The Gambler’s Fallacy


I’ve lost the last eight rounds, I’m due
for some good cards. We’ve won every coin toss so far. Our luck must be running out. This type of thinking might be common, but
that doesn’t stop it from being wrong. This is called the gambler’s fallacy, or
the Monte Carlo fallacy. The mistaken idea that if something happens
more or less frequently than normal during a given period, that it will happen more or
less frequently in the future. It’s an incorrect assumption when each event
is independent from the last. A coin has a 50% chance of landing on heads,
and a 50% chance of landing on tails. If on the first three tries, you get three
heads, that does not mean tails needs to “catch up” or that heads is “on a roll”. It means there is still a 50/50 chance for
the fourth flip. Why in many games does it seem like somebody
is on an unbeatable winning streak or a terrible losing streak. This is because of the nature of randomness. Various professors have split their students
into two groups and then left the room. One group was to flip a coin 100 times and
record the results. The other was to fake a sequence of 100 flips
and record them. Almost every time upon return, the professors
were able to tell which one was real and which one was fake. This is because humans are really bad at random
generation. We’re prone to all sorts of biases. The real sequences almost always included
long strings of 7 or more of the same result in a row. Meanwhile, the fake results often alternated
too much. You can test your skills at random generation
with a cool web page built by some students at the University of Illinois. Try and be as random as possible for 200 coin
flips. Compare your results to statistics students,
pi, the golden ratio, and the super bowl coin toss. All this is only for games involving coins
or dice, but what about cards? It all depends on whether or not all the cards
are shuffled at the end of each round. In most games, they are, which makes the principle
similar to that of coins. For example, if in poker your pocket or first
two cards have been bad for five straight hands, with proper shuffling it does not mean
that those bad cards will continue. Cards are different from coins in the sense
that there are more than two outcomes, which leads to more complexity. There are also games where the cards are not
shuffled after every hand, like blackjack. This allows card counting. Using past information to determine the most
likely outcome. In a regular deck of 52 cards, there are four
aces. The probability of any card being an ace is
4 in 52, or roughly 7.7%. If it is indeed an ace and that ace is removed
from play, the probability of selecting an ace again is 3 for the number of aces left
divided by 51 the number of total cards left, which is roughly 5.9%. This is not how actual card counting works,
just the same principle of using the past to know when the odds are in the player’s
favour. You are able to do this because the events
are dependent. The chances of getting an ace are related
to the number of aces already played and removed from the game, while the chances of getting
heads on a coin flip has nothing to do with the last outcome. But don’t be fooled. Just because you can know when the odds are
in your favour does not mean that you can predict the future based on whether or not
you won the last round. That is again an example of the gambler’s
fallacy. Outside of fun and games, how is this relevant? People who don’t understand this concept
or choose to ignore it are not only at risk of losing a lot of money, but also at risk
of believing supernatural forces are controlling the outcome of events and falling for other
types of misinformation. That might not be inherently dangerous, but
it certainly isn’t reality as far as we’re aware. But you know what is reality? Randomness is strange, and so are the minds
of people. And until next time, thanks for watching.

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