What is an expected value of playing the lottery?
Poker players know all too well what expected value means and many of them find the discrepancy between these estimations and what actually happens frustrating. The concept stands for the amount that the player is expected to win by playing his game of choice and calculating it accurately allows him to determine whether it is worth to keep playing or not. Unlike poker games where players have a certain degree of control over the outcome of each hand, lottery depends entirely on luck and this makes it even more important to calculate expected value.
Factor in lower tier prizes
Everyone knows that the chances to win a prominent lotteries such as the Powerball are minimal, but this doesn’t have a deterring effect on them. Only those who play have a chance to win, yet it doesn’t hurt to know exactly which are the odds of winning anything. Expected value can be used to calculate both the chances of scooping higher amounts and the rock bottom payouts, as both of them are estimated in the same manner. It all begins with knowing the probability of winning a prize in each category and luckily those who choose the Mega Millions, Powerball or other prominent lottery have them available online.
The probability to win the Powerball is one in 175 million but there are many more categories and prizes awarded to those who match five, four or less numbers. Players are expected to spend two dollars for a Powerball ticket and after factoring in the odds of winning in every single category, the expected value is reduced to $1.20. One doesn’t need to be a rocket scientist to realize that these numbers make the lottery game unprofitable, nevertheless it is the potentially huge jackpot that keeps players wired.
Jackpots worth playing for
In addition to calculating the chances of winning any prize, expected value is also useful for determining whether the size of the jackpot makes the investment worthwhile. When it comes to Powerball, the numbers tell us that it is only worth purchasing tickets for those draws where the jackpot is about $276 million. Only a handful of players has won such jackpots which means that the smart thing to do is to refrain from playing in most draws. Regular players say to themselves that the difference between winning more than $276 million and slightly above $100 million is negligible and they would gladly settle for less.
It is hard to argue with them, especially with the odds of winning the jackpot being the same but those who are methodical and understand the importance of expected value will stick to the rules. Those who use the PowerPlay multiplier should know that the calculations change dramatically because by paying the additional dollar, the expected value changes. Players can win more by matching five numbers without the Powerball, but the break even jackpot will need to be consistently higher.
Check out How to beat the Lottery System as well.
