The Lottery, the Casino, or the Sportsbook: Who Came Out Ahead?
Have you heard about the Tennessee man who has 22 children to 17 different women? He was interviewed the other day, and when asked how he supports all his kids he was quoted as saying:
"I'm just hoping one day I'll get lucky and might scratch off the numbers or something. I play the hell out of the Tennessee lottery."
Well, what would it look like if a person really did play "the hell" out of the lottery? Say you spent a year buying one $10 scratch-off ticket each day. How likely would you be to come out ahead? And for that matter, how would the lottery compare to making a $10 sports bet or a $10 roulette bet?
I already found that the expected value is negative for each game. But instead of just calculating the average, I want to see how this would play out in real life.
Luckily, instead of actually spending money myself, I used Minitab Statistical Software to simulate the bets for me. But I didn't stop at 1 person. Since I was simulating the bets, I had 300 people make a $10 bet once a day for a year. 100 of them bet on a football game, 100 played a single number of roulette, and 100 bought a $10 scratch off lottery ticket called Neon 9s.
Let's get to the results and see how they did.
Did I Win?
Before we get to the results, let’s see what we would expect. Our football betters have an expected value of -$0.45, so by making 52 bets we would expect them to lose $23.40 on average. We would expect roulette betters to lose $27.56 on average, and the lottery players to each lose $144.56 on average.
Now let’s see how our random data turned out! I summarized the winnings for each person below.
We see that the football and lottery groups both lost about as much money as we would expect. But just because the average was negative doesn’t mean everybody lost! We can look at the maximum to see the biggest winner. A football bettor won $167.24 over the course of the year and a lottery player won $890. Just because the number are against you doesn’t mean it’s impossible to win.
Speaking of impossible…the roulette group has a positive average! That means the 100 people making the roulette bets won an average of $16.40 per person! As a group they won $1,640. At first I thought I messed something up. But looking at the results, our roulette players won only 149 times out of 5,200 tries. That’s 2.87%, and a One Proportion test shows that statistically it isn’t significantly different from the real value of 2.63%
And yet that small random departure of 0.24% from the average was enough to win our group some money! However…it wasn’t distributed evenly. The results below show the breakdown of the different amounts won and lost by our roulette group:
We see that 29 people lost all 52 bets, while another 26 lost 51 of them. That’s over half of who didn’t come out ahead! And the three people who won $1,280 only won 5 of their 52 bets. When the payout is that high, it doesn't take many wins to rack up the money.
So I Should Run to the Nearest Roulette Table, Right?
No, you shouldn’t be in too much of a hurry. The One Proportion test had a p-value of .155, meaning there was only a 15.5% chance of the roulette bettors winning as much as they did. While it’s not impossible that might happen again, it’s not likely.
But let's compare all 3 groups again. We already saw that despite having the group win money overall, only 45 of the 100 people came out ahead. Seeing as how the football and lottery groups both lost money, I would assume the number of people that came out ahead was a lot lower. Let's look at the results.
There were 28 people who won money overall in our football group, and only 8 people who won money overall in the lottery! And we already saw that the maximum win for the lottery group was $890. That means despite buying 5,200 tickets, nobody won the three largest prizes ($10,000, $30,00, and $300,00). Those prizes are so big that it's tempting to buy a ticket, but the odds of winning them are so low that, as far I'm concerned, it's not worth it.
I think the biggest takeaway is how much of a difference there was between the lottery group and the other two groups. As a group, the lottery players lost $15,370, and only 8 people came out ahead! The other groups don’t even come close to that. It just shows how that difference in expected value can really add up. And perhaps somebody should tell that Tennessee man that investing his child support money in the Tennessee lottery isn't the best of ideas.
If you really want to have money, it looks like saving it is your best bet.