Let's say I have calculated the probability of a win in two games to be $60\%$. I have $2$ bets I am looking at.
For the first bet I need to risk $165$ to win $85$.
For the second bet I need to risk $263$ to win $237$.
Risk/Reward for first bet is $1.94$ and for second $1.1$.
If I calculate first bet to be $(0.6 * 85) - (0.4 * 165) = -15$ it is losing.
If I calculate second bet to be $(0.6 * 237) - (0.4 * 263) = 37$ it is winning.
But how do I get the minimum win percentage I need for a bet based of money I am risking?
I get confused because the risk is more than reward. All calculations I have seen assume risk is less than reward.
I feel like in your case you would win the amount over the bet. So you would do something like this $win\implies 165+85$ and $lose\implies -165$ so you’re expected value should be something like this assuming that $p=P(win)$ $$\mathbb{E} (bet)= p(165+85)-(1-p)(-165)>0 $$ Solving this for p will give you the interval such that you can have an expected positive value of money after betting. Please note that however this is only the probability, people might have different preferences associated to how much they’d like to risk.