AP ImagesDon't buy these.The Powerball lottery drawing for Saturday evening has hit a record-high estimated jackpot prize that was $800 million as of this writing, after no one won the jackpot in Wednesday's drawing.
While that's a huge amount of money, buying a ticket is still probably a losing proposition. When trying to evaluate the outcome of a risky, probabilistic event like the lottery, one of the first things to look at is expected value. Prizes are then given out based on how many of a player's chosen numbers match the numbers written on the balls.
Powerball's website helpfully provides a list of the odds and prizes for each of the possible outcomes. Our first problem is that the headline $800 million grand prize is paid out as an annuity: Rather than getting the whole amount all at once, you get the $800 million spread out in smaller a€” but still multimillion-dollar a€” annual payments over 30 years. On the other hand, the state is investing the cash somewhat conservatively, in a mix of various US government and agency securities. We need the expected value contribution of the jackpot to counter the very negative and very likely outcome that we win nothing, offset by the contributions from the smaller prizes. Under our assumption that we could lose up to half of our winnings to taxes, that means we need the pretax prize to be $981,867,643.44.
Since we are inclined to take the lump sum rather than the annuity, factoring in the importance of time value of money, if we assume the same ratio between the annuity and the lump sum that currently holds a€” a $800 million headline prize compared with a $496 million cash lump-sum prize a€” that means that, to even get close to a breakeven value, we would need the headline annuity prize to be a whopping $1,583,657,489.42. Of course, even at that astonishingly high, nearly $1.6 billion headline prize, we could run into the problem of the possibility of splitting that prize with another winner.


More control of your money.A When Ohio state workers are given the choice between a reduced pension check or annuity when they retire, Koos always tells them to take the check.
Probability based on number of tickets available for a game rather than on individual purchases. Match any of "YOUR NUMBERS" to any of the WINNING NUMBERS and win the PRIZE shown below your matching number(s).
The CLC makes no representation or guarantee as to the accuracy of the information contained on this website.
The expected value of a randomly decided process is found by taking all of the possible outcomes of the process, multiplying each outcome by its probability, and adding all of these numbers up.
If my expected value for playing the game, based on the cost of playing and the probabilities of winning different prizes, is positive, then in the long run the game will make me money.
As of October in Powerball, five white balls are drawn from a drum with 69 balls, and one red ball is drawn from a drum with 26 balls.
We can use those probabilities and prize sizes to evaluate the expected value of a $2 Powerball ticket. If you choose to take the entire cash prize at one time instead, you get much less money up front: The cash-payout value at the time of writing is $496 million. Powerball points out on its FAQ site that in the case of the annuity, the state lottery commission invests the cash sum tax-free, and you pay taxes only as you receive your annual payments, whereas with the cash payment, you have to pay the entirety of taxes all at once.
It's quite possible, though risky, to get a larger return on the cash sum if it's invested wisely.


While state income taxes vary, it's possible that combined state, federal, and in some jurisdictions local taxes could take as much as half of the money.
Divide both sides by that insanely low probability that we win the jackpot and we get our desired take-home winnings to be $490,933,821.72. Factoring in further issues with the lottery then, we would need a prize at least twice as high as the current record to even consider buying a ticket, and even then it's still probably a bad idea. The states like you to take the annuity, because they have control of the majority of the money for a longer time. Further, having more money today is frequently better than taking in money over a long period of time, since a larger investment today will accumulate compound interest more quickly than smaller investments made over time.
We asked Libertas Wealth Management advisor Adam Koos to give us his take, and he told us the lump sum wins by a longshot. Putting that into a super conservative portfolioa€”without touching the principala€”that returns around 3 percent would generate a princely $7,585,500 in a year, says Koos.



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