Gambler's Fallacy

Gambler's Fallacy

• We tend to see pattern as independent, random chain of events
• We believed that based on a series of previous event, the future event is more likely to occur than the actual odds suggest

Coin Flipping

After flipping a coin for 8 times, it came out heads 8 times in a row. One would assume that it is more likely that the next flip will more likely be tails. If it still result in heads, the 10th flip will even more likely than the 9th flip to be tails.

However, no matter how many times the coin is being flip. The probability of heads or tails for the next flip remains at 50%.

But why does it shows 80 heads and 20 tails when I flip the coin 100 times?

The answer is Variance.

The Gambler's Fallacy is the main reason why people use the Martingale strategy, which involves increasing their stakes after a loss. However, there is no guarantee that a wager will win because the probability remains the same, and a series of past events has no influence over future events.

Still unconvinced? I know some of you insist that tails will seriously more likely to appear after a long streak of heads.

In May 2014, after gathering more than 550,000 sports bets from more than 700 online gamblers, (Xu and Harvey, 2014), found out:

• Hot hands really exist (winning or losing streaks)
• Gamblers believe in gambler's fallacy 
• Hot hands is caused by the belief in gambler's fallacy

People who win, are more likely to win again, because they chose safer odds to bet on, which were more likely to win. 

People who lost, are more likely to lose again, because they chose risker odds to bet on, hoping to recover their losses, which were more likely to lose.

By selecting safer odds after winning and riskier odds after losing demonstrates that gamblers believe in the gambler's fallacy because they expect their luck to reverse the next bet. Thus, by believing in gambler's fallacy, they create their own hot hands.

References

Xu, J., & Harvey, H. (2014).  Carry on winning: The gambler's fallacy creates hot hands effects in online gambling. Cognition, 131,2, 173-180.