Lottery

The Low Down on the Lottery - Death to the Idiot Tax

Only 8 states out of 50 have no state lottery. Nevada is one of the eight, along with Alabama, Alaska, Arkansas, Hawaii, Mississippi, Utah and Wyoming. Most states that have no lottery have made that decision because the lottery is a form of gambling, and gambling is frowned upon. Nevada has no lottery because gambling by private operators is an important state industry. Most states that do have lotteries use them as a means of raising revenues in lieu of taxation. (Some states say the lottery is for “supplemental” programs in education or public improvements, but that is a fallacy. All money is green. There’s not more state spending because of the lottery; it’s just that less of the money that is spent must be collected as taxes.).

Rarely does a lottery represent a fair bet. For this reason, they are often called a “regressive tax” or a “poor man’s tax” because the result is that lottery players contribute strongly to the finances of the lottery owner, mainly the state. Most lottery players come from the ranks of the poor and the uneducated for two reasons: most people on earth belong to that group and those who are rich and educated do not need to buy a dream for a dollar.

Lottery bets are often so unfair that they would not be permitted by the state authorities, except for the fact that the state authorities are running the show. Most state lotteries would not be permitted by the Nevada Gaming Commission as having too obscenely high an advantage for the operator. State lotteries are sometimes also called a “tax on stupidity,” or the “math tax” because the financial expectation is so much lower than the true odds of winning. In fairness, a good bit of the disadvantage of the lottery is hidden from the wagerer by the marketers of the game, so the bettor may not be stupid, but rather misled.

Since the days of private lotteries in the late 18th and early 19th centuries, the mechanism of a lottery has remained pretty much the same. It is also the same mechanism as the common raffle, still used by churches and other non-profits for fundraising, even where gambling is not permitted.

The elements are: (1) a time period in which bets must be placed; (2) a drawing in which certain winning numbers or combinations of numbers are selected; and (3) a prize for the winner(s). In the case of a raffle, the numbers are simply given to the bettor at the time the raffle ticket is sold. This means that there will only be one claimant for each prize. In the case of a lottery, the bettor determines which numbers to play from a specific universe of possibilities or range of choices. This is established at the time the bet is placed by purchasing the lottery ticket. The drawing simply specifies winning numbers from the same universe of possibilities or range of choices as that used by all the bettors. In this system, it is possible to have multiple winners to split the jackpot.

The mechanism for selecting the numbers is random in an honest game. In earlier times, numbered balls were placed in a cage and mixed thoroughly before a disinterested person made a blind withdrawal. The common solution currently is to have ping pong-like balls in air chamber, each with a number on it. They blow around in random directions inside the air chamber until the chamber access is opened, and one blows out into a receiving area. Equally feasible, but considerably less dramatic, would be the operation of a reliable random number generator.

The prize offered for a winning ticket is usually cash. Some states, however, do not offer a lump sum payment, but annual payments over many years. They total these payments up without considering the present value of a future income stream, thus overstating considerably the value of the prize. For example, a $20 million prize payable in ten annual installments of $2 million is not worth $20 million at the time the prize is won. If the opportunity cost of money is taken as 7.5%, say, the prize is really worth only about $14 million.

The prize money, of course, is taxable. Some of those taxes are collected by the same state that paid the prize. In this regard, the lottery is no different from any other gambling winnings. Marketers of state lotteries never tell potential lottery ticket buyers that there is a substantial withholding from all payments, just to cover federal and state taxes.

In all, lottery winners get to see about $.35 out of every dollar of “nominal” lottery winnings. If a private company were to promote a product this way, the state attorney general would be breathing down its neck!

Some state lotteries avoid the moral problem of offering sucker bets to the populace by stating right on the ticket that the game is “for entertainment value only.” This means that the ticket has no financial value, at least not a positive one. Other states assuage the onus of exploitation by running ads thanking everyone for playing and showing pictures of all the wonderful things the lottery money has been able to accomplish. In truth, some people may be playing the lottery for the entertainment value received in the thrill of checking the numbers or in the satisfaction received from knowing that the money is going for causes of civic improvement. Most lottery ticket purchasers enjoy daydreaming about what they would do if they won the lottery. The daydream has more reality to it if the person actually buys a ticket. But the ability to do that may be worth far more than $1 for many people whose real lives contain little hope of riches. Thus, if people truly derive some satisfaction from these non-financial aspects of playing, it may be true that they get their money’s worth for the tickets that they buy. This explanation is used, for example, to account for why people buy insurance policies, in which the cost of the policy is probably higher than the expected value of economic loss. The difference is made up by “peace of mind.”

