2B
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11
If you have access to a multiple-precision math software package like Mathematica, then I can tell you how to figure it out - or at least get a close approximation. The numbers are too big to work out on a standard graphing calculator that I have here.
Assuming you are playing 45 hands an hour, then in 250 hours you are playing 11,250 hands. For a +50 profit, you are winning 5650 and losing 5600. Probability of winning a hand is approx .49 and losing .51. If these numbers arent accurate enough to just use the below formula with your own probabilities.
You have to compute the probability of getting at least 5650 wins in 11,250 hands.
Sum across "i" => ["11250 choose i"] x [.49^i] x [.51^(11250-i)]
The sum runs from i = 5650 to 11250.
It wont be exact but it will be close. I am not factoring in doubling, surrendering, or any other kinds of strategies. Just basic win/lose.