bet/(bet + pot) is useful in all gambling situations.
It is more generally stated as risk/reward.
If the total you have to risk
divided by the total that someone will win
is equal to your chance to win,
then it is a 0 EV gamble.
If your chance to win is greater than this ratio, then it is +EV to risk.
If your chance to win is less than the ratio, then it is -EV.