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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?

Question:

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?

Attempt

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.

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You are correct the solution is negative, $B=-1000$. What that is telling you is that it is a losing bet. You need to take the other side with $1000$ to expect to win $100$.

The way you set it up, if you make two bets and win one, you win $1.80$ on the one you win and lose $1$ on both of the bets for a total of $2$. You then lose on average $0.1$ of the amount you bet.

If the $1.80$ odds is on top of returning your stake the equation becomes $$100=1.80\cdot 0.5 \cdot B-0.5 \cdot B$$ because you only lose your bet half the time. This is a winning bet with $$B=250$$

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  • $\begingroup$ I think I may have blended ideas when attempting this. The original question I was asking myself was "How much would I have to bet on a daily basis to make \$100 profit if I have a success rate of 50%?". Then when thinking about it more I thought "maybe I need an avg set of "odds" to try and figure out the amount I need to bet". That's where the 1.80 came from. The first idea seems like what I was thinking about, but the second idea you mentioned is more what I envisioned happening from the first idea. Am I making sense in how I'm explaining things? $\endgroup$ – dc3rd Feb 8 at 18:37
  • $\begingroup$ You need both success rate and odds to know if a bet is good and how good it is. Once you have both you can do the computation. The point about whether the odds quoted are on top of returning your stake or not is very important. $\endgroup$ – Ross Millikan Feb 8 at 21:32
  • $\begingroup$ I did want to ask you what you meant by the odds quoted on top of returning your stake......................would the scenario I bet \$10 at 1.80 odds.....would Odds quoted on top of returning my stake mean the payout of \$18.00 = \$10 (bet) + \$8 (return from win) ? $\endgroup$ – dc3rd Feb 8 at 22:09
  • $\begingroup$ If the odds are on top of returning your bet you would put 10 on the table. Your opponent puts 18 on the table and the winner takes it all. If the odds do not include returning your be your opponent only puts 8 on the table. Your equation did not include returning your bet. $\endgroup$ – Ross Millikan Feb 9 at 0:51

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