Marbles Cascading Down a Staircase

From the top of a staircase with at least 44 steps, you release 10001000 marbles. Independently for each marble, at every step it encounters it settles there with probability 0.50.5 and otherwise tumbles onward to the next step (probability 0.50.5). On average, how many marbles come to rest on the 44th step?

Answer

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