I am trying to work out what my betting level should be due to limited trip bank roll. The game is BJ but pretend the game is biased coin flip.

I can bet 1 dollar per game.
Expected return is 1 cent per game.
Table max bet is 50 dollar.
No draws, either win or lose.
The bank is 100000000000 dollars
The trip bank is 200 dollars.
The trip is 80 hours.
The bet level cannot change once it is decided.

How much should I bet?
If I bet small, then can play the full 80 hours. but profit would also be small.
If I bet big, then bigger profit, but may only get to play 10 hours.

Is there a general formula to work out optimal bet level to max profit?
What if I can adjust bet level, every 10 hours, based on current trip bank?