0

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?

zthomas.nc
  • 427
  • You know that "the expected value is negative". What does it mean? That you have to expect that bet to make you loose money. – Crostul Sep 06 '16 at 16:42
  • @Crostul Agreed -- although for a given bet, more likely than not I will make more than $0. – zthomas.nc Sep 06 '16 at 16:46
  • 1
    The expected utility criterion (since Cramer and D. Bernoulli in the XVII century) argues that it comes down to the risk attitude. People who use the expected value are said to be risk-neutral and they would turn down this bet. But people who are risk-prone might take it. – mlc Sep 06 '16 at 16:50

0 Answers0