# Risk Probability Question W/ Expected Value and Standard Deviation

 Sci Advisor P: 3,300 I'm not in finance, but my effort to mind-read the purpose of that question is as follows: The most elementary point is that if the game has some possibility of a negative gain then you have to worry about the problem of "gambler's ruin" even if the expected value of the gain is positive. In other words, you can't make your decisions based on the assumption that you can play the game as many times as you want to because you might run out of cash (or whatever "gain" is being measured with). Various pundits have commented on the the recent financial crises in the USA and one of the points they make is that a weakness of conventional financial forecasting is that it doesn't take in to account the possibility of rare events leading to gambler's ruin. To decide whether (and how often) to play the game, you would have to evaluate your utility function. (For example, one important question is whether you enjoy the game. Would you be willing to pay (i.e. to lose) a certain amount of money just to play?) Another factor is "opportunity cost". You should compute the expected gain per hour and compare this to what you could earn per hour doing other possible activities. I'm not sure what the question wants you to say about the standard deviation. Let's assume each play of the game is an independent event (i.e. you don't get better with practice). A big standard deviation increases the probabiity of "gambler's ruin" and also increases the probability of larger than expected gains in a given number of plays. The expected gain in N plays is N times the expected gain in 1 play. The expected standard deviation in N plays is $\sqrt{N}$ times the standard deviation of 1 play. So both the gain and the standard deviation increase, but the standard deviation increases in a "sub linear" manner. You can make playing the game many times look attractive (if it has postiive expected gain) by phrasing things in terms of ratios. If we look at the expected gain "per hour" it is the same for 1 play as for N plays. But the standard deviation of the gain per hour is smaller for N plays than for 1 play. I don't know what conclusioin your financial interviewer wants you to draw from these facts, but you should know the facts themselves.