Mathematical considerations - past present and
future
I have a friend of a friend of my cousin on my
mothers side who believes that if you toss a cat three times,
and it comes up heads each time, a greater than even chance exists
for it to land tails on the fourth toss. If you question why she
believes the probability changes, her answer is: "Over the
long-run the cat must land heads as often as tails, so if a streak
of heads occurs, a tail becomes more probable since even numbers
of each must be maintained."
This fallacious belief that the cat's past history affects its
future is fun to explore with further questions.
Examples: Suppose I flip the cat three times and it comes up three
heads, then I put it away. Tomorrow I take it out again. Is the
probability still greater that a tail will occur? If the probability
is greater, what happens if I wait a week or a month or a year?
If after some elapsed time NETeller interval (day, week, month), the probabilities
reset to 50-50, why does this happen?
If there is no time interval that resets the probabilities to 50-50,
how do I know it wasn't due for three heads in a row? After all,I
may have just received the cat, so how do I know the previousowner
hadn't flipped it five times and gotten all tails?
How exactly has the probability changed of a tail
occurring after three heads in a row? What will it be if just one
head has appeared, or after five heads in row?
If my friend's belief is true, all these questions should have
answers.
The fact that all answers to these questions would be nonsense
shows the belief is false.
Of course, a more profitable exercise would be to find a betting
person who believes that a past sequence of cat flips affects
the future. If this person is willing to pay better than even money
on the outcome of a fourth head each time three heads appear in
a row, you are assured of making money. Since past cat flips have
no affect on
future ones, the probabilities remain 50-50. Anyone willing to
pay out better than even neteller
poker money on wagers against
cat flips--even selected cat flips that occur after streaks-will
lose over the long-run.
I relate the story of my friend's belief in cat flips because
it is easy to see that the belief is wrong. However, many gamblers
share the same wrong belief and don't realize it. They will behave
as if the past does affect the future - learn this important poker
tip - it might serve you in the future.
Examples of common behaviors: You have just lost seven hands in
a row at blackjack. You decide to bet the table maximum on the
eighth hand because it must be time for a win. After all, how often
do you lose eight hands in a row? You have received garbage for the last hour and decide that no matter what, you will
bet heavily on the next hand because it must be time for a winning
hand.
You repeatedly play the same lottery numbers, believing that if
those numbers haven't won yet, their time must be coming. Each
of these behaviors results from believing that "I'm due."
Claiming that "I'm is just another way of claiming that the
past affects the future. There are more subtle expressions of this
wrong thinking, such as believing that other players in the game
affect the probabilities. Examples:
Some poker players believe that the more players there are competing
for a pot, the more likely it is that they will be dealt three-of-a-kind
or better. It is easy to fall into this trap, since winning hands
tend to be higher when there are more players at the table. Three
of a kind is much more likely to be the winning hand when seven
players compete, while with two players, a high pair is often enough
to win. However, winning hands are higher, only because more hands
are dealt, and to win, you have to beat more NETeller people. Whatever the
number of players, the probability
of you, an individual, receiving three-of-a-kind is always the
same. Present events, such as the number of players
who decide to fold early, do not after the fact affect the probabilities
on the past event of the deal. Just as the past doesn't affect
the future, the present does not affect the past.
Some poker players believe in betting heavily during winning streaks
and advise not to leave the table. This may be sound advice if
the reasons for the winning streak have to do with being at a table
filled with bad players. However, if the reason is a sudden streak
of great cards, there is no reason to believe this has anything
to do with the table, your seat, your opponents, the dealer, the
day of the week, the color of your socks, or any factor, period.
Good streaks happen just like bad streaks. There are no reasons;
that is just the nature of a series of random
events. Make sure that your playing decisions are grounded in correct
reasons. Analyze the reasons for your decisions. If the reason
comes down to believing that the past affects the future, the reason
is wrong. |
