Thursday, March 29, 2012

Mega Madness

How to Play the Mega MillionsMy dad is a retired physics professor. I’ve mentioned him before here, including once in a post titled “Physicists & Poker” in which I pointed out how when I was a kid watching Road Runner cartoons, he couldn’t resist stepping in whenever Wile E. Coyote ran off of a cliff and hung for a moment in mid-air before plummeting downward.

Dad could never allow such a blatant disregard of the law of gravity to go by without making sure his kid understood the folly of what he was seeing. I was exaggerating just a little with that story, but it is nonetheless indicative of how matter-of-fact Dad is. I mean really, he’s a very grounded guy. (Rimshot.)

As such, Dad has little patience for the lottery. Our state (North Carolina) was pretty much the last one on this side of the country to give in and allow its citizens to play the lottery, like around 2006 or so. If asked, Dad will proudly point out he’s never once bought a lottery ticket. Actually he’ll occasionally point that out even if not asked, if something inspires him to do so.

“A tax on the dumb,” he calls it, knowing that it’s never a +EV game to play. And while he’s not really a poker player he appreciates the huge difference between a game like poker in which one really does stand a chance of winning -- especially if one is skilled -- and the guessing game that is the lottery.

Was thinking about Dad this week as I read about the Mega Millions, the big multi-state lottery, having grown to its largest jackpot ever. Actually, we’re now talking about the largest lottery in the history of the U.S., with the Mega Millions having rolled 18 times since it was last won back in January.

The next drawing is tomorrow (Friday) at 11 p.m. Eastern time. Right now the estimated prize is about $540 million, crushing the previous all-time high of $390 million split by two players back in March 2007. It sounds like the winner could either take a single payment of $360 million or so or get $19-20 million a year for the next 26 years. (Those figures will probably go up over the next 36 hours, I imagine.)

I read with interest an article tweeted by my buddy F-Train yesterday in which a computer science researcher broke down the relative expected value of a Mega Millions ticket, showing how it changes as the jackpot grows. The article was penned back in January 2011 at a time when the Mega Millions had also ballooned large enough to get the attention of lots of folks.

Expected value of a $1 Mega Millions ticket, according to jackpot sizeAccording to the author, Jeremy Elson, the expected value of a $1 ticket actually peaks right around the point that the jackpot hits the $420 million mark, then slides back down again from that point forward. He’s taking all sorts of factors into consideration, including the possibility of multiple winners, non-jackpot prizes, taxes, and so forth. In other words, we’re already on the downslope of that graph now that the jackpot has pushed up over $540 million.

However, even at its peak the expected value of a $1 ticket only reaches 69.3 cents according to Elson. “Thus,” he concludes, “Mega Millions tickets are never a rational investment, no matter how big the jackpot grows.”

He adds a disclaimer concerning professional poker player friend of his who plays the lottery and then declares the cost of tickets as tax-deductible. For him, the peak point of the graph actually sneaks up over $1 for a time, but Elson kind of dismisses that as not too terribly significant to the larger point that the lottery is no way to invest your cabbage.

In fact, he ends on an anecdote that sounds a heckuva lot like one my Dad likes to tell, the one suggesting your chances of getting killed driving to the store to buy a lottery ticket are much, much greater than your chances of buying a winner.

“That’s why I plan to walk,” jokes Elson as a final punch line.

I’m kind of thinking I might just walk up to the corner and get one myself. However, I’ll be looking up as I go, you know, to make sure there aren’t any genius coyotes falling from the sky.

Wish me luck. Also, please don’t anyone tell Dad what I’m doing.

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3 Comments:

Blogger TripJax said...

Was listening to The Dave Ramsey Show and he said you're more likely to be struck by lightning SIX times and LIVE than you are to win the lottery. Yikes!

Of course he hates the lottery.

My wife and I used to by tickets occasionally when we would travel to SC or VA and we always commented about how much easier it would be if/when it came to NC. Now that it has, I probably haven't bought more than 2 tickets in all those years.

I might have to buy one tonight. And don't tell my Dad, or Dave Ramsey, either.

3/29/2012 1:28 PM  
Blogger There are some who call me... Tim said...

Shoot - I've spent $10 on my own tickets, and another $10 on tickets in company pools.

That <$1 return on each $1 investment is being subsidized by three days of dreaming. Sure, the dreams are about as useful as a Reese's Pieces Sundae, but since I don't have a Friendly's in town....

3/29/2012 2:29 PM  
Blogger Robert Dudek said...

“Mega Millions tickets are never a rational investment, no matter how big the jackpot grows.”

The assumption here is of an extremely narrow view of rational investment.

Consider the concept of quality of life - is it possible for a $1 lottery ticket to be +EV in terms of an investment in quality of life? Of course!

Suppose we numerically grade our current quality of life on a scale of 1 to 100 with 1 being suicidal and 100 feeling like you are in heaven on earth.

Now, let's say I'm a happy person, but I can imagine myself having a better life, so I rate it a 70.

What will my quality of life be with a loss of $1 on a ticket that doesn't win? It will still be 70 - that is no loss.

But let's say I win a major prize. I can buy that grand piano that I've always wanted but couldn't afford. I could do many things that were not within my financial resources. So let's say my life improves to an 85.

So the downside is zero and the upside is +15. So as long as there is a non-zero chance of winning, it is +EV to buy the ticket and play.

Now if we are talking about spending 5% of your income, week in week out on lottery tickets and not winning anything significant, then a case can be made that this behavior can easily be -EV because it can lower your quality of life.

But a single purchase of a $1 ticket is not going to lower anyone's quality of life.

That is the difference between expected financial return (which the author is concerned) and a truly rational
approach.

3/29/2012 11:27 PM  

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