Lotteries

Doug Taylor and Rabbi Morton Moskowitz

"Mind if we make a quick stop?" I asked.
"Not at all," said my friend, the King of Rational Thought. Which was good, because he was driving.
"Any convenience store," I replied. "I just want to pick up a lottery ticket."
He glanced sideways with a raised eyebrow. "Why do you want to buy a lottery ticket?" he asked, quietly.
The question surprised me.
"Well, so I can win, of course," I replied. "Be rich. Cash in my chips. Quit my job. Live the good life."
"I see," he said. "You have a math background, right?"
"Yeah. Why?"
"If I toss a fair coin, what are the odds it will come up heads?"
"And how many times - on average - would you need to toss the coin to win once?"
"Two times," I said.
He turned a corner. "Now if I paid you one dollar every time heads came up, what would you think about that?"
I laughed. "It depends on what you charge me for each toss of the coin."
"Forget it," I said. "That would mean that - on average - I would have to invest a dollar fifty, that is, 75 cents a toss for two tosses, in order to get a one dollar payoff."
"I agree," he said. "Now I think I recall hearing years ago that the odds of winning the lottery were one in 38 million."
"So?"
"So, based on this analysis, and assuming the jackpot is one million dollars, how much would you have to invest in the lottery in order to get an average return of one million dollars?"
I thought about it. "Let's see, it would take -"
I stopped. Not because I didn't know the answer, but because I suddenly did know the answer.
"Yes?" he prompted.
I cleared my throat. "Uh, 38 million dollars."
"You'd have to invest 38 million dollars to get one million dollars back?"
"Uh, yeah."
"And does that seem like a good investment to you?"
"Now wait a second," I protested. "We're only talking about a dollar here. What's the big deal?"
"Ok," he said, "let's lop off a few zeroes and look at it differently. I'll offer you an investment. You pay me a dollar for a single try at a pot of 100 dollars. Your odds of winning are one in 3,800. How does that sound?"
"Lousy," I said. "I'd have to invest an average of 3,800 dollars just to win 100 dollars." My mind started working. "Hmmm," I said, half to myself. "So if that's true, why am I so interested in buying a lottery ticket when the odds are about the same?"
The King of Rational Thought let me chew on it.
"Is it because of the sheer size of the prize?" I finally asked.
"Close," he replied. "It's the fantasy. The fantasy of winning big. Few people would take up a bet with such poor odds when the payoff is small. But lots of people buy lottery tickets because they hope to become instantly rich. The Lottery Commission knows this, and they feed it. Listen to their ads. They try to get people in touch with the fantasy of being wealthy. Yet on the face of it, viewed in realistic, financial terms, a lottery ticket is a terrible investment. You'd be better off to put your dollar in a savings account."
I wasn't overjoyed with the conclusion, but I couldn't argue with his logic. In fact, it occurred to me that if I were already wealthy, I would never buy a lottery ticket. I'd invest instead.
He pulled the car into a convenience store parking lot.
"Why are you stopping?" I asked.
"I thought you wanted to buy a lottery ticket."
"Oh. Well, I changed my mind." Then I decided to goad him a little. "I've got a better idea."
"Really?"
"Yeah. I got this great offer in the mail from a guy selling a sure-fire method for winning at the races. You see, all you have to do is..."
He shook his head and drove on.