# Binary Options or Roulette?Author: Hamish Category: Binary Options Articles Date: 19th April, 2012

#### Binary Options or Roulette?

Introduction

One of the interesting features of the plethora of binary options platforms that have come to the fore over the last 3-4 years is the fact that the offer their products in a percentage return manner thereby disguising the binary options over-round. There are a number of probable reasons for this, including:

a.    Globally understood means of trading,
b.    Not a sports-like fixed odds format, i.e. an investment, not a bet,
c.    Disguises the true value of the bet(!) in terms of over-round.

This article strips bare the actual profit margin of the binary options platform and ultimately compares the profit margin with the game of roulette.

Binary Options Over-Round

The binary options over-round is the book-maker’s profit margin. In an ‘event’ the probability of all the outcomes has to add up to 1, or 100%. If one added the equivalent probabilities of a book-makers price for each individual outcome in a single event then the aggregate will be in excess of 1, or 100%. This margin in excess of 100% is the book-maker’s over-round which reflects the book-maker’s profit margin. The higher the over-round the more profitable the book-maker which in turn means lower probability of winning for the punter.
For example, if there were two Muhammad Ali’s in the ring, the second Muhammad Ali being cloned from the first so that they were exactly as good as each other, then the probability of each winning would be 50%. Since the probability of all the contestants winning in any event is 100%, in this case the probability of one of the ‘Ali’s’ winning is made up of the sum of the individual probabilities of the two boxers winning, i.e. 50%+50%.
Around the world this probability can be expressed in numerous ways, e.g. the word ‘Evens’ or ‘Even Money’, 100 in the US, 1.0 in China, -1.0 in Malaysia, 2.0 in continental Europe etc.. Assuming fractional odds, i.e. ‘Evens’, then if the book-maker offered both boxers at Evens then his over-round would be zero, i.e. 100% – (50%+50%) = 0%
If the book-maker offered each boxer at 10/11 (11/10 ON) then his over-round will now be in excess of 100% and therefore assuming a balanced amount of money goes on each boxer, then the book-maker is guaranteed a profit. Why? Because 10/11 reflects the probability of 52.381% providing the bookmaker with an over-round of 4.762%.

Probability = 1 / (Odds + 1)

Probability = 100 / (10/11 + 1) = 52.381%

Percentage Returns to Binary Options Over-Round

So how does this work for binary options platforms? Instead of two ‘Ali’s’ in the ring there are two new contestants, one is called ‘Over’ and the other ‘Under’, or better known as a binary call and binary put. Furthermore, if we assume Efficient Market Theory’ then at any one time the market has a 50% chance of going up and a 50% chance of going down. But the prices are not offered in a fixed odds format as above, they are offered in a percentage return format so it is necessary to translate this format in to a probability.
In the example above, if the book-maker had offered each boxer at 100% return then the book-maker’s over-round would be 100%. This is because the formula for translating the percentage return to probability is:

Probability = 1 / (Percentage Return/100 + 1)

so each Ali would be have probability of:

Probability = 1 / (100/100 + 1) = ½ = 50%

If we take the example of a leading binary options platfrom they advertise their offer at 71% for Over and Under bets. So the probability reflected by 71% is:

Probability = 1 / (71/100 + 1) = 58.48%

So this platform’s binary options over-round (profit margin) is:

Binary Options Over-Round = (58.48% + 58.48%) – 100% = 16.96%

This profit margin is high: but the argument is that short-term forecasting is a game of skill, not chance, and therefore a high profit margin is required for protection.

Binary Options v Roulette

If you believe in Efficient Market Theory and believe that playing the markets is a ‘crap-shoot’ then go to the casino and play ‘Black’ or ‘Red’ at the roulette table since the probability of winning is:

Probability of Red or Black = 18/37 = 48.65%

So the casino roulette over-round (profit margin) is:

Casino Over-Round = ((100% ― 48.65%) + (100% ― 48.65%)) – 100%

= (51.35% + 51.35%) – 100%

= 2.70%

The downside of the casino? You have to dress up like James Bond and/or have beautiful fawning women like Sharon Stone standing over you……….