Lottery - Expected Value

Expected Value

The expected value of lottery bets is often notably low. In the United States, an expected value of 50% of the purchase price is available only in the small-payout, non-jackpot games. For example, when a player buys a "pick-4" lottery ticket for $1.00, he might be getting a ticket with an expected value of only $0.50. Hence, buying a lottery ticket reduces the buyer's expected net worth. This is in sharp contrast with financial securities like stocks and bonds whose prices are theoretically based on their economic value, as judged by the markets at any given point in time.

Lotteries are sometimes described as a regressive tax, since those most likely to buy tickets, and to spend a larger proportion of their money on them, are typically less affluent people. It is also often referred to as a voluntary tax. The astronomically high odds against winning the larger prizes have also led to the epithets of a "tax on stupidity" and a "math tax" (or both epithets combined gives "tax on the mathematically inept"). Although the use of the word "tax" is not strictly correct, these descriptions are intended to suggest that lotteries are government-sanctioned operations which will attract only those people who fail to understand that buying a lottery ticket is a poor economic decision. Indeed, after taking into account the present value of a given lottery prize as a single lump sum cash payment, the impact of any taxes that might apply, and the likelihood of having to share the prize with other winners, it is not uncommon to find that a ticket for a major lottery is worth less than one third of its purchase price. In other words, if a lottery ticket costs US$1 to purchase, its true economic worth may be only US$0.33 or so at the time of purchase. Of course, this is just a hypothetical example, and the actual value will depend on the details of each lottery. Some lotteries may offer tickets that are worth less than 20% of their price, while others may be worth over 50%. To raise money, lottery operators must offer tickets worth much less than what one pays for them, so the lottery is a bad choice for customers trying to come out ahead.

In a famous occurrence, a Polish-Irish businessman named Stefan Klincewicz bought up almost all of the 1,947,792 combinations available on the Irish lottery. He and his associates paid less than one million Irish pounds while the jackpot stood at £1.7 million. There were three winning tickets, but with the "Match 4" and "Match 5" prizes, Klincewicz made a small profit overall.