One of my favorite places to observe behavioral finance is actually on the casino floor.  Three well-documented heuristics that can be observed both in investing and gambling are: anchoring, framing, and the Gambler’s Fallacy.

  • Anchoring – The principle that suggests that individuals rely heavily on only one piece of information, or experience, to make decisions
  • Framing – The principle that suggests that individuals make decisions based on how the information is framed, or presented
  • The Gambler’s Fallacy – the mistaken notion that the odds for something with a fixed probability is affected by recent occurrences.

Since I hadn’t partaken in the activity for quite a while, I decided to saunter around the floor of a New Jersey casino.  This time, I was drawn to the roulette tables, the roulette informational display, and the frequency with which players were referring to it.

display-boardSource Matsui-America, LLC

As most of the readers probably know, the display provides a variety of information.

  • A Number Stack – listing the last 16 results
  • “Hot and Cold” numbers – the most and least frequent numbers over the last, say, 300 spins
  • “Odd vs Even” statistics – the percentage of outcomes that were odd, as well as even
  • “Black vs Red” statistics – the percentage of outcomes that were black, as well as red

Try as I might, I could not find any disclosure, or warning, relating past results and future results.  Really!?

To the avid believer, I am sorry to report that the information on those boards cannot have any relevance for the next wager.  Unless the wheel/process is biased, each spin is independent and thus future spins cannot be a function of historical ones.  It should be further stressed that casinos have an incentive to have unbiased wheels (See famous cases of people taking advantage of biased wheels).  So why do casinos display the information of irrelevant historical outcomes?  The answer is simple: to anchor, frame, and exploit our belief that if, say, red has been frequently observed over recent spins that black is due.

Placing a bet on “Black” at the american roulette table has a negative expected return (-5.26%) and a standard deviation nearing a staggering 100%.  These numbers together encompass the sheer brilliance of the game. We expect to lose 5.26 cents on every dollar wagered.  But with a standard deviation so high, we actually observe people winning over short periods of time. This seeming volatility to individual gamblers turns into virtual guarantee to casinos thanks to the Law of Large Numbers, which generally states that the average of a large number of independent trials tends toward the theoretical average.  In other words, the more frequently we bet, the greater the guarantee the casino takes 5.26% of each dollar.

Let us compare that to the investing world.  Long positions in most financial instruments, such as equity and fixed income, have higher expected returns and much lower risk!!  Yet, each presentation of historical performance in the financial industry must come with warnings of past performance not guaranteeing future results, various risks, and even potential loss of principal amount invested.

Could someone explain to me why casinos are allowed to frame information and to do so without proper disclosures?

I guess that on the face of it, depicting historical information is no crime; however, I find it pretty appalling when the content is not only completely irrelevant for the next wager decision and also blatantly done to take advantage of pretty well-known cognitive heuristics.

Category: CAIA, CFA, CIMA

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