Knowing the count

I just finished Ed Thorp’s new autobiography A Man for All Markets and I really enjoyed it. Thorp is, among other things, the man who wrote Beat the Dealer in 1962, the first truly mathematical approach to beating blackjack. He was first to calculate that while betting strategy was important, it had to go along with the cards as they were dealt. It mattered what cards had been dealt, and what was left in the deck. Thorp’s research proved that the more 10s, face cards and Aces that were left, the better the player’s odds became over the dealer, moving from a basic house advantage to, at times, a significant player advantage. Thus card counting was born, a system of tracking which high cards (lowers the count) and low cards (raises the count) have been dealt. Beat the Dealer changed America’s fascination with gambling, created leagues of professional blackjack players and inspired stories like Bringing Down the House, the book that later became the movie 21 with Kevin Spacey.

As a guy who likes math and card games, I loved the first half of A Man for All Markets. Thorp opines on risk, betting and tradeoffs and eventually made his professional career in running a hedge fund trading strategy after he discovered how wildly mispriced the options market was before the advent of the Black/Scholes option pricing model (which Thorp himself essentially discovered a few years before the Nobel prize winners).

While there are parallels between betting at the tables and the investment markets, most people’s experience won’t be Thorp’s. For one, the low hanging fruit in options pricing that Thorp uncovered is now nowhere to be found.

But more importantly, making long-term investments isn’t playing Blackjack. At the table, several things need to happen to make counting cards work for the player. First, like any system built on probability, you need to play over and over and over again to effectively build a large enough sample set and eliminate noise. That means having a fairly large bankroll and lots and lots of patience. Even when the odds are well in your favor, you’re going to lose many bets. Thorp parlayed this into the hedge fund business because he could identify his opportunities (there were many!) and make multiple bets on multiple positions over and over and over again each day. Some went against him, but enough went for him.

For most investors, we only really get a few chances. A long-term stock investor in the prime of his/her earning and savings years will probably see 3-4 major market cycles for the rest of their investment lives. Not exactly a huge sample set for making probabilistic bets.

Counting cards in Blackjack works so well because it is a known, closed system. You know how many decks are in the shoe. You know how many of each card is in each deck. You know when the dealer re-shuffles the decks. You know the odds on each hand based on the dealer’s Up card. You can even sit with a cheat sheet that tells you how to act based on cards on the table!

Markets aren’t anything like this. There’s no closed system. You don’t know how many decks are in play, or if the dealer might add a few more without your knowledge. You could be “up big in the count” (let’s say that’s really cheap stocks by P/E or something similar) and the dealer could keep drawing 2s and 3s because his deck is essentially limitless. Remember, markets can remain irrational longer than you can remain solvent. You can go from stocks being worth 15x earnings to 10x to 7x to 5x. There aren’t any rules about how markets work. It’s not a card game.

Once more, think about how often “the count” is big enough to bet big. It’s less often than you think. At the table, you could reasonably expect the count to get above +5 or +10 on a somewhat regular basis depending on how many decks are being dealt. So your opportunities to increase your bet size come across pretty regularly. But big delicious fat pitches in the markets, if we’re talking about massively undervalued or overvalued stocks, aren’t so readily apparent. Most of the time we’re middling in the parallel of -3 to +3. Nothing too exciting to make a big bet on.

My advice is: don’t get overconfident about your ability to beat the dealer. Investment markets aren’t a closed, rule-based system. They are complex, messy organisms driven by the whims of humans.

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