 rfxsignals May 6, 2019 No Comments

Probability in Trading: The Roulette Wheel

Know what your chances are before you enter the casino

This article is not meant to be the definitive one on the subject of probability, which is so large and in-depth as to be beyond the scope of a simple web page.

It is intended to give a few extremely important examples of probability that any forex trader should be aware of, in order to minimise risk in their trading.

Many people – and it seems, most traders – think they understand probability, at least on a basic level…

For example, in my home town (Melbourne, Australia) summer weather is reasonably predictable: a series of increasingly warm days leading up to an almost unbearably hot day which crashes into a storm and its following cold spell.

Perhaps I’m jaundiced from having lived here so long, but most Melburnians seem to agree. So it stands to reason that if we have just had three or four increasingly warm days in a row, we could expect there to be a cool or cold change coming in the next few days. As it turns out, this is how it usually happens.

This is a rather simplistic notion of the idea of probability however. It certainly doesn’t translate very well to the idea of probability in trading, which is much more mathematically aligned.

Probability in Trading: The Coin Toss

The coin toss: the simplest and probably best illustration of probability in trading forex

The type of probability we refer to in trading markets is best illustrated by the common example of tossing a coin.Any toss is equally likely to result in either a head or tail. We therefore compute the probability for either result as being 50%.So if we toss the coin a hundred times we can reasonably expect there to be somewhere near fifty heads and fifty tails in the total result.The variation from 50 in fact can quite commonly go down to 40 or even lower. But if we were to repeat the experiment 100 times i.e. 100 series of 100 coin tosses, the actual result would be a lot closer to 50/50.

This introduces one of the major laws of probability,The Law of Large Numbers. This states that the larger the sample of coin tosses, the closer we can expect the actual result to match the expected result.

We use this law in backtesting trading systems: the more iterations of a test, the more accurate our results.

Probability is also involved in calculating Expected Value. This is the calculation of how much we expect to either win or lose from each trade taken by a given trading system. It’s based on the numerical probability of the number of times the system wins combined with the size of each win. Go to How Much Money Do I Need to Trade for a full explanation.

You’ve probably heard the title “A Random Walk down Wall Street”. The Random Walk referred to here is also based on probability. The probability in this case is a 50%, or coin toss event. If we set out on a walk and walk one block north, then flip a coin to decide whether we will next walk a further block north or head back south one block, we are illustrating the concept of the random walk.

There are some fascinating results from this. Given an infinitely long walk – one in which we go on forever walking one block and flipping a coin to see which direction we will walk in next – the probability that we will eventually return to where we started from is 100%. In other words, we will always return to our point of origin at some point.

Paradoxically, the chances of us at some stage being one hundred blocks from our point of origin is also 100%!

You may ask what is the point of stating these facts? I give them because traders often make the mistake of thinking that a trading system with a small probability of winning more than it loses can be traded profitably.

The simple fact is that you should base a system’s worth on its Expected Value, nothing else. The concept of Gamblers Ruin may drive the point home.

Gamblers Ruin is a variation of Random Walk. Suppose a gambler starts with \$1000. Each bet they place is for \$100. If the probability that they win is 50% – as in flipping a coin – then there is a 100% probability that they will eventually lose all of their money! They will give all of their \$1000 to the casino if they play for long enough, just as the walker in the random walk eventually gets to be one hundred blocks from home at some stage.

Some other facts regarding probability that you may like to know if you are considering using a system with a very slight edge:

What is the probability of flipping a coin two hundred times and encountering at least one string of six or more heads or tails in a row?

What is the probability of having at least one string of five heads or tails in a row?

Don’t forget those strings of heads and tails translate to strings of losers in any trading system that wins around 50% of the time. So if you trade such a system, it’s important to be prepared for such streaks of losses, they are inevitable!

The last example is perhaps the most startling of all…

Suppose you are gambling on a roulette wheel. You know you have an almost even chance of either red or black coming up (the double zero and triple zero, which result in a win to the bank, mean you have slightly less than 50% chance, which is the casino’s edge).Further suppose that the wheel has just been spun ten times and every time the ball has landed on black. Would you be tempted to put your money on red for the next spin of the wheel?And if it also came up black, would you be even more tempted to back red again, reasoning that “odds are that red must come up soon!”?If you would be so tempted, perhaps you would like to know the record for the number of consecutive reds on a roulette wheel in a casino?

Probability in Trading: The Lotto Ball