# Powerball Lottery redux

OK, I’m mathematically confused again about whether there are unusual times when the *after tax expected return on a lottery ticket can be > \$1*

Powerball website reports these odds for the Grand Prize:  1 in 146,107,962.00

I assume an extension of this means that you could *guarantee* a winning grand prize ticket if you bought a ticket with *every single possible combination*.  This would cost \$146,107,962.     Now, the recent payout was way above this, about 341,000,000.    Even with a tax bite of 50%  if you were the *only winner* you’d be way ahead.      However, if there were other winners  you’d have to share but I’m not clear that the previous analysis I noted had taken a prize of this size into account.

So, anybody out there willing to lend me \$146,107,961 ?   I *promise* to split the winnings with you!

## 3 thoughts on “Powerball Lottery redux”

1. When the King of France asked Casanova if this new fangled lottery to finance the Royal Military Academy meant that the King would have to pay out that Grand Prize of Umpteen Zillion Francs even if only one ticket for a measly sou had been sold, Casanova told him “Yes and that would be the best thing to happen for the Royal Treasury, but unfortunately there was little chance of its happening”.

What you are suggesting is the opposite: that someone buys every combination and gets a guaranteed payout that is higher than the total purchase. Well, suppose just ONE other person has the same idea? What is your guaranteed payout now? Its like someone who bets on each and every number on the roulette wheel: each spin will indeed give him a winning bet. Yet it will give him guaranteed losses each and every time. It may be fun, but its not going to land him in the plus column.

This has happened with some lotteries for houses or the like. Inexperienced nonprofit organizations find that they don’t sell anywhere near as many tickets as they thought they would and yet someone wins. Sometimes these wind up in the courts. Don’t think the state lottery commissions are going to be inexperienced. They know what they are doing.
You can view it as “good” or “bad” but they know whats going on.

2. No FG – I’m not talking about lotteries on average, rather the rare case where, due to randomness, you have very large jackpots as just happened. In effect the state has already “banked” a lot of the excess in this case by not paying out a big jackpot, and clearly if taxes were not a factor this is a positive bet. Yes, others will play so there is a chance from miniscule to 100% that you’d need to split the pot but since the total goes up with increased purchases I think in today’s scenario your expected *pre-tax* return would be >1.00

3. “OK, I’m mathematically confused again about whether there are unusual times when the *after tax expected return on a lottery ticket can be > \$1*”

How come ? \$1 ? It’s strange .