So I am trying to solve what I deemed as a simple algebraic problem but I'm having difficulty getting a solution. Perhaps I am framing it incorrectly?
Say that I want to generate a profit of \$100 on each bet that I make. Given that I have a success rate of $50\%$ on each bet made and the odds of the bet are $1.80$, how much would I have to bet in order to make \$100 profit?
Let $B$ represent the amount I would have to bet. Taking into account that I am only right 50% of the time I thought a simple equation of the following form would solve my problem:
$$100 = (1.80)(0.50)B - B$$
But solving this I get a negative number, which cannot occur in this situation. All this high-level university math I am working on and I can't solve a simple algebraic equation.....Some help would be appreciated.