In last week’s blog, in a semi-fictionalized story, I had a conversation with a recent college graduate, “John,” about whether he should become a professional gambler. I think I should have given him the “Stan and Pearl” test to see if he understands the basics of gambling.
I first discussed Stan and Pearl in my Million Dollar Video Poker autobiography. (Actually, it was my first autobiography. I’m considering penning Million Dollar Video Poker: The Next 25 Years if the new tax law provides me with a lot more free time than I currently have. We’ll see.) Every student who attended one of my “Secrets of a Video Poker Winner” classes has heard this story, and I’ve written about it in this blog at least a few times — but not for several years, and some of my readers haven’t been exposed to it before.
Most people believe the Stan and Pearl problem is very easy. And it is. Surprisingly, however, a high percentage of people get the wrong answer the first time they hear the problem. People who correctly understand what successful gambling is all about get it correct every time. People who don’t understand successful gambling, but think they do, often get it wrong.
Stan and Pearl are imaginary video poker playing friends. They play video poker with a level of skill and discipline far beyond what is found in most players.
The game they play perfectly is $1 9/6 Jacks or Better — without a slot club, returning a bit more than 99.5%.
Stan plays 10 hands every day and then, win or lose, stops.
Pearl plays 10 hands every day. If she has hit a flush or higher (paying 30 coins or more), she plays another five hands (costing 25 coins). If in those five hands she connects on another flush or higher, she plays another five hands. Eventually she’ll hit a five-hand dry spell and will quit for the day.
Stan stops and Pearl parlays. “Parlay” is a term with quite a few different definitions. Here I’m using it to mean she bets with her winnings.
The question is: Assuming Stan and Pearl follow their strategy perfectly, who is likely to have the better cumulative score at the end of one year?
Don’t let the genders of these imaginary friends influence your decision. The names were selected for wordplay reasons. I could just as easily have made them both men —Stan and Paul — or both women —Stella and Pearl.
When I teach it in class, I ask the students to raise their hands if they think Pearl will have the better score. I then ask the people with a hand up why they chose Pearl. The answers typically include:
“She’s riding a hot streak — betting more when she’s winning.”
“When she’s not winning anymore, she stops.”
“She’s playing more, giving her a better chance at getting lucky.”
Pretty soon we exhaust the reasons why people select Pearl. I then announce that anyone who voted for Pearl having the better annual score has no clue about what the winning process is all about.
I then ask if someone who voted for Stan having the better score will explain why. Almost always I get the correct answer: 9/6 Jacks or Better without a slot club is a game where the house has a half-percent advantage. Since Pearl plays more when the house has the advantage, she will lose more than Stan, on average. Since Stan plays less of this negative game, he will lose less. They will both be net losers, but Stan will lose less.
I then give them the second version of the puzzle. This time they are playing the same 99.5% game but there is now a 1% cash slot club. Stan still plays 10 hands per day, and Pearl still plays at least 10 hands, and more if she hits a flush or higher. Now who likely has the better score?
Most of the class correctly vote for Pearl this time. With the slot club, the player has a half-percent advantage over the house and now whoever bets more has the better chance of coming out ahead.
In summary, if you have the advantage, over time you’ll likely come out ahead. If you don’t, you likely won’t.
The reason I’m bringing this story out again is that in the scenario I outlined in last week’s blog, I had a discussion with a recent college graduate about whether he could pursue a life as a professional gambler.
I wished I had given him this test. Anyone wishing to succeed at gambling should get the right answer for the right reason.
Simple math is a dying art.
There’s an old book, Innumeracy, by John Allen Paulos. Everyone should have it.