Say you have the following distribution of streaks of wins & losses of length N. (A streak is defined by exactly N wins or losses in a row, followed by a new streak of the opposite kind.)

(Sorry this table did not display properly; replace the spaces w/ tabs & it should be OK.)

WIN_STREAKS LOSS_STREAKS

LENGTH NUMBER SUM_WIN LENGTH NUMBER SUM_LOSS

1 206 206 1 179 179

2 89 178 2 81 162

3 49 147 3 52 156

4 8 32 4 19 76

5 4 20 5 18 90

6 3 18 6 7 42

7 1 7 7 4 28

360 608 360 733

So 360 winning streaks and 360 losing streaks, with the overall probability of a win of 608 / ( 608 + 733 ) = 45%.

I would like to create a table that provides the probabilities of a streak continuing/ not continuing once it has reached length N. For example, what is the probability that a single win will be followed by another win? that two consecutive losses will be followed by exactly one loss, or more than one loss?

Here's my thinking so far:

Assume you have 1 win: You could go on to have another win, thus starting a longer winning streak, or you could have a loss. So probability of a loss following the win = 360 / ( 360 + (360 - 206) ) = 70%, i.e., the number of losing streaks divided by the total number of streaks, excluding the streak of 1 win.

Assume you have 6 wins in a row: Probability of another win = 1 / (1 + 360) = 0.28%

Am I on the right track here?

Thanks for any help!