Looking for a strategy for trading binary options that actually has some math behind it and not just some schmuck selling snake oil? Well this one has been around for quite a while and used successfully to make money in areas as diverse as casinos and stock markets (well not all that diverse I guess).

This is less what some folk call a “strategy” (and is in fact properly termed a “tactic”) – as in some specific play. Rather it is a method for broadly determining whether a given play is sound and in particular for determining appropriate money management parameters.

Money management is an aspect of trading that far too many people completely overlook, focusing instead on trading tactics (or what they erroneously call strategies), despite the fact that even the very best trading tactics can result in total wipe-out in the absence of a sensible scheme for allocating of funds.

Anyway, if you’ve come here purely for the binary options Kelly Criterion calculator then cut to the chase and click the link, otherwise… are you sitting comfortably?

Let’s be clear – all binary options trades entail placing a financial wager on a future outcome. It’s called gambling folks and if you want to be a successful gambler then the best bet whenever betting is to first and foremost understand the fundamental nature of the particular game.

And you can’t get much more fundamental than the fact that the future is intrinsically uncertain – dubious “math” such as Fibonacci retracement ratios not withstanding.

No matter how hard you try, it is impossible to actually predict what will happen – which is a bit of a bugger when that is precisely what you want to do.

However, there is an interesting property of uncertainty that you can use to your advantage and that is the fact that it is measurable.

You can in fact measure many, if not most, types of future uncertainty with a very high degree of accuracy. Furthermore you can put these measurements to profitable use.

Take perhaps the simplest form of gambling possible: flipping a coin. Now you can never be sure whether the coin will land showing heads or tails (it’s a stochastic variable, to use the jargon) but you can be completely certain that it will be one or the other and that the likelihood of either event is identical.

## Taming Uncertainty with Probability

In other words, even if we don’t know what the future holds, we do (in very specific cases) know the **probability** of any one particular outcome over any other.

For coins, the odds are simply one in two, which can be expressed as: a ratio 1:2; a fraction 1/2 (or 0.5); or a percentage 50%. So 1/2 the time it will be heads and 1/2 will be tails. Sure, you may get a run of tails or more heads in any given sequence of ten throws, but ultimately it will always yield a near perfectly balanced result. So how does that help? Let’s find out…

So how does understanding probabilities help when devising a strategy for trading binary options? Well, in some respects a binary option resembles that flip of the coin. The outcome is that you win or you lose; your prediction either pans out or it doesn’t; heads or tails.

Only it’s not quite like that, primarily because the financial risk/reward aspect isn’t evenly weighted (and neither in all likelihood is the probability of the outcome).

This shouldn’t surprise anyone; after all, it’s well known for example that casinos fix a 5% advantage over their punters. With a typical binary option you can reasonably expect your stake back plus an 80% gain for winning and a 100% loss for, well, losing.

The implication of course is that in order just to break even you need to average 5 correct predictions for every 4 incorrect (assuming you’re not into totally idiotic “trading strategies” such as accumulators, where all you’re doing is playing Russian Roulette with an ever mounting pile of money to instantly blow away).

The “house” (in our case the broker) has a clear built-in advantage. So if, for example, you place a series of $100 trades and the first 4 lose then obviously you’re down by $400. But say you then start winning and pocket $80 “profit” each time. Obviously, after 5 wins you’ve recovered your $400 and are back to where you started.

So to end up all square you have to somehow counter the 5:4 mathematical advantage of the house with one of your own. Anyone placing essentially random bets will lose their money and most likely rather quickly.

## Dealing with the Known Unknowns

The thing is though, it is *possible* to identify potential trades where the probability of a particular outcome offsets the payout ratio that is biased to favor the house.

*Correction: it’s possible for anyone prepared to put in the research, if not for the legions of dumb asses who think it is somehow easy to just start making money using binary options with no prior expertise or experience.*

In such cases, the math is on your side for once and among the best known equations for sorting the wheat from the chaff is the Kelly Criterion.