Many people enjoy playing “magic numbers” like the ages of their children, an important date or the number associated with a specific dream as catalogued in a dream book. Some numerologists make a business out of recommending lottery numbers. Lottery ticket tips can be found inside in a good many fortune cookies. Many lottery players can not be bothered with the process of hand selecting their choices. They are aware that a random selection of six numbers has no worse a chance of winning than six carefully selected numbers. For this, the lottery machine has a “quick pick” function, which allows the system to choose the numbers at random for the player.

Now a fair number of lottery players are persuaded that the cosmos conspires to favor some people over others, and – even though the mathematics of the lottery do not admit of this -- the power of intending to win, or the effort of wishing to win, or the player’s virtue or need to win might influence how the forces driving the universe reach out to cause the selected lottery number to match up with a carefully constructed ticket. The essence of the observation is that things that seem to be random really are not. It is very hard to argue with that. No amount of observation of a number will tell you whether or not it is truly random. And as for the process itself, well, the metaphysics of cosmic causation transcend the humble objectives of this discussion.

The modern lottery ticket is electronically readable, and the terminals that issue them are connected to a central point of administration (either in real time or by distributed processing of some sort). The lottery operator will know immediately if any point of distribution has sold a winning number.

Typically, the jackpot starts at some minimum level, like $1 million, and then grows for each session in which no winner appears. A winner will have to match all numbers on the ticket with all the numbers drawn by the lottery operator. In addition, tickets with high numbers of matches, but not all, will be awarded smaller prizes. Unlike a raffle, in which each ticket holder is in competition with all other ticket holders to win the prize, a lottery can have no winners at all, or it can split prizes claimed by more than one winner.

The state usually does not reveal how many people have entered a specific lottery session, so the profitability of the lottery is impossible to measure from one session to the other. The size of the jackpot, its rate of growth if there is no winner, and the sizes of the other prizes are independent of the number of tickets sold.

In theory, more money could be won in a lottery than was collected in the sale of tickets. As far as anyone knows, this has not ever happened with state lotteries, though it was an abuse when private lotteries were legal, and later, when underworld numbers rackets were common. The only modern scenario would be when a new jackpot is established (after someone had just won the old jackpot), and a new winner is determined before the amounts wagered have come up to the amount offered in the minimum jackpots and other prizes.

A typical modern lottery will allow the gambler to pay $1 and receive a ticket with six numbers from, say, 01 to 42 on it. Many people will buy five or ten tickets at a time, in which case the “ticket” itself will have five or ten rows of numbers, each with six numbers from 01 to 42 printed on it. The lottery ticket will also give the date of the drawing. Most states have drawings twice a week, on Wednesday and Saturday. This illustration is a facsimile of a Colorado lottery ticket.

The payoff table below is representative of the financial aspects of the lottery ticket. In this case, there are 1 to 42 possible numbers. The number of combinations of 6 numbers out of a universe of 42 is 5,245,786. One of them will win a jackpot. So, absent double winners, the expectation (the probability times the value of the prize) is $0.59. The other prizes add almost six cents more to the recipe, so the basic one dollar ticket is worth about $0.65. This is not a good bargain, but 45 cents of the ticket price does go to help pay the public’s bills.

Note also from the table that 98.6% of all lottery bets are losers. There is a very understandable and human tendency to think that by buying 10 tickets, one increases the prospects for the bet. If one ticket can win, ten tickets have ten times as much of a chance to win. And that is true. But this is much like the retailer who lost a little on each sale and tried to compensate by selling in volume. If a $1 bet is a bad one, then a $10 bet is surely no better, and probably ten times worse.

When is it rational to buy a lottery ticket? Every once in a while the jackpot climbs very high because no winning ticket has been purchased in several sessions in a row. Under the rules described above, a $5 million grand prize (with appropriate adjustments in the lesser prizes) would be just about a break-even bet. This makes some sense, as the expect value of winning on one combination out of 5.2 million possible combinations is slightly less than 1.0, and the inferior prizes, though small by comparison, push the deal into positive territory. When the jackpot gets as high as $8 million, the ticket is worth almost 60 cents more than its price, and it is a good bet.

There are two precautions about the positive bet situation. As the jackpot rises to put the bet in positive territory, more and more people will be willing to buy a ticket. Once breakeven is reached, the probability of having a winning ticket in any given session is very high. Whole communities might band together to buy lots and lots of tickets on a shared risk basis. This should not discourage anyone from making a bet, but it does explain why a jackpot seldom ventures too far into positive territory before somebody wins it and the game starts over from scratch again.

The other precaution directly affects taking a risk when the lottery has a positive expectation. As the chances improve of having a winner (because so many tickets are being sold) the chances also improve of having to share the prize with someone else if you should be lucky enough to win it. As it is usually impossible to estimate the number of tickets sold for any specific drawing, it is difficult to gauge what the chances are of having to share the prize. At the $8 million level, as posited in the example, the appearance of a co-winner drops the jackpot below the break even point, so all bets become negative expectation bets all over again.