Summary: I have a bet where, for one bet, the probability of getting a positive amount of money is positive. However, the expected value is negative. Should I take this bet? What is useful to think about when making this choice?
Longer version: I have the following probability mass function:
f(x) = \begin{cases} 0 & x < -3 \\ .145 & x = -3 \\ 0 & x = -2 \\ .26 & x = -1 \\ 0 & x = 0 \\ .59 & x = 1\\ 0 & x > 1\\ \end{cases}
We can note that $P(x>0)$ is 0.59 -- in other words, more than half.
That said, $E[X] = (.145)(-3) + (.26)(-1) + (.59)(1) = -.105$
How should I resolve this?