Background: the Monty Hall paradox (here are some of my tips for understanding and explaining it). Optional: David Sklansky, Theory of Poker.
I was at my neighborhood pub last night when I overheard a snippet of conversation that nearly made me pick my first bar fight. (I've been in plenty of bar fights, just never picked one before.)
WOMAN: "Do you think you made the right decision?"
MAN: "So far."
So far? I shook my head and took a drink. This guy sounded just like all the lousy poker players I've ever known: people who think drawing to an inside straight is fine as long as they hit their hand. They confuse the payoff with the play. His decision was right, I fumed, if it was arrived at in the right way, not if it does or doesn't pay off in the actual event. (Many a fisticuff has arisen over this important point of principle.)
This very idea had just come up in my Rediscovering Math class. We were playing the Monty Hall game, with me as the host, and with an imaginary jeep as the prize behind one of the doors. The student who was the game's contestant said, "OK, I'll switch because I believe the math, but if the jeep is behind my first guess, I'll be pissed." In reply I said, "But would you be pissed, really?" And here another student said, "Personally I think it would be OK even if I lost, because by switching my guess, I at least put myself in a position to win." That's how you keep the payoff separate from the play.
When the woman asked, "Did you make the right decision?", why is it so much to ask that the man should answer, "Well, I made the best decision I could based on the information I had at the time; it's working out so far, but win or lose, I think I made a sound decision on this one." More head shaking, another sip of my drink.
But as I sat there longer, I continued to reflect on the man's "so far" answer. My hackles went back down as I registered the helplessness behind his words. What decision had he been facing, and how did it feel to be still waiting for the other shoe to drop, wondering if everything would turn out all right? It struck me that there is a cruelty in this common view of decisions, this picture of accounts that remain open until the final score is tallied. But when you don't know how to assign yourself points for making rational and careful decisions, what other way is there to keep score?
Rational and careful is not synonymous with mathematical or robotic, and in fact, being rational demands that we pay attention to emotional factors. Good decision-making doesn't ask us to quantify emotions and values, nor does it ask us to ignore them in favor of "objective" considerations. But it does demand that we gain some distance from these emotions and values by naming them, and by investigating them as factors in our decision-making process. This is not something we often do naturally, but it is, I hope, something we can be educated to do, and something we (I) can improve at throughout the course of our lives. Another thing I hope to teach my students in Rediscovering Math is that a momentous decision with real consequences for ourselves and for others is not only a process of sorting through emotions and values, but also a process of discovering crucial facts, of being creative about options, and of bringing our clearest sort of thinking to bear. One of my students today pointed out that it is especially in a problem fraught with emotion that thinking systematically can help us cope.
If I could reclaim the last point for a mathematician: Poker is a poor metaphor for life, but it illustrates one essential feature of the rational life, which is that even the major life decisions are about (as my student put it) "putting yourself in a position to win", not winning or losing in the event. If this message helps us not to feel regret when the world inevitably fails to give us what we ask for, then there is a way in which the rational is in fact the most human option, because the most merciful.