If you know the probability of an event and how many times you will perform the event there is a formula that will work out your likely maximum winning and losing runs. As with all stats be careful how you use this, as this formula is an estimate of what you would be likely to see and relies on losses and gains being independent from each other. It's a wonderful flaw of human psychology that where money is involved people exhibit behavior that means losses and wins no longer remain independent.

However, Let us assume that the variable S equals the number of times you play this game / perform the event. In this case a coin toss. S=555 coin tosses. For success in this trial we will need to throw a head. There are only two events so our chance of success is 1/2 or 50%

Fire up Excel and type the following formula

=ROUND(LN(555)/-LN((1-0.50)),0)

Gives the answer: -

= 9

In 550 throws you will get a maximum run of nine heads in a row.

You could of course work out the maximum run of losers which, as this is a 50/50 chance, is exactly the same. Try varying the % figure (0.50) to see the effect of a better or worse strike rate. If you are confident that you know the % success of the event this is a good calculation for working helping out how much bank size you could stake. I have done lots of work on this subject but far too much and too complex to post here.

The day trader and losses

If you were a stock market trader and had a 25% success rate with a fixed loss per trade, say 10% of capital. Being simplistic, you would only need a run of 10 consecutive losers to go out of business or maybe a couple of average bad runs. However, You would have to be unlucky to make 10 straight losing trades, right?

Let us assume the following about this trader, Their trading career would last 20 years and they made a trade every 20 days, in a year which contained 260 trading days. That's 13 trades a year or 260 trades in this persons career.

Using the above formula this person would not stay in their career for 20 years. With a success rate of only 25% and 10% of capital going on each losing trade this trader can expect a maximum losing run of 19 trades based upon their historic success rate and staking strategy. If they reduced the fixed capital stake to 5% they would only just survive this bad run, which is entirely to be expected. No bad luck required!! Therefore the options open to our trader is to increase his success rate or decrease his percentage loss.

If the success rate rises to 47% the losing run reduces to just under nine in a row and our trader can expect to carry on in business much longer. But they would still expect a large draw down at some point in their career.

Real life example

I have often used this calculation to give me a rough estimate of my own potential to blow up in a market. It's useful to know what your consecutive run of losses could be as this will not only allow you to come to terms with that when it occurs. But it will also allow you to allocate capital accurately according to your bank size.

When I ran this calculation against my strike rate it indicated that I would not have a losing run exceeding six in a row. My maximum losing run over many years has been, you guessed it, six in a row. It did get the maximum winning run wrong however. In that same period, over five years, I had a winning run of 82. But, as I mentioned earlier, this is most likely due to me modifying behavior once that big run had started.

At least I modified behavior in a good way, typically, you see people in the market doing the completely the opposite and this, I suspect, is why people find they still lose money / make horrific mistakes even with perfectly good approaches to the task in hand.