Monday, December 19, 2016

What I'm Reading: Gambler's Fallacy and the Hot Hand

Most of our visitors know this stuff but here we have such a good exposition it may be worth a gander for even the time-constrained reader
Bold emphases mine.
From Frontiers in Psychology, Feb. 5, 2015:

Small samples and evolution: did the law of small numbers arise as an adaptation to environmental challenges?
Gorka Navarrete1*, Carlos Santamaría2 and Dan Froimovitch3
  • 1Laboratory of Cognitive and Social Neuroscience, Psychology Department, Universidad Diego Portales, UDP-INECO Foundation Core on Neuroscience, Santiago, Chile
  • 2Cognitive Psychology Department, University of La Laguna, Tenerife, Spain
  • 3Department of Physiology, University of Toronto, Toronto, ON, Canada
In the context of casino gambling, only a minority (~15%) of players presented with a streak of at least length 6 in roulette disregard recent events in deciding their next move, which is the normatively optimal approach to such a decision (Croson and Sundali, 2005). The majority of people would instead subscribe to a belief in a recency effect. This intriguing pattern of reasoning is categorized as either the gambler's fallacy, when the subject perceives negative recency (GF; Laplace, 1951; Tune, 1964; Tversky and Kahneman, 1971), or as the hot hand fallacy, when positive recency is perceived (HH; Gilovich et al., 1985). Such tendencies demonstrate, among a variety of things, that magical thinking is not exclusive to astrologists and tarot fanatics. Both the GF and HH refer to instances of the subject projecting a relationship between prior and present events, albeit in opposing directions. 

For example, subsequent to observing a run of 6 “heads,” a subject committing the GF would expect “tails” on the next coin toss. Alternatively, a subject committing the HH, following a similar streak of, say, successful basketball throws, would expect another “hit” on the next throw. Both fallacies have been posited as consequences of our immanent adherence to the law of small numbers—a distorted conception of chance, according to which short random sequences are considered highly representative of their underlying generating process (Tversky and Kahneman, 1971; Gilovich et al., 1985); But, counterintuitively, when dealing with sequences governed by chance, the short sub-sequences that we mistake as essentially representative of the overall generating process, actually deviate systematically from sequential properties on the global level; such small sub-sequences, on the basis of which we draw predictive inferences, are rather misrepresentative, containing excessive alternations and lacking sufficient long runs (Gilovich et al., 1985).

When predicting the next outcome in a random bivariate sequence of events, after having observed a local streak in either direction, we tend to fall into one of two behavioral categories, depending on how random the underlying process is perceived to be (Burns and Corpus, 2004). In accordance with the law of small numbers, when the conception of a random generating process is committed to, we expect the next event following a streak of a particular signal to switch to the alternate signal. Alternatively, when the generating process is believed to be nonrandom, we tend to expect the next signal to be consistent with that of the preceding streak. In very simple terms, given a streak in one direction (e.g., three heads in a row):

(a) When a causal mechanism explaining the streak does not easily come to mind, we tend to commit the GF (e.g., after a few heads, we believe the next throw is more likely to land tails). This occurs most often when the sequential probability is perceived to be fixed (Navarrete and Santamaría, 2012).
(b) When a causal mechanism is easily accessible (e.g., tampered coin, hot hand, etc.), and the sequence appears to be non-representative of our typified notion of a random sequence, we tend to commit the HH (e.g., after a few successful shots, the player is more likely to succeed again).
In general, we hold—or are inclined to feel as though we hold—a certain degree of control over the events of our immediate environment (Harris and Osman, 2012). We tend to think that the probability of experiencing a car accident is related to our performance behind the wheel; and while this is oftentimes the case, it is definitely not the case as frequently as we would like. The difficulties humans encounter in dealing with phenomena of fixed probabilities are likely related to the fact that, amidst our proximal surroundings, things rarely appear to occur by pure chance. 
Ordinary events around us are sourced in recognizable causes and elicit appreciable consequences. 

Moreover, we are innately specialized in discerning patterns (Lopes, 1982) and cause-effect relationships between successive events—especially those in temporal proximity to one another. From an ecological standpoint it is rare for one to observe sequential events that are completely independent of each other (Ayton and Fischer, 2004). Thus, it is of little surprise that we exhibit a distinctive ineptitude when it comes to handling random sequences.

Situations in which past events bear no influence on those of future ones, and, in particular, in which the probability of sequential outcomes is fixed, are primarily confined to games of chance, psychology laboratories, and sample spaces that tend toward infinity (Navarrete and Santamaría, 2012). Games of chance are known to be commonly addictive—a feature perhaps attributable to an illusory sense of control linked to an incapability to understand how they operate.

One could argue that games of chance were created with the intent of deceiving humans (Pinker, 1997). Moreover ecological circumstances in which the sample-size accessible to the subject exceeds a few dozen events are virtually absent from a rural or hunter gatherer setting (and likely from any other). Throughout our evolutionary history, it is likely that humans confronted minimally-sized samples exclusively, for which our current limited-capacity numerical cognition served us adequately (as a cautionary side note, see (Navarrete and Santamaría, 2011) for a comment on why such evolutionary arguments should be treated with special care). The numerical representations we seem hardwired to invoke are ill-suited for the processing of large samples....MUCH MORE 
Also at Frontiers in Psychology:
Nepotistic patterns of violent psychopathy: evidence for adaptation?

Previously in Gambler's Fallacy and the Hot Hand:
"How to Make a Bad Decision"
How Gamblers Get Hot (the 'hot hand' is real)
Recognizing and then managing a trader's hot streak is one of the more challenging things you can do in finance especially when the trader can't articulate what's going on, whether in credit derivatives or octopods who pick World Cup winners....
Baseball and Investing: "The ‘hot hand’ might be real after all"
"Luck vs. skill: What Bill Gross and Bill Miller have in common"
Taxonomy of Logical Fallacies (or How to open your mouth without removing all doubt*)
Speaking of fallacies (post immediately below)....a repost from August, 2009. You'll find the Gambler's Fallacy under the Probabilistic fallacies:... 
A Glossary of Luck
The language of luck, from “gris-gris” to “Irish lottery.”
apophenia: The tendency to perceive connections or meaningful patterns in random data; often used in ref. to divination, as in reading of tea leaves, or Roman practice of finding meaning in entrails. (See also gambler’s fallacy.) 
depressive realism: A psychological hypothesis that claims depressed people judge their control of events more accurately than do nondepressed people.  
Predicting the Improbable
"The ‘Hot Hand’ Debate Gets Flipped on Its Head"
Baseball and Investing: "The ‘hot hand’ might be real after all"
Luck vs. skill: What Bill Gross and Bill Miller have in common
More on The Top Earning Hedge Fund Managers and The Metaphysics of Moolah
"Can Investors Profit Using Academic Research?" 

Investing Tips From the Dalai Lama 
Remember When the Unluckiest Man in the World Won the Lottery?