Shots Across the Bow

A Reality Based Blog


Lottery Dreams and Realities

"Players Have More Fun!"

"Some Lucky Dog's Gotta Win!"

The Lottery trades on dreams, but what are the realities?

I started this article as a comment in response to Rev. Sensing's post saying that accepting a Hope Scholarship is immoral if you believe the lottery is immoral. I have no problem with his logic there, but he went on to claim:
If you, gentle reader, are one who thinks lotteries are either benign or neutral, morally speaking, then you need read no farther, for you are uninformed. I urge you to research the true impact of lotteries on your own. My own position on this issue is what ancient philosophers called invincible: I have examined in detail all arguments to the contrary and found them all inadequate, usually hopelessly so.

Now them's fightin' words to me, since I regard playing a lottery as foolish, but not inherently deceptive or immoral.

So, I went to the link provided by the reverend, and examined his "invincible" argument.

Invincible is not the word that first came to mind: "Deeply flawed" was more like it. (OK, that's two words. Live with it.) The Rev. deeply opposes gambling on both a practical and a moral level, and that's fine, and you can build a good argument for that position. Unfortunately, he lets his beliefs get in the way of the facts, leading to several logical and factual errors.

His first error is to claim that since tuition only covers about a third of the cost for a year in school, and the other two thirds are funded through general tax revenues, in effect the lottery is an involuntary tax increase on all Tennesseans, not just those who play. The fact is that, regardless of how they are funded, all tuition assistance programs are subject to the same economic consequences; it isn't a problem specific to the lottery. Is the Reverend in favor of abolishing all educational assistance programs, or just those forms he finds morally questionable?

Next he claims, accurately, that it will require about $900 million in lottery sales to produce the estimated $300 million in Hope Scholarship funds. Then he goes on to characterize that $900 million as lost sales to retailers, resulting in lost tax revenues of $75 million. The flaws in that are many. First, economics is not a zero sum game. In fact, over half of the stores who add lottery tickets see their merchandise sales go up. Additionally, stores receive a 6.5% commission on all tickets sold, introducing a new revenue stream that more than offsets costs to the owner. That, combined with increased traffic and sales, indicates that the lottery does not have anywhere near the negative impact Rev. Sensing accords it, and in about half the cases results in increased sales.

The Reverend compounds his error by suggesting that the loss of $900 million in sales costs the state $75 million in lost sales tax revenue. Since we've already seen that the $900 million figure is bogus, it is obvious that the $75 million figure derived from it is also bogus. But even if the state loses $75 million in one revenue stream, it's picked up $300 million in another for a net gain of $225 million.

Even if the state lost $75 million in sales tax revenue, which as shown above, it doesn't, it gains $300 million in lottery revenue, a net gain of $225 million. Since the state will actually lose far less, the resulting gain is also greater.

His third error is to describe incorrectly how the odds are calculated. He claims that in most Pick 6 type games, you must guess the correct numbers and in the correct order. This is flat out wrong. In some of the pick 3 and 4 games, order does matter, but in every state I've seen a lottery, the pick 6 is number only; position is irrelevant. (Multi-state games are another matter) Strangely, the odds he quotes(about 14,000,000 to 1 against) are calculated correctly; if he were correct in his description, the actual odds would be 10,068,347,520 to 1 against.

These are his principle points, and in each of them, he's in error. But I agree with him that playing the Lottery is essentially a foolish waste of money, even if it is only a dollar or two.

To describe why, I'm going to have to throw a little math at you. Don't worry, there's no test afterwards, and I'll try not to go too fast.

First, you have to understand how the odds are calculated. We'll take a standard 6 number game, with a total of 49 possible numbers. There are 49 balls in the hopper, once chosen, that number is removed from play leaving 48. Extending the series, we end up with


This is the total number of arrangements of six numbers out of 49. But in most games, arrangement doesn't matter, so what we need to know is how many possible combinations of 6 numbers are there? Well, it's not too difficult to get there from here. We just have to divide the total by the number of possible arrangements of any 6 numbers. We can follow a simple process like we just carried out, only this time, there are only 6 balls in the hopper. There are 6 possible balls for the first number, 5 for the second and so on, giving us

6*5*4*3*2*1 or 720 possible combinations of 6 numbers, all of which are winners by the rules of the lottery. So, out of 10068347520 possible arrangements of the numbers, 720 will win, giving odds of

10,068,347,520/720, or 1 in 13,983,816.

Now, on smaller games, like pick 3 or 4, position is important, so you don't get to allow for different combinations, so you only go through the first step. Also, numbers are not taken out of the hat each draw, so numbers can repeat. This makes calculation much simpler.

For example, a 3 digit number from 0 to 9. The number of arrangements is 1000 (10*10*10) so your odds of winning are 1 in 1000.

Multi state games are a little different, as they include one ball where the position in important, which changes the calculation significantly. Take the Mega Millions game as an example. The 6 numbers drawn come from two separate pools of 52 numbers. Taking the five regular numbers first, those that can be in any order gives us


Now, the next ball comes out of a new hat, so there are 52 different chances, only one of which is a winner, so we now have

2,598,960*52=135,145,920 or 1 in 135 million against.

So, now we know how to calculate the odds. Is it worth playing?

Consider the payouts: a typical Pick 3, where the odds against you are 1000 to 1, pays $500. That means for every $1000 you spend on Pick3, you can expect to lose $500. To put this into perspective, most slot machines pay out at around 95%, or for every $1000 you play, you only lose $50. A good blackjack player can expect to lose $20-$30 dollars for every $1000 he wagers. To put it in another perspective, if a stock loses 50% of its value, investors bail and you can count on lawsuits.

It's a sucker bet, folks. You're better off investing in Enron and Imclone than buying a lottery ticket.

But it isn't a tax; it's not unethical, illegal, or (in my opinion) immoral. Nor is it the job of the state to protect us from our own stupidity. The people of Tennessee wanted a lottery; they got it.

UPDATE: In the interests of complete disclosure, I freely admit that I have been known to place a sucker bet or two.

Hey, somebody's gotta win, right?
Posted by Rich
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