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.