The unthinkable has happened: neither I, nor most certainly you, have won the lottery.
Notice I did not use the word “inconceivable”, but merely “unthinkable.” For while it was surely conceivable (and more) that I (we) would not win, it was not a thought that repaid thinking. One of the main purposes of the lottery after all is to provide cheap, harmless entertainment, to allow one to indulge in legitimate fantasy (as I did yesterday).
For the record, the winning numbers were: 2, 4, not mine, not mine, not mine, and Mega Ball not mine.
Now, I noticed some odd things in the mania which led up the drawing. The most prominent is the number of people who were careful to tell us that they did not buy a ticket, news which they thought imbued them a certain level of sophistication, of announcing they at least were above the fray.
You Are More Likely To Die Horribly
The lottery, particularly the jackpot-style gambles like Mega Millions, are oft called “idiot taxes” and with some justice. The chance of winning (for buying one ticket) is 1 in tens and tens and tens and etc. of millions, and the payout is usually low. It really is like throwing money away for ordinary payouts—but not necessarily for huge jackpots. The irony is that it takes a large number of ill-advised bets—weeks and weeks of them—to build a jackpot to the level for which it makes sense to play.
For this jackpot, it did make sense to play, at least for most folks. More on this in a moment.
More than a few sites reported that you were more likely to get run over by a bus than to win the lottery. Or there was a higher probability of falling on your head and splitting it open (I saw this somewhere but can’t rediscover where), or to die of a horrible disease, or to be struck by lightning, and on and on. One gruesome calamity after another.
Why must the comparison always be with something evil? Why not say it is probable you’ll get your book published, or that you are seven times more likely to be discovered by Hollywood, or that there is much more of a chance you will be the guy to rescue a box of puppies from a raging flood?
Well all of these are the wrong numbers, utterly irrelevant calculations. Your buying or not buying a lottery ticket does not, in an any way, affect the chance you will be struck by lightening—unless you were stepping into a bodega to buy a ticket and fortuitously avoided a storm. It’s the same with any other good or bad thing which might happen to you: unless that thing has to do with the money you spend on tickets, the numbers are meaningless.
Fair Games & Expected Values
I spent one dollar; I bought one ticket. I figure this was a fair trade for the chance at the money I might have won and for the fun I had in writing up the fantasy of what I would have done with the winnings. I’ll note that the “calculation” which justified this outlay was valid for me, but perhaps not for you. For a guy who is struggling to find money for food and rent, making the gamble is ill-advised.
As to the size of the actual payout, we can use the rough rule of thumb to divide by 3 the advertised jackpot. This is because the government will step in and take their enormous bite, and you do not actually win the jackpot but the cash which would buy a twenty-five-year annuity (for the Mega Millions). The cash for this lottery will be about $280 million.
Now there is in statistics a calculation called “expected value”, which does not mean what its English words would imply. It is simple to produce, however. It is the probability of the event times the value of the event, summed over all possible events. For the lottery, there are only two events: winning the (modified) payout and winning nada. So the “expected” value is p * $280 million + (1-p) * $0 million, where “p” is the probability of winning, which for the Mega Millions is about 1 in 176 million. Thus, the “expected” value is about $1.60.
Statisticians call a gamble “fair” or even desirable if its expected value is larger than or equal to the cost of the gamble. $1.60 is greater than a dollar, so the gamble is “fair.” But that figure also means that you should have been able to buy lottery tickets from a vendor and then gone out onto the street and sold the tickets for $1.59 each, since anybody who paid this price still “expects” to win a positive amount for each ticket. As the kids say, good luck with that.
One of the problems with the “expected” value calculation is that it treats money in a way differently than human beings. Doubling your fortunes from $1 to $2 is much different to a human being than is going from $50,000 to $100,000, while both of these are the same to the soulless mathematics. To get around this, economists turn money into “utility”, an attempt to turn the calculations into something meaningful. The difficulty is that everybody has a different “utility”, so this is merely giving the problem a label and hoping it goes away.
The solution is that everybody must decide for himself whether the gamble is worth it or not. For me, the payout was not just cash, but valuable fantasy points which I spent freely. And I repeat: for me, the gamble was fair.
More Than One Winner
Word is that the money will be split three ways, for there were three winning tickets. That there would have been multiple winners was easily foreseen, as lottery officials have compiled data which show that the number of tickets sold is roughly proportional to the size of the jackpot, and this was the largest jackpot in history. Just how many winners there would be nobody knows in advance, but we could use the data to estimate the chance that there would be just one winner, just two, etc.
Any gambler worth his spurs would have figured this into his “expected” value calculations. If he figured there would have been three winners, then he would have divided the $280 by 3 and produced an “expected” value of about $0.53, which according to traditional wisdom makes the gamble “unfair.” But that’s only if you treat money linearly, which again human beings do not. I knew of the possibility of multiple winners, yet I still figured the gamble fair (for the reasons given above).
There is folk wisdom which says that you should not pick “common” numbers, because common numbers are by definition also picked by other gamblers. For example, there are many tickets sold for the sequence “1 – 2 – 3 – 4 – 5 – M6”, a set which has the benefit of being easily remembered. Too, that sequence has just as much chance as any other sequence of arising, so just because you pick novelty numbers does not make it less likely it will arise.
If the bouncing balls do spit out the sequence “1 – 2 – 3 – 4 – 5 – M6” you will share the jackpot with the other comedians who bought this set of numbers. And since that is so, your “expected” winnings are consequently lowered, just as they were for yesterday’s drawing.
But this calculation, while valid, is the wrong one. Just think: if you pick an uncommon sequence and eschew the sequence “1 – 2 – 3 – 4 – 5 – M6” but this common sequence comes up, then how much do you win? Nothing. It’s true that before the drawing your “expected” payout was higher for your uncommon set than the “expected” value for the saps who picked 1–6. But you can’t spend “expected” money (if you think so, before the drawing try selling your ticket for more than a dollar). And you still lost. You split nothing with yourself, while the comedians split something. And something is more than nothing.
The real strategy, since nobody knows what sequence will arise and all sequences are equally likely, is to either pick numbers which you can easily remember, or let the machine do it for you since that is faster. But do wait until the jackpot pushes past a couple of hundred million. Anything less makes it less likely you’re gambling for entertainment and instead engaging in some perverse investment strategy.