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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…

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