Does My Gut Need an Algorithm?
There’s something we admire about persons who make firm, gut-decisions and then take decisive action. But, do gut decisions pay or are we better off going against our intuition and relying on calculated odds? For over a decade Monty Hall, of Lets Make a Deal showed contestants three curtains. One hid a big prize like a marvelous 1974 Pontiac LeMans. The other two hid lesser prizes called “goats.” You can play the game by using the link below:
1. Try to choose the door that hides the car.
2. Two doors hold a “goat.” Monty will reveal one of them after you’ve chosen a door.
3. Monty will give you the chance to switch to the closed door you didn’t choose.
4. The simulator will tabulate your results. Click on a door to begin.
As you play, you’ll notice that once a “goat” door is shown, you have only two possible doors that can hide the car: the door you picked or the door you can switch to. That’s a 50/50 chance–why switch? Surprisingly, the wiring inside us can work against our making the better choice.
This puzzle, coined the “Monty Hall problem,” appeared in Parade magazine. As you might have noticed, there is a preferred (but unintuitive) solution that doubles the chance of winning. The solution, when put forward by one columnist, was contested by nearly a thousand PhDs. The well-known mathematician Paul Erdos insisted it was wrong until he was shown a computer simulation, perhaps like the one above.
I’ve looked at dry calculations showing why what appears to be a 50/50 choice is in fact not. It occurred to me there is a simpler way to understand it.
1. There are two goats and one car, so we have a two-in-three chance of picking a goat.
2. If we pick a goat and opt to switch our choice, we’ll always win the car.
3. Therefore, there is a two-in-three chance of winning the car, provided we switch.
Put another way, we are shown one of two goats. If we’ve initially chosen a goat, and there’s a two out of three chance we have, we will always win by switching. If we don’t switch, there’s is a one-in-three chance of winning. Monty affects the odds by showing the goat. This seems like a helpful gesture, but in fact allows our faulty reasoning to work against us.
There are at least three ways in which Let’s Make a Deal stacks the odds in its favor. Probability and psychology play big roles. The first is by making our choice appear to be what it is not: a 50/50 shot. The second is by banking on our counterfactual, or faulty gut tendency to not switch doors. Third is the show’s advantage in running a series of games to virtually assure its odds. Choose “1000 runs” after clicking on the above link to the game. First, pick “keep the choice” and note how you never deviate much from ⅓ wins and ⅔ losses. Next, pick “change the choice” and notice that you uncannily win about ⅔ the time, just as expected. This predictability is an advantage the game show enjoys but not individual contestants who play only once.
We experience faulty (counterfactual) thinking when we refuse to sell a poor investment or purchase a stock at a price higher than what we once paid. We might find the industry’s use of odds in league with our counterfactual thinking when media baits us to adopt a herd mentality, giving us a gut-prompt to chase a stock’s returns or to seize the latest “hot” investment by tempting us with historical returns and other poorly predictive data.
In fact, by the time such hot tips hit pulp and print, most of their value is likely wrung dry. What seems like helpful tips, similar to Monty’s showing the goat, may in fact only serve to eke out greater sales for reduced value investments all at the cost of forgoing better investments.
A question is whether investors and advisers who act on poorly predictive media tips, display a counterfactual behavior that is in fact predictive and therefore, exploitable by financial media and the industry.
One Response to “Does My Gut Need an Algorithm?”
Interestingly, this points out that making each choice in the moment with the facts in front of you will cause you to be more vulnerable to that Monte Hall decision. Which perfectly ties into the idea of selling at a loss, it is just knowing when that loss isn't an overall loss. I.e., it doesn't seem to make short term sense, but is required for a longer term success. Which begs the question of exactly when to make that call, and supports the idea of getting professional advice!