# Elasticity!

Remember the last time we talked about Powerball?

I theorized that a powerball price hike to \$2 would result in lost sales. There was one dynamic that I completely failed to foresee:

Megamillions is, according to this ticket here, 363 Million. Now, let’s say that you had an opportunity to purchase a lottery ticket at your local gas station.

Would you spend \$2 on the chance to win \$50 million or would you spend \$1 on the chance to win \$363 million?

Yeah, me too. As such, I’m pretty sure that the Powerball folks are thinking long and hard about the \$2 price hike given the fact that nobody with the choice between the two is going to purchase Powerball until after Mega Millions is back down to its normal \$10 million reset point.

### Jaybird

Jaybird is Birdmojo on Xbox Live and Jaybirdmojo on Playstation's network. He's been playing consoles since the Atari 2600 and it was Zork that taught him how to touch-type. If you've got a song for Wednesday, a commercial for Saturday, a recommendation for Tuesday, an essay for Monday, or, heck, just a handful a questions, fire off an email to AskJaybird-at-gmail.com

1. Brandon Berg

Would you spend \$2 on the chance to win \$50 million or would you spend \$1 on the chance to win \$363 million?

No.

But doesn’t the less-bad alternative depend on what the odds are?

• According to ColoradoLottery.com, the odds of winning Powerball are 1 in 176 million. The odds of winning Mega Millions are 1 in 175.5 million.

2. Patrick Cahalan

Actual odds of winning: 1 in 171 175 million. Present day cash value (you did take the cash value payout option, right?) \$259 million.

It’s actually worth it to play, if you’re the only one who hits the right numbers. Even the mathematicians can feel okay about blowing a buck.

• Actually I can’t. I’ve internalised the laws of probability so completely that I can’t even fantasise about winning the lottery because my forebrain overrules and says I’m not going to win so I should just stop thinking about it.

• Colorado does not force you to pick how you take your payout prior to purchasing the ticket. You are allowed to put off agonizing over that choice until *AFTER* you win.

3. Patrick Cahalan

Dammit, somebody bought my island.

• Mary

Don’t you hate when that happens?

• Ah but the odds of winning are the same no mttaer how many people play. It’s just the odds of sharing the prize that go up.Also the odds this week were higher, because unlike previous weeks someone had to win, so likely (as happened) it would only rely on 5+power-ball rather than the full 6 numbers. Personally I don’t subscribe to Lotto, i find it an exercise in greed, but just thought I’d point out the flaw in the logic.

4. Patrick Cahalan

Nobody got it.

470+ million projected for the next drawing.

Friday’s movie quotes quiz will have a theme.

5. Pyre

The analysis is incomplete.

When Powerball made their change, they changed three things.
Price went up from \$1 to \$2 on a normal ticket and \$2 to \$3 on a Powerplay ticket. (At the time, they justified this by saying that most people bought the \$2 ticket anyway. This is true but for reasons that I’ll get into.)
The numbers you picked went from 62 to 59, thus marginally increasing the odds. (Powerplay numbers didn’t change if I recall correctly. By way of comparison, the numbers for Colorado Lottery are from 1-42 and Mega Millions is 1-56.)
The payout went from a straight multiplier of X2 to X5 to X3 for the lowest prize and X2 for the rest. (In fairness, they also shrunk the tiers to \$4, \$7, \$100, \$10K, and \$1 mil)

Now the odds are largely irrelevant when compared to ticket price and payout. Despite what people think, most people who play regularly do not believe we’ll hit the jackpot. Sure, it’d be great but we know that we’re really playing for the lower prizes. Under the old system, when I put my \$2 in, I had a chance of winning \$8-20 at the lowest and \$14-35 at the next tier. With these payouts, you would say “What a bargain. That is a bargain for me!”

Then you’d go buy some chopsticks.

Now, when you put your \$3 in, you’re playing for \$12 and \$14 respectively. Sure, maybe you’ll get one of the higher prizes (even though they suffer from the same issue as the multiplier) but, for the most part, the prizes that you used to get have shrunk.

Then you look at the other options. For \$1, I can get better odds and the same payouts at the lower levels from the Colorado Lottery than I can from the \$2 Powerball ticket. For \$2, I can get better odds and roughly the same payouts with Mega Millions than I can from the \$3 Powerball ticket. (Plus, Mega Millions has a Tues + Fri drawing. The Mega Millions psychology here for choosing Tues & Fri was that people could possibly win Tues, Weds, Fri, & Sat. That’s 4 days a week if they added Mega Millions to their state/Powerball routine instead of 2.)

So where is my incentive to buy Powerball? It’s more expensive for roughly the same payout. (The odds are also worse but very few are really doing the math on the comparative odds.)

If you look at the Colorado Lottery site, you can see that, despite being initially okay, sales for Powerball have been at a stagnant low. The current Mega Millions jackpot has made things worse but even after Mega Millions resets, Powerball will still be doing poorly as compared to how it used to.

In my opinion, the Powerball folks are probably looking long and hard not just at the price hike but at whether getting rid of the multiplier was a good idea. In my opinion, if they kept the price hike but brought back the X2-X5 multiplier or vice versa without changing the new odds, they’d probably be okay again.