Speech # 9: Persuade with Power
Gambling is immoral, unprofitable and illegal, or at least it used to be. Once it was only legal in Nevada, then Atlantic City followed suit, now joined by casinos on Indian reservations and riverboats. Donald Trump even wants to open a casino in New York City. This isn’t church, so I won’t preach about morality. That leaves the economics. The house edge varies depending on which game you play. In roulette, there are 38 numbers, one through 36, zero and double zero, so if you bet $100 on red or black, on average you will get back a bit less than $95. That $5 is the house’s edge; it pays the croupier’s salary, the cost of the casino and dividends to the shareholders. You can get slightly less unfavorable odds at the craps table or if you are skillful at blackjack.
Gambling is exciting; so most visitors to casinos describe it as entertainment, for which they budget. They will set aside a certain amount of their holiday money for gambling and the longer it lasts the more fun they have. Very occasionally they will come away winners, but in general, the more bets you make, the more likely it is that that house will win. If your objective is to win a certain amount of money, risking only a given amount, then the highest probability of doing so is to place only one bet, risking your whole stake at the lowest odds that will let you win enough. Let’s say you lost your wallet and airplane tickets in Las Vegas, but you still had $100 in chips. You need $300 for the plane ticket home, and if you don’t catch the next plane you will get fired from your job, miss your sister’s wedding or suffer some other calamity. Your best bet, (if you stick to roulette because you understand it) is to bet on say, one to 12 coming up (a 31.5% chance), with the whole hundred. If you win you bum a ride to the airport and catch your plane. If you lose you call your credit card company for a replacement or a friend to wire some money, but too late to avoid the calamity. If you bet only $50 a time and tried the same wager until you either were up to $300 or broke, you would only have a 21.3% chance of being on the plane. Thus, if you decide to gamble when the odds are against you, the least worst method is to “go for it” on just one wager. This won’t pass the time and you will get strange looks from the croupier, but it is a far better bet.
That strategy can’t be applied in a casino if the amount you seek to win is very much greater than your stake. The longest odds at roulette or craps are 35 to 1. There are progressive slot machines that accumulate to larger payoffs, but I am not sure what kind of odds they offer. Racetracks offer longer odds in combination bets like quinellas where you have to pick 5 winners in a row. The house edge in pari-mutuel horse race betting is about 15%, worse than casinos, but at least you get to watch the race. Because it is a betting pool, wagering more can mean pushing the odds against you, so winning a phenomenal sum is not possible.
Most states have now entered the gambling industry, with their lotteries. Their edge is huge, often 50% or 60%, meaning that it is a terrible bet. It could be correctly described as a tax on people with poor mathematical abilities. States have truth in lending laws, where we that work at banks must disclose the APR on any loan. They are much less forthcoming about the odds on their lotteries. The purpose of this speech is to reveal the truth. The segment of the gambling market that the state lotteries have targeted is really, really long odds, people who want to risk a dollar to win $3 million or more. About ten cents of every lottery bet goes to fund the minor prizes, from a free replay up to $200,000 for five out of six plus the bonus number. Thirty to forty cents goes to the big prize, which gets carried over if there is no winner.
But, you say, “it’s only a dollar and besides, I wait until the prize has built up to $15 or $20 million. I heard that the odds of winning are about 1 in 18 million, so it seems like a fair bet.” Think again! They announce the prize to be paid in 26 annual installments, if you want it up front, the cash value is about half of the advertised figure. Plus, the prize is taxable, so figure on only keeping about 60% of the cash value. Only when the prize builds up to $60 million dollars would the after tax cash value be worth the $18 million that makes it seem like a fair bet. And that ignores the possibility of multiple winners splitting the prize. It is likely that lotto fever would be raging, so an average of two winners would be expected, cutting your take in half. Thus the NY State lottery may never be a good bet, certainly not unless the prize is over $100 million.
Other states have Power ball type games, where you must pick five numbers out of five drawn from 50 and the power ball drawn separately from 25. The odds of getting this right are about 1 in 53 million, so a similar computation should lead to disinterest at prizes below $250 million.
How then, should one play lotto, using the lesson we have learned about gambling and the odds? Let say you were willing to risk a dollar a week, $52 a year. The main idea is to wait until the prize gets above a certain threshold and then play with the full $52 dollar stake. The prize seems to get up to $30 million at least once a year, so that might be a reasonable level to get in at. If the apparent opportunity is in power ball instead, then you should wait to more than $100 million, but get in a group that are pooling their tickets. To most people the $36 million after tax that a power ball win would leave is not worth four times as much as the $9 million after tax that you could get from a $30 million NY prize. If $9 million will leave you set for life, what do you need $36 million for? If you agree, then find three others willing to go in for equal amounts, and increase your chance of winning a sufficient prize four fold. If this works, and you win, remember where you heard the idea. If someone else wins, well that is what you expected anyway. The difficult situation is if nobody wins. Do you dip into next year’s stake? That is a slippery slope.