Powerball And the Statistical Wagering Concept No One Talks About
For the past week, the Powerball jackpot has been at a place (and grown exponentially from that place) where legitimate and amateur statisticians and probability theorists alike show off how smart they are by multiplying (5/69)*(4/68)*(3/67)*(2/66)*(1/65)*(1/26) to get to the magic number of 292,201,337-to-1 of hitting the jackpot.
People who would never play the jackpot at $40-million proudly display their arithmetic chops by quoting the chance of winning the jackpot and asserting that $500-million (or $900-million, or $1.4-billion) is the time to play because there is a positive expectation on your money.
And while that’s true, it ignores two key points. The first is more philosophical, and the second is more deeply rooted in mathematics.
1. The size of the prize is actually immaterial.
Whether you’re playing for $40-million or more than a billion, the bottom line is that you’re risking $2 on a 0.0000003% chance to change your life. Yes, you can do more with a bigger jackpot, but the essence of the prize does not change with the technical value of it.
But we set thresholds not because anyone is looking for “value” (in the horseplayer sense of the word) in Powerball, but because most of us know how ridiculous it is to chase the jackpot on a near-daily (Mega Millions offers similar prizes two other days/week) basis.
Which brings us to the second point:
2. Your risk of ruin playing Powerball is so significant it’s still not a good bet even when the jackpot exceeds the chances of winning it.
One story I’d like to read but haven’t is where people who have already dumped “mad money” into the last two missed jackpots are getting the money to reload. It’s very unlikely there has been a payday between Saturday’s drawing and tonight’s, but people will bet more than ever before.
Some of this is money from new players, of course, but enough of it isn’t that this is a legitimate question. What is being sacrificed in order for certain people to play again?
Usual boilerplate about only betting what you can afford to lose, treating any game of chance as entertainment, and bet with your head not over it always applies, but after two substantial drawings and a third forthcoming, it’s not out of line to question how many people have gone broke chasing the Powerball.
And that’s my issue not only with the Powerball narrative but also a lot of what is written on horse racing handicapping (as well as the move toward more jackpot wagers). Players’ bankrolls just can’t sustain the swings of low-probability wagers, and that would be the case if they were perfect handicappers in a zero takeout game, let alone one with the possibility of error that includes takeout.
That’s not to say racing can’t be a good bet. Of course it is—both from an “investment” and entertainment standpoints—but you have to pick your spots.
Let’s say you perfectly identify horses who have a 20% chance of winning who are 9-to-1. This is a tremendous overlay (and you are the world’s greatest handicapper)! But if you bet 10% of your bankroll on these horses you still have a 14.83% chance of going bankrupt. Make it only 1% of your bankroll, though, and the likelihood of tapping out is practically nil.
And this is why betting favorites (or low-risk bets) gets a bum rap.
If you can pick 6-to-5 winners with 50% accuracy your risk of ruin betting 1% of your bankroll is again practically nil.
Powerball is picking a 500-million-to-1 winner with 0.0000003% chance of happening. It’s a positive expectation given infinite time and funds and negative for everyone else, which is to say everyone.
So have fun dreaming about the jackpot but save most of your bankroll for TwinSpires.com.