As the introduction in the previous link makes clear “The central problem for gamblers is to find positive expectation bets. But the gambler also needs to know how to manage his money, i.e. how much to bet.” This by the way was written by Edward Thorp whose reputation as a mathematician, gambler and investor strongly suggests he probably knows what he is talking about. He was also a good friend of the eponymous John Kelly (physicist, daredevil and all round interesting character)…

The Kelly strategy boils down to a formula for considering the probability of winning combined with the potential payout in order to calculate how much of your current “bankroll” to place on any single bet.

The equation in it’s simplest form is: f = p – q

where:

f is the fraction of the current bankroll to wager

p is the probability of winning, and

q is the probability of losing (basically 1-p, so f = 2p -1 is another form)

This assumes an even money bet where you win or lose the full value of your stake. Already you can see that it is well suited to binary bets. However, as already noted, real binary options don’t pay even odds but more like 80% (plus return of stake) for a win and take 100% for a loss. So we instead use this form of the Kelly equation:

f = (b*p – q) / b

where:

b represents the net odds for a win

## Enough with the Math, What’s the Fucking Answer?

Let’s run some sample data… say you have a 60% chance of winning an even money bet. The equation says to place (1*0.6 – 0.4) / 1 which comes out at 0.2 or 20% of your bankroll in order to maximize your returns over time.

How about this: odds of winning a mere 30% with a payout of 300% gives us (3*0.3 – 0.7) / 3 or 0.0666 recurring (about 6.67 percent). This tells us that even with a poor probability of success, a decent payout can mean that we will consistently make money by allocating 6.67 percent of the bankroll to this particular bet. And the converse also hold true, so a poor payout (like 80%) can be negated by a higher likelihood of success.

You can try it out for yourself using the calculator below, which is preset to a standard 80% payout and 50% probability (for the typical clueless eejit coin tosser, operative word being tosser). **Note** that a negative or zero result indicates a losing position and furthermore be fully aware that this is a mathematical model and no claims are made herein for its efficacy when applied to real life situations.

So what does all this tell us? Let’s sum it up…

## So What Have We Learned?

Interestingly, with 80% odds then Kelly indicates you need to improve your probability of winning from a random 50% to just 56% and allocate 1% of your resources each time in order to creep out of the zone of certain ruin and maintain (admittedly agonizingly slow) positive returns.

And therein lies a BIG CLUE – the Kelly trading strategy is asymptotically dominant over using, for example, flat bets and it is crucially also dependent upon accurately knowing your “edge” (the probability that you will win).

If you either don’t have an accurate handle on the odds or are not prepared to play the long game so as to allow probability to work its magic in your favor then you may as well fall back on guessing and good luck to you (you’ll be needing it).

**Quick tip:** One good way to stretch your resources out and thus mimic the long play is to place numerous small bets rather than fewer larger ones. Remember it’s binary, like coin tossing, so you need lot’s of goes to see the effects of probability kick in.

But let’s say that you are willing to study the data. How hard is it to discover a trend that occurs with a 60% probability? Doesn’t sound like much – 60:40 – does it? Another way to look at it though is that 80% of the time you will lose as often as win, but that extra 20% of the time is all winnings.

And that is exactly what Kelly confirms (try it with even odds i.e. 100% and 60% probability). Even when accounting for the less than stellar 80% odds that binary options offer, you still have a 10% win ratio advantage.

The key is never to over-bet. If the calculation indicates you should wager say 5.5% then so long as you stay at or under that level of exposure you will in all probability (pun intended) consistently win. The fastest route to sure ruin is over-betting – try it and see.

The other feature you may notice is that although the individual bets can jump around pretty wildly with Kelly, over time the results are remarkably consistent since the equation is using feedback to correct these oscillations and smooth things out.

So, the real take home lesson here? Even if you don’t want to trade according to the Kelly Criterion you can still use the simple calculator above to gauge whether any particular payback/probability combination represents a likely winning or losing scenario (and if you don’t really know the probability then it’s (probably) a losing one). Because ultimately…

The best binary options strategy is to comprehend that binary options trading, like all forms of gambling, is a numbers game and you need to understand how the numbers play out if you are to stand any chance at all of walking away with a pile of loot (or at least the shirt still on your back).