Wednesday, April 1, 2020

Gambler's fallacy ! people with higher IQs are more susceptible


There was a time when there were lottery tickets sold with so many NE State names – Tripura, Meghalaya, Nagaland, Manipur – promising crores for Rs.50 or 100 and the business thrived. Then there was the ‘single digit’ lottery – simple it would appear – cost of ticket was Rs.11/- (for 100 you will get 9 tickets and 1 Re back) – you scratch to clear and see the No.  – if the last no. tallied – you get 100; if last 2 tallied, you would get 500; for 3 – Rs.1000/- and more ..

The probability of winning was what ? – numbered to end from 0 – 9 – ie., 10 nos. – so, if one were to buy 10 tickets in Series – one would surely get Rs.100 ! …**


Horse racing, like all sport and entertainment, relies on social approval - what is often referred to as social licence - to thrive and prosper. The casual sports fan, the once-a-year punter, and the regular whose life merged with horses and their history  will turn up on the big race days.  At Guindy race course,  there would whiff in the air, crowds – so many, trying to hit a jackpot.  Remember seeing a Muthuraman film, where he would embezzle [take out Rs.10000/-] office cash on a Saturday thinking that he would play horse race, earn big  and put back money on Monday – but would end up losing the money and losing life !  ~ had heard of an employee, receiving PF loan for daughter marriage, withdrawing cash, fly to Bangalore, book a star hotel, lose the total money – much to bewilderment of his family !!  ~ there have been many sob stories of punters.   This is no post on race-goer and the plight of their family ! – to hit a jackpot may not be simply by chance, it could well be a rocket-science or great Mathematic algorithm !  .. .. ever heard of Gambler’s fallacy !

                      Gulfstream Park is a racetrack and county-approved casino in Hallandale Beach, Florida.  It is one of the most important venues for horse racing in the USA. The 20-cent Rainbow 6 at Gulfstream Park was solved Monday when a bettor cashed for a $1,208,573.86 jackpot payoff with a $51.60 ticket played at Xpressbet. The winning ticket was 5/1-8/4,5/1,9/1-8/6. The Rainbow 6 had gone unsolved for 14 consecutive racing days.  Moving slightly away, how predictable is the toss ? and are there proven ways of winning a toss.  It is all about probability and when a coin gets tossed on air – it is 50:50 for head or tails.

Yet in India at JSCA stadium, in a bid to end his losing streak at the toss, South Africa skipper Faf du Plessis brought Temba Bavuma as proxy captain for the third and final Test against India at the JSCA Stadium.  Still luck eluded him. Virat Kohli won the toss and chose to bat for the third time in 3 matches. After winning the toss, even Kohli couldn't help but laugh at the helplessness of the South Africa captain.   However, Faf is not the worst sufferer.  Du Plessis'  boss, CSA Director of Cricket Graeme Smith, lost the toss on no fewer than eight consecutive occasions during 2008/09 – and there was Naseer Hussain who lost the toss 10 consecutive times.

The gambler's fallacy can be illustrated by considering the repeated toss of a fair coin. The outcomes in different tosses are statistically independent and the probability of getting heads on a single toss is 1/2 (one in two). The probability of getting two heads in two tosses is 1/4 (one in four) and the probability of getting three heads in three tosses is 1/8 (one in eight). The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the erroneous belief that if a particular event occurs more frequently than normal during the past it is less likely to happen in the future (or vice versa), when it has otherwise been established that the probability of such events does not depend on what has happened in the past. Such events, having the quality of historical independence, are referred to as statistically independent. The fallacy is commonly associated with gambling, wherein it may be believed for example that the next dice roll is more than usually likely to be six because there have recently been less than the usual number of sixes. The term "Monte Carlo fallacy" originates from the best known example of the phenomenon, which occurred in the Monte Carlo Casino in 1913.

Here is something interesting read in a BBC article.  The “gambler’s fallacy” - which can affect everyone from athletes to loan officers - creates deceptive biases that lead you to anticipate patterns that don’t really exist. Fifteen years ago, the people of Italy experienced a strange kind of mass hysteria known as “53 fever”. The madness centred on the country’s lottery. Players can choose between 11 different wheels, based in cities such as Bari, Naples or Venice. Once you have picked which wheels to play, you can then bet on a selection of numbers between 1 and 90. Your winnings depend on how much you initially bet, how many numbers you picked and how many you got right. Sometime in 2003, however, the number 53 simply stopped coming up on the Venice wheel – leading punters to place increasingly big bets on the number in the certainty that it must soon make a reappearance.

