The Mathematics - Runs of Outs or Losing Streaks


The longest expected losing streak (or winning streak) can be calculated using the following formula:


Formula longest losing streak


n = number of trials (i.e. total number of bets)
ln = natural logarithm1
P = probability2
| .. | = absolute value or ‘modulus’

Simply put, let's say you are betting on Heads in a coin toss (with a 50% expected value). You are still going to have runs of losing streaks and winning streaks.

Over 500 coin tosses, you are LIKELY to have a losing run of at least 9 losers in a row during that period.

If your Strike Rate is 40%, you are LIKELY to have a losing run of at least 12 losers in a row during that period.

It's very important to understand and appreciate this, and realise that even on a losing day, the next winner and winning streak is also statistically set to occur.

On the positive side, over 500 coin tosses, you are also LIKELY to have a winning run of 9 winners in a row during that period, and if your Strike Rate is 40%, you are also LIKELY to have a winning run of 7 winners in a row during that period.

In fact, on say a 40% win strike rate, the expected time of occurrence of 5 losers in a row is after just 13 bets, and 10 losers in a row after just 165 bets.

Once you aware of this, you realise the power of betting with a bank, and simply following the staking and not getting too emotional over any winning or losing period.

Stick with your services and the strategies, and you will be rewarded.

The world's most successful investor, Warren Buffet (who incidentally started his career in horse racing) once famously stated 'the Stock Market is a device for transferring money from the impatient to the patient".

The statement is equally adept for punters also.


Below are tables that show you the LIKELY losing streaks based on pure mathematics in relation to each expected win rate. It’s very important that people understand that this is not the possible losing streaks, but the LIKELY losing streaks.



Take the 50% win rate example above (tossing a coin). Many can’t comprehend that when tossing a coin 100 times, you are LIKELY to hit 7 losers in a row during that 100 toss period.


Many successful and highly profitable horse racing punters and tipping services operate with expected win rates between 30% to 40%. It’s important to note that favourites generally win between 30% to 35% of the time.


Yet some individuals sign up for a very profitable service, and then unsubscribe or switch to another service the moment a losing run eventuates, even though this is LIKELY or frankly CERTAIN to happen at some point.


Let’s take the example of a very profitable service operating with a 30% win rate (but may have an average win price of $5, making it very profitable long term with a big edge. If you subscribed to such a service, and then had 13 losers in a row early on, would you simply unsubscribe? Many would, and do, despite this being a LIKELY mathematical scenario. It doesn’t mean there is anything wrong with the tipster, service or methods, it is just pure mathematics. This number creeps to 19 LIKELY losers in a row after 1000 bets.



The above table shows how quickly the LIKELY losing streak will happen based on the expected win rate of any method. As you can see, it is surprisingly quickly that a losing run will be experienced even when you have a 50% win rate (such as tossing a coin). This is why many members get the feeling that they are ‘bad luck’ or that the service isn’t performing as advertised. It’s simply because they don’t understand the mathematics.


So the question is, will you stick solid when a profitable service has it’s mathematically inevitable losing period? Or will you simply give up and move onto the next service, hoping that the inevitable mathematical certainty of a losing period miraculously and magically doesn’t happen to it?