simply keeping both charts on your screen while refreshing your browser: in each game, the lower chart will always produce a curve sloping up, while the chart above will produce random curve with ever-changing inconsistent results.

Based on the above, it’s easy why it’s senseless to risk even one dollar on the markets without a verified and constantly monitored edge.

After this theoretical excursion you may want to check out our new edge calculator, and verify that your trading program has an edge. Mindful trading!

The Remek! Interactive Edge Calculator