“In fact, every copy of Shirley Jackson’s “The Lottery” has been checked out from the Springfield Public Library. Of course the book does not contain any hints on how to win the lottery, it is rather a chilling tale of conformity gone mad.”
Kent Brockman (The Simpsons)
As has been mentioned in previous articles, people from all demographics have a taste for gambling. As a Personal Finance blogger, I may not seem like the type of person who is intrigued by lottery payouts, but the recent Mega Millions drawing was estimated at a lump sum payment of $462 million. If we assume a 1 in 176 million chance to win and a 50% tax rate, the expected value of a $1 lottery ticket seems to be $1.31! Additionally, losses are tax deductible against other gambling winnings (meaning that $1 may only cost you $0.75 or less) and a significant portion goes to fund state governments, very often in the form of education subsidies.
You’ve heard the gambling bull case… now, let’s discuss some issues. In a commonly referenced paradox regarding probabilities and expected value, the St. Petersburg Paradox demonstrates how expected values are often incorrect assessments of value. In this paradox, let me present to you a casino game. The house flips a fair coin until a tail appears. For every head the house flips, the payout is that power of 2. If the house flips 0 heads, the payout is $1. If the house flips 1 head, $2; 2 heads, $4; 3heads, $8; and so on and so forth. If we calculate the expected value, however, we have a 50% chance of $1 ($0.50) , a 25% chance of $2 ($0.50) a 12.5% chance of $4 ($0.50) as an infinite series. Adding up all the $0.50 shows that the expected value of playing this game is infinite. Therefore, how much should the house charge for playing this game? If the expected payout is infinite, they should not accept any offers for under an infinite (or near-infinite, like $1 billion) amount of money. As a player, would you pay more than, say, $20 for a game like this? Most people answer ‘no’. This is an example of the lottery, where if an expected value is weighted toward an extremely unlikely, extremely lucrative payout, the amount somebody would pay for it decreases.
Perhaps expected value is not the best way to describe a game of chance!
Another issue: randomness. Are the balls truly randomly weighted? It is difficult to determine whether the selection method is truly 100% random. Gonzalo Garcia Payelo is reputed to have taken millions of dollars off of casinos who relied on their roulette tables being truly random. Slight imperfections in the concavity of the ball, the edges of the wheel or the way the dealer inserts the ball into play could all alter how a “random” drawing of a roulette wheel will be determined. The same attention to detail and precision may not be properly exercised in drawing lottery balls, which might alter the true chances of a payout. Without inside information, however, all of this is idle speculation as opposed to a lottery strategy.
Even though the current expected value for a single-winner jackpot is positive (in isolation – in reality, the EV drops with each additional entry), there may be reason to believe that the pot will most likely be split as opposed to a sole winner; more than one person enters into every lottery which brings down the odds. When it comes to pot splitting, some number selections may show up more frequently in lottery guesses than others (that would be for self selected entries, not quick picks). One common example that may ring true for fans of the hit-TV Series (and sixth-season disappointment) Lost. Playing the numbers ‘4 8 15 16 23 42’ may not give you all that you hoped for, and not just because of the supposed curse surrounding the numbers. A fear of odd numbers has been noted by some, which may lean toward more clustering of choices in even numbers. Expected value may then be higher in selecting more odd numbers than evens.
One other interesting point that the lottery brings up is the idea of ‘diminishing marginal returns’ guaranteeing that the lottery provides an uneven distribution of wealth. The argument is that the dollar from each participant is much more valuable to them (the difference between $50,000 and $49,999 for example) than the winner’s dollar (the difference between $250 million and $249.999999 million). By offering the lottery, then, the government is taking valuable dollars and giving them to somebody who does not value them as much. Robin Hood be damned!