Mark, one formula I have seen for calculating longest run of outs is :

'logarithm of 0.005 divided by the logarithm of the probability of failure'

(from Dick Mitchell in Winning Thoroughbred Strategies)

So in your example of 48% strike rate (0.48) the calculation becomes

LOG(0.005)/LOG(0.52) = 8.102314

To a certain extent the question as asked is a bit like 'how long is a piece of string' because the LRO for a given strike rate will increase as the number of bets increases. i.e. in your example the LRO over 500 bets would be 8 or 9 but for a sample of 10,000 bets the expected LRO would extend to 14.

I think the above formula should give you a fair approximation of LRO for your everyday use.

Regards,
Wun

Note : Probability of failure equals 1 minus the probability of success (your strike rate) so 1-0.48 gives the 0.52 used in the equation.