We have estimated the expected value of the Powerball to be about -$1.54, but for a base prize for a jackpot of $20 mln. The money will roll over to the next if there’s no winner. So there is a probability of increasing the prize to higher and higher.
So, how can one increase the expected value? EV is a product of two parameters, but one can not modify the ‘probability’, which is fixed as in the combination calculation we did earlier. As mentioned earlier, the jackpot amount grows in case there are no winners, implying an increase in the expected value.
It is good news and bad news. The good news is that the number of tickets sold increases as the prize gets heavier and the chance of winning (as per the binomial distribution). The bad news is the number of winners who will eventually share the jackpot also increases.
I see recommendations to choose unique numbers to reduce the chance of sharing, but that looks silly. The person, shared or not (plus taxes), is more likely to get more than the $2 she spent on the ticket as the jackpot! So why waste time selecting what she thinks is unique?
