The Powerball Lottery is upto $340m. It is time to play.

Here is why…..

If you look at the odds on the Powerball website, your odds of winning the grand prize are 1 in 146,107,962. When making bets, what matters is the expected value of the bet. Example: How much would the payoff have to be to be $1 on a coin flip? Answer: $2. A that point you would break even becasue your expected value of each bet would be $1, or equal to the wager.

Powerball tickets are $1. What matters isn’t the total amount of the prize, because that amount can only be distributed over a period of 29 years. The exptected value of your $1 ticket isn’t over $1 when the prize gets to $146m, because the actualized value of the jackpot is actually much less, either in terms of the payout or factoring interest over 29 years, and taxes. Assuming the cash payout is 50% of the total amount of the pool, that is the point at which the expected value of your $1 purchase is over $1. It is now clearly above that.

When lotteries get a payout above the expected value of the ticket, they almost always end immediately because the number of tickets purchased is so great.

One thing I’m also omitting is the odds of multiple winners. This is a real possibility when this many people start buying tickets and I have no idea what the odds are of multiple winners, because you can’t know the number of tickets purchased before the draw, and you can’t know the number of unique numbers picked. This would also decrease your expected value of the ticket.

….but, when you get right down to it, its only $1.

(The title of this post is really really obscure. Bonus points to anyone who can figure it out. Its not the most direct reference to this topic)

## 4 replies on “JON-A-THAN!! JON-A-THAN!!”

I think you underplay the effect of multiple winners. Basically, I suspect that you almost never have EV+ on the lottery, because the odds of having to split the pot with someone will always make it not worthwhile at payout amounts above a certain point. I’d be interested to see a graph of tickets sold versus jackpot size.

However, you also have to assign value to the entertainment you get from playing the lottery, and also factor in diminishing returns. Basically if I win > [whatever number, let’s say $2 million] I never have to work again and I don’t care if I get it by winning a small jackpot by myself or by splitting a large jackpot with others. So you could be EV- but still be theoretically correct in playing.

The question of multiple winners is really an empirical one. I suppose you could go back and find out how many jackpots have had multiple winners and adjust your expected value accordingly.

Lotteries most definately can get an expected value above the cost of a ticket. However, they can only hit that point by multiple weeks of people winning nothing, and the fact that it gets that big will increase the odds of getting multiple winners.

ding ding ding. Points awarded to the well dressed brown man.

What is “Rollerball,” Gary? Please rollover my bonus points into Powerball tickets. Thank you and have a nice day.