Hope you find it interesting - post any questions about it that you might have.
4. Summary* The average number of loss runs until the next expected number of losses in a row.
* The average number of loss runs until the next n losses in a row.
* The average number of loss runs until the next greater than n of losses in a row.
This and the handy table of values should be enough to get you started. However wouldn't it be better to condition the average number of loss runs on probability rather than n runs? That way you wouldn't have to calculate which n is sufficiently unlikely, and allow you to set a limit of, for example, a 1% probability loss run? That and more next time.