<P> In 1796, Pierre - Simon Laplace described in A Philosophical Essay on Probabilities the ways in which men calculated their probability of having sons: "I have seen men, ardently desirous of having a son, who could learn only with anxiety of the births of boys in the month when they expected to become fathers . Imagining that the ratio of these births to those of girls ought to be the same at the end of each month, they judged that the boys already born would render more probable the births next of girls ." The expectant fathers feared that if more sons were born in the surrounding community, then they themselves would be more likely to have a daughter . This essay by Laplace is regarded as one of the earliest descriptions of the fallacy . </P> <P> After having multiple children of the same sex, some parents may believe that they are due to have a child of the opposite sex . While the Trivers--Willard hypothesis predicts that birth sex is dependent on living conditions, stating that more male children are born in good living conditions, while more female children are born in poorer living conditions, the probability of having a child of either sex is still regarded as near 50% . </P> <P> Perhaps the most famous example of the gambler's fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row . This was an extremely uncommon occurrence, with a probability of around 1 in 136.8 million . Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an imbalance in the randomness of the wheel, and that it had to be followed by a long streak of red . </P> <P> The gambler's fallacy does not apply in situations where the probability of different events is not independent . Where this occurs, the probability of future events can change based on the outcome of past events, such as the statistical permutation of events . An example is when cards are drawn from a deck without replacement . If an ace is drawn from a deck and not reinserted, the next draw is less likely to be an ace and more likely to be of another rank . The probability of drawing another ace, assuming that it was the first card drawn and that there are no jokers, has decreased from 4 / 52 (7.69%) to 3 / 51 (5.88%), while the probability for each other rank has increased from 4 / 52 (7.69%) to 4 / 51 (7.84%). This effect allows card counting systems to work in games such as blackjack . </P>

Chances of flipping 10 heads in a row