I stole this Explanation from somewhere on the web.

Calculating Expected Losing Sequences
The formula for calculating expected losing sequences is as follows:


1 divided by (Losing Strike Rate divided by 100) to the power of 'number of run of outs'.


Important note: The Losing Strike Rate is 100 minus the Win Strike Rate.


Here is an example for a system with a winning Strike Rate of 22% to see how often you should experience a sequence of, say, 14 losers in a row:


=1/(78/100)^14
=1/.78^14
=99.35
=99 (rounded)


The "conclusion" is therefore that every 99 bets you may expect to see 14 losers in a row.


Heres more stuff

A mathematician has done some work on these losing runs, based on the average % of winners usually selected.

Note: these are not set in concrete but are a reasonable guide as to what you may expect to happen from time to time.

"Usual" percentage of winners
"Average" Possible Losing Run
"Worst" Possible losing Run

50% (unlikely)
4 to 5
12 to 14

40% (still unlikely)
6 to 7
18 to 20

33% (favourites?)
9 to 12
26 to 37

25% (average - good)
16 to 18
48 to 55

20% (average) 25 to 28
75

15% (oh dear) 40 110 to 120

Obviously, you will hit these average and worst case scenario losing runs now and again. However you select your winners, work out your average hit rate and change your staking plan according to what you may expect to happen in order to limit the damage.

If you hit an average of 20% winners, and your level stake bet is $10, you will need a bank of at least $750 to outlast any worst case scenario losing streak, or, as we call them, "Armageddon".