If you think about it the question "What is the average number of plays before you get a string of losses of some length?" is a perfectly well defined question with a specific answer.

If you toss a coin until you lose, then on average you will toss it 2 times.
In Vector notation that is the dot product <1,2,3,4,...> * < 1/2, 1/4, 1/8, 1/16, ... > = 2

If you toss a coin until you lose two times in a row, then on average you will toss it 6 times.

If you toss a coin until you lose six times in a row, then on average you will toss it ? times.

If you don't know how to do this problem, then read the paper dooglus and I wrote. Please comment
https://just-dice.com/Just%20Dice%20Streak%20Bet.pdf