As I'm writing this, the country is beating itself into a frenzy not over politics but over a lottery. The Mega Millions Lotto has an estimated prize of $640 MILLION. That would make it the largest jackpot in the world. Lotteries tend to have paybacks of about 50-60% so they aren't exactly a wise wager. Yet, as I have often written, people are more willing to wager in games with bad paybacks if the top prize is life altering. I think more than half a billion dollars meets that requirement. I have to admit that if Nevada participated in Mega Millions, I would've tried to get some tickets. I was NOT motivated enough to drive to nearby California to get them, however.
Even when your choice of game is something like a Lotto, I think you should go in with your eyes open. The odds of winning the top prize is about 176 million to 1. To put that into a casino perspective, that is a little higher than the odds of being dealt a sequential Royal (10-A or A-10) in SPADES on the deal in video poker! Of course, even if you're playing a Reversible Royals video poker machine, you're only going to get paid maybe $40,000 for that hit, not $640 million.
Unfortunately, unlike most casino games, it is a bit more difficult to determine the expected value of this week's drawing for one major reason. The $640 million dollars will be SPLIT by each of the people who have a winning ticket. The lottery has stated that $1.5 billion worth of tickets have been sold, but from reading further it would appear that this is the TOTAL number of tickets sold since the last time the jackpot was won. This does NOT represent the number of tickets sold for this particular drawing which is all that matters. If we actually knew how many tickets were sold for this drawing, we could determine a more accurate expected value.
Armed with this information - and $176 million, it might actually pay to buy every possible combination of numbers. We would then actually be wagering on how many other people hit the same set of numbers. If less than 3 others, we would actually make some money on the deal. Well, BEFORE Uncle Same takes hit cut anyhow. To really make money, we'd probably have to be the only one to have the winning ticket. History tells us this is unlikely and even less so if you were to add in someone who bought EVERY ticket.
No one plays these types of lotteries believing it is a wise investment. We all know that the odds are very long. The payback of the lottery is normally around 50-60% and even when it grows this large, it is probably no more than 70-80% when we consider that we are likely going to have to share it should we get struck by lightning and actually win. What I find most amusing about these situations is the comments we get from some people.
Today, I was reading a rather whimsical article about just how much money the $1.5 billion that was spent on lottery tickets really is. It talked about how many families it could feed and how many trips to the space station you could make with this type of money. Sadly, it also explained how it was only 0.1% of the national debt. The article then moved on to quote some people who chose to play and why. Of all the things I read, the one that made me to a double take came from an accountant in Louisiana (I won't post his name here):
The article stated that the gentleman had bought 55 tickets and that he knows buying that many tickets doesn't mathematically increase his odds, and that his $55 could have gone elsewhere. He spent it anyway.
"Mathematically, it doesn't make a difference, and intellectually we know that. But for some reason buying more tickets makes you feel more lucky," the accountant said. "Even people who know better are apt to feel that way."
Maybe, he bought 55 tickets all with the same numbers? Mathematically, buying more tickets doesn't make a difference? So, if I buy one ticket I have the same chance to win as someone who buys 2 tickets? What about the guy who buys 10? or 50? or 55? or 176 million? As an accountant, I would think he would understand numbers a bit better. If you buy 2 tickets your probability of winning doubles as compared to buying 1 ticket. If you buy 10 tickets your probability of winning multiplies ten-fold. This gentleman bought 55 tickets, so he brought his odds down to a mere 3.2 million to 1 of hitting the big jackpot.
Fortunately, playing the Lotto takes as much skill as playing slot machines. But many of the same people walk into a casino armed with about the same level of knowledge of the games. Yes, mathematically, we know in the long run that we are likely to lose, but that doesn't mean we should take prudent steps to keep our losses to a minimum and give ourselves the best chance to win in the short run. Because, in the end, mathematically, it all makes a difference.