Against the Odds

The similarities between trading and gambling begin with the idea that both involve speculation.  But they don’t end there. 

Blackjack played with a perfect basic strategy typically offers a house edge of less than 0.5%.  However, a successful card counter who ranges his bets appropriately in a game with six decks can achieve an advantage of approximately 1 percent over the casino, with advantages up to about 2.5 percent possible in various situations.  These numbers vary, obviously, on account of skill and other factors. 

Thus a counter with an average bet of $100 is looking for a return of about $1 or so per hand or about $50 per hour.  However, variance is high.  Thus the standard deviation for that player is about $1,400 per hour.  That’s a tough way to make a living, even without casinos actively trying to prevent card counting and frequently banning those who do (except in Atlantic City since New Jersey law prohibits the banning of card counters). 

Ed Thorp, an academic and advanced math expert, is generally viewed as the “father” of card counting – he certainly pushed it into the public consciousness.  His 1962 book Beat the Dealer outlined various strategies for optimal blackjack play. It should be noted that although mathematically sound, some of the techniques described in Thorp’s book no longer apply, as casinos took counter-measures (such as no longer dealing to the last card).  In any event, Thorp wrote the book on card counting – both literally and figuratively.

A surprising number of traders either got their start in the gambling world or are also involved in it.  It should be no surprise, then, that Thorp followed up Beat the Dealer with 1967’s Beat the Market and became a hedge fund manager. As well as being the “father” of card counting, he’s probably the “father” of market quantitative analysis too (see Scott Patterson’s engaging book, The Quants for more).

Doing the probability analysis to be a card counter is similar to probability analysis done by traders, and the connection is obvious.  Today’s high frequency traders may well be, in effect, card counters (their success rates suggest that they are).  But the connection between sports betting and the stock markets may be closer still.  One of my favorite mortgage traders from the 1990s got his start towards trading as a college student gambling on sports, often betting both sides and taking advantage of bookies’ shading the line in an era before the internet and immediate information when disparities of 3 points or so between “home” and “road” bookies was commonplace. 

That said, sports bettors, like most investors, aren’t very good overall.  In both situations most are driven and undone by their emotions.  For example, recent research from Sports Insights suggests that the higher percentage of bets the favorite receives, the less likely they are to cover (favorites receiving 75 percent or more of the wagers covered the spread just 46.1 percent of the time).  This animal spirits tendency is well-known.  So much for efficient markets in sports betting at least.

But since sports bettors must pick 52.4 percent winners just to overcome their inherent 11:10 disadvantage (sports books are in business to make a profit, after all), this is very significant information.  Although good data is obviously hard to come by, most analysts suggest that the best Vegas touts have a win rate in the area of 55 percent (see here for more).  Indeed, it appears doubtful that more than 5 percent of touts have a lifetime win rate of the 52.4 percent needed for profitability. That makes sports gambling a very difficult way to make a living – the margin of error is small and, as with blackjack, variance is high. 

For example, suppose a bettor went 58-42 (a very respectable 58% win rate) over the course of an NFL season, betting $1000 per game.  That bettor’s end result would be only $11,800. You’d need a hedge fund and lots of leverage to make that a big money-maker. Yet if someone were confident that s/he could win 80 of his or her next 100 bets, s/he could turn $1,000 into $15 billion by proper proportional betting – all over the course of a single season. 

In Vegas, many touts claim ridiculous win rates against the spread.  Some (try listening to Saturday morning sports radio) suggest “investing” in sports gambling.  Similarly, most active managers would have you believe that they are all you need to access untold riches.  In each scenario, it is very possible to succeed.  But success is far less frequent than advertised and far less lucrative as well.

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