By early 2005, 53 fever had apparently led thousands to their financial ruin, the pain of which resulted in a spate of suicides. The hysteria only died away when it finally came up in the 9 February draw, after 182 no-shows and four billion euros worth of bets. While it may have appeared like a kind of madness, the victims had been led astray by a reasoning flaw called the “gambler’s fallacy” – a worryingly common error that can derail many of our professional decisions, from a goalkeeper’s responses to penalty shootouts in football to stock market investments and even judicial rulings on new asylum cases.

Research has found that people with higher IQs are more susceptible to the gambler’s fallacy, perhaps because they believe they can better predict patterns. To find out if you fall for the gambler’s fallacy, imagine you are tossing a (fair) coin and you get the following sequence: Heads, Heads, Tails, Tails, Tails, Tails, Tails, Tails, Tails, Tails, Tails, Tails. What’s the chance you will now get a heads? Many people believe the odds change so that the sequence must somehow even out, increasing the chance of a heads on the subsequent goes. Somehow, it just feels inevitable that a heads will come next. But basic probability theory tells us that the events are statistically independent, meaning the odds are exactly the same on each flip. The chance of a heads is still 50% even if you’ve had 500 or 5,000 tails all in a row !  For the same reason, HTHTTH is just as likely as HHHHHH. Once again, however, many disagree and think that the mixed sequence is somehow more probable than the streak.

As its name suggests, the gambler’s fallacy has been of most interest to researchers studying games of chance. Indeed, it is sometimes known as Monte Carlo Fallacy, after a notorious event at one of Monaco’s roulette tables in 1913, with 26 blacks in a row. Observational studies – using casino security footage – have confirmed that it continues to influence bets today. Surprisingly, education and intelligence do not protect us against the bias. Indeed, one study by Chinese and American researchers found that people with higher IQs are actually more susceptible to the gambler’s fallacy than people who score less well on standardised tests. It could be that the more intelligent people overthink the patterns and believe that they are smart enough to predict what comes next.

Bank loan officers were up to 8% more likely to reject an application after they had accepted two or more in a row.  Whatever the reason for these false intuitions, subsequent research has revealed that gambler’s fallacy can have serious consequences far beyond the casino. The bias appears to be present in stock market trading, for instance. Many short-term changes in stock price are essentially random fluctuations, and Matthias Pelster at Paderborn University in Germany has shown that investors will base their decisions on the belief that the prices will soon “even out”. So, like Italy’s lottery players, they trade against a streak. “Investors should, on average, trade equally ‘in line’ with the streak and against it,” he says. “Yet that is not what we can see in the data.”

One team of researchers recently analysed US judges’ decisions on whether or not to grant asylum to refugees. Logically speaking, the ordering of the cases should not matter. But in line with the gambler’s fallacy, the team found that the judges were up to 5.5% less likely to grant a case if they had granted the two previous cases – a serious decline from the average acceptance rate of 29%. Consciously or not, they seemed to think that the chances of having the same judgement three times in a row was just too small, and so they were more inclined to break the streak. The researchers next analysed bank staff considering loan applications. Once again, the order of the applications made a difference: the loan officers were up to 8% more likely to reject an application after they had already accepted two or more in a row – and vice versa.

As a final test, the team analysed umpires’ decisions in Major League Baseball games. In this case, the umpires were about 1.5% less likely to call a pitch a strike if the previous pitch was also called a strike – a small but significant bias that could make all the difference in a game. Kelly Shue, one the co-authors of the study, says that she was initially surprised at the results. “Because these are professionals and they're making decisions as part of their primary occupation,” she says. But they were still vulnerable to the bias.

In the single digit lottery mentioned in para 1 – yes the ticket numbers must end from 0 – 9 and thus 10 wickets could well have to end  – 0,1,2,3,4,5,6,7,8,9. But as one would have experienced and going by the theory of Gambler’s fallacy – if you had bought say 5 tickets and the ending nos. had been 3,5,8,8,0 and if the winning no. were to be 4 – even if you are to buy 100 tickets more,  still you get that ticket ending 4. For every new ticket  - be it your 1st buy or 231st buy – the probability still starts afresh and would give you the option of anything between 0 – 9.   Have seen mounds of paper left over by the gamblers searching for that elusive win – losing all their money and ending up disappointment.

** In a reported instance, a man sold his truck for Rs.125000/- - with the cash on hand, saw a single digit lottery shop nearby – thought would play a small part of the money, trying his luck out ! – sadly, by dusk, he had lost all his money – gained nothing and went back without his truck nor the money gotten from the sale of truck. Strange are the ways of people.

Interesting !

With regards – S. Sampathkumar
20.02.2020

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