There's not a lot you can do to increase your odds of winning the lottery tonight. With the PowerBall at $500 million though, a lot of otherwise rational folks might be tempted into playing. For those of you newly tempted, it is important to remember an interesting fact about the lottery--if two players hit the jackpot simultaneously, they split the money. So if $500 million is a jackpot is just large enough for your expected value to be greater than the cost of a ticket, the $250 million after splitting one time is not!
While you can't increase your odds of winning with the numbers you pick, you can decrease your chances of sharing the winnings. This is because of two simple facts:
- Lottery numbers are drawn randomly
- Human players of the lottery choose their numbers non-randomly
Remember, the PowerBall consists of 5 numbers chosen from 1:59 (without replacement) and 1 number (the PowerBall) chosen from 1:39.
Statistics about lottery numbers chosen by players are hard to come by, but we can use a little common sense to help us understand how people might choose numbers. For example, people who choose their own numbers overwhelming use personally significant numbers, like dates and times (aka integers less than 31). Since the 5 white balls include 28 digits that are not in that range, it might make sense to draw disproportionately from these numbers. Again, this does nothing to hurt our chances of winning--it just decreases our likelihood of choosing a number that is also chosen by another player.
Additionally, by letting our own random number generator pick the numbers, we remove the human element--which has been documented to be decidedly non-random--and thus increase our chances of winning independently of any other player.
So, if you are looking to play the lottery tonight, I present a simple R script to help you pick your winning numbers! And don't worry, few enough people will use it that it should have a near-zero effect on your chances of splitting the winnings with a fellow R aficionado! (Bonus problem: calculate how many users of the script it would take for this to be untrue!)