Predicting winning session %

Not sure if this question makes sense, I'm just interested to know if it can be answered.

If a "session" lasts 100 hands
- And I have a standard deviation of 14/100
- And I have a win rate of 1.5 BB/100
- And I keep playing indefinitely

What % of my sessions will be winning sessions?
What if a session is 200 hands?

[Abbaddabba]

Though i don't know the precise calculations, I'm going to throw out a random guess of 50.25%.

Do we get a prize for guessing closest, like you would for guessing the number of gumballs in a jar?