Lies, Damn Lies, and Statistics

 

The Gambler

You've got to know when to hold 'em,
Know when to fold 'em
Know when to walk away,
Know when to run
You don't ever count your money
While you're sitting at the table
There'll be time enough for counting
When the dealing is done.

Do you know when to hold ‘em?

There is a classic problem in statistics named after a game on Let’s Make a Deal hosted by Monty Hall. The Monty Hall problem involves making one of three choices of doors, only one of which is a winner. The host, in this case Monty, opens one of the unchosen doors. It is inevitably not a winner. The player is then given the chance to remain with their original choice of doors or to change to the remaining door. When the correct answer, that you should always switch, was presented by Marilyn Vos Savant in Parade Magazine it created a controversy. PhDs who should know better could not believe that answer. In subsequent studies it was found that 85 to 90 percent of players would choose exactly the wrong strategy.  There is a fancy term for this, equiprobability bias. Humans assume that all outcomes are equally likely. When presented with a choice of two outcomes, one of which is clearly 67% probable, humans insist on acting like the probability of each choice is 50%.

 In Vos Savant words, the  Monty Hall dilemma does not involve competing theories of statistics. It reveals something about humility and human frailty. “ The disbelief that we could be wrong.  The tenacity sometimes aggrieved, which we hold our earlier judgment, especially when we feel certain”. So don’t be aggrieved. Know when to hold ‘em.