Unfortunately, I have a very personal reason for choosing the gambler’s fallacy as my next topic. I am experiencing the effects of this fallacy with someone close to me who is in the grips of a gambling addiction. For years, she has exhorted me that winning depends upon making large bets. She believes that betting more money improves the odds of coming up lucky on her vice of choice, the slot machine. No amount of patient explanation of statistics and odds can dissuade her from this belief. She also falls prey to the classic version of the gambler’s fallacy, which essentially states that the odds of one event are influenced by the outcome of the preceding event. This can sometimes be true. For example, in cases where numbers are drawn and not replaced, as in bingo, the odds of the remaining numbers being drawn increase with each subsequent draw (that is, in a bag of ten numbered balls, the odds of drawing any of the numbers is one in ten. Once the first ball is drawn, the odds of drawing any of the remaining numbers becomes one in nine, and so on). However, it is not true for simple odds such as coin tosses. Each and every toss of a coin is an independent event. So, even if you get nine tails in a row, the odds of getting heads on the tenth toss remains exactly the same as it was for the preceding nine tosses; that is, 50 percent. Yet, many people will believe that the tenth toss has much greater odds of being heads because the previous nine tosses were tails. This is the gambler’s fallacy.
It is amazing how many people fall for the gambler’s fallacy. You see it operating not only in casinos but in lotteries. When a lottery jackpot gets really big, it is because several drawings have passed with no winner. And of course, the bigger the jackpot gets, the more people buy tickets. Many people do this simply because they hope to win the huge jackpot, not because they believe their odds are any better; but I have had conversations with many people who insist that they are more likely to win when the jackpot is bigger. Their argument is a perfect example of the gambler’s fallacy: because no winner has been drawn for so many weeks, the odds of a winner must be greater for the bigger jackpots! This is actually true in one specific sense, because the more people who buy tickets, the more potential combinations of numbers there are in the ticket pool. But the big jackpot and the long time elapsed since a winner does not change the fundamental odds of drawing, say, five numbers out of 56. No matter how big the jackpot, the odds remain exactly the same for each and every drawing. For the Mega Millions lottery, the odds of drawing five particular numbers and the Mega number are 1 in 175,711,536. Again, these odds remain the same no matter how big the jackpot and no matter how many tickets have been purchased. It seems that attaching money or some other consequence to the outcome of a random event scrambles people’s ability to rationally judge the odds.