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)