Powerball Drawing: Odds And Payoffs

Is each ticket worth $6? Nah, more like $1.42.

If you bought a $2 ticket for the October 11 Powerball lottery you immediately made yourself 58 cents poorer, by my reckoning.

I expect the jackpot to be $1.75 billion, slightly more than the official forecast.

The chance of winning the big prize is 1 in 292 million. But the value of a ticket is considerably less than $1.75 billion divided by 292 million, which would come to $6. Three haircuts must be applied.

First is that the advertised jackpot is to be pocketed over a period of 30 years. Take it immediately and you get only the discounted present value. That’s the advertised sum divided by 2.28.

Next is that there is some chance that, if you win, you will be sharing the prize with one or more other winners. How much this shaves off the expected payoff depends on how many tickets are sold. I’m guessing this number will be 129 million for the October 11 drawing, enough to take away 19% from the apparent value.

Last little problem is your tax bill. This damage depends on where you live. In the table below I allow a 42% loss to state and federal taxes.

The little prizes, starting at $1 million and working their way down to $4, are worth a collective 19 cents after tax.

One more odds calculation: If my estimate of sales is on target, there’s roughly a 2-to-1 chance that the jackpot will get no winner on Wednesday and will grow. In that case it’s likely to top $2 billion in advertised size for the October 14 drawing.

There’s a fuller discussion of odds calculations here, in a review of the similar lottery game Megamillions.