You there. It’s time we had a talk.

graystoke Wed Nov 4, 2015 10:07pm EST 3 Comments

Perhaps you’ve had a stock fall through a trap door on you recently. You’re eying your position with every ounce of loss aversion fallacy (nobel prize winner!) your lizard brain can muster. Your cost basis is substantially higher than where this POS is currently trading, so high in fact you’re considering doubling down, or –what the hell– going all in.

Howdy stranger, welcome to the Martingale.

A Martingale is any of a class of betting strategies that originated from and were popular in 18th century France. The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake.

Since a gambler with infinite wealth will eventually flip heads, the martingale betting strategy was seen as a sure thing by those who advocated it. Of course, none of the gamblers in fact possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt “unlucky” gamblers who chose to use the martingale. It is therefore a good example of a Taleb Distribution – the gambler usually wins a small net reward, thus appearing to have a sound strategy. However, the gambler’s expected value does indeed remain zero (or less than zero) because the small probability that he will suffer a catastrophic loss exactly balances with his expected gain. (In a casino, the expected value is negative, due to the house’s edge.) The likelihood of catastrophic loss may not even be very small. The bet size rises exponentially. This, combined with the fact that strings of consecutive losses actually occur more often than common intuition suggests, can bankrupt a gambler quickly.

I did this once at Luxor in my early 20’s. The dealer took me from the $5 minimum bet to the $5k limit twice in less than two hours. Fortunately, I got lucky on both $5k hands. The soldiers-on-leave, sitting at our table loved the drama, and bought us rounds of drinks. My wife looked on in disgust, realizing she’d married the village idiot. My long-time buddy who we were vacationing with at the time, thought it hilarious. (Pretty sure he was disappointed I didn’t bust and that my wife didn’t ask for a divorce. BTW, this same rat bastard bet red –and won against a string of 13 roulette blacks that I had bet against– while I was at the ATM, pleading with it for more cash. Good thing he’s fast, or I’d just be getting out on parole about now. Never liked that guy.)

A fellow by the name of Edwardo Thorp is likely one of the primary reasons math & physics majors are in such demand on wall street, and why their computers algorithms now drive world markets.

Look pilgrim, I’m not going to tell you not to double down.

I am going to tell you to read this before you do.