# Should I take the bet?

If I win the bet I get 200 dollars and my winning probability is 0.1 and if I lose I give 20 dollars. Should I take the bet?

• It depends entirely on how you value the outcomes, which relates to how you value money and risk. – Glen_b Oct 6 '13 at 7:28
• I wouldn't. Winning \$200 won't change my life, nor will losing \$20. So why waste my time on this? – Harvey Motulsky Oct 6 '13 at 15:27

• Am I completely off or isn't the expected income 2? $0.1 \cdot 200 + 0.9 \cdot -20 = 2$. Then I'll think it is a quite good bet, though, depending on the factors Glen_b mentions. – Rasmus Bååth Oct 6 '13 at 21:06
• This answer is incorrect for two reasons. First, the expected income is $200*0.1-20*0.9=2$, so this is a positive expectation bet. Second, if it were not a positive expectation bet, then it would not be a good idea to take it even if you could do it as many times as you want. Yes, you would eventually end up with a positive amount of money, but the expected value of the amount of time until this happens is infinite. Moreover, if you have a finite bankroll, and you play long enough, then with probability $1$ you will eventually go broke. – mpr Oct 6 '13 at 22:15