odds of spending x time in losing ground in evenmoney games

first of all I wish to express my gratitude for the existence of the forum and especifically to those people that help us, the ones that have a math problem and have no idea how to solve it, like me. So thank you for your help in a world that has become too selfish for my taste. Thank you.

My question simply put is what is the probability of spending x bets on the losing side of the standard deviation curve.

For example of blackjack with a S.D. of 1.14 what are the odds of spending 100 hands losing before going over to the winning side of the standard deviation curve?

Now if there is no time limit the odds while be 100% right? But say we play for 10000 or 100000 hands, in that time what is the probability of spending x number of hands on the losing side? How to calculate this is my question.

I hope this is a correct place to ask this and that I made myself clear enough.

thank you in advance for your reply