Gambling/Roulette probability question
How to calculate the probability of guessing n number of times in a row in a particular
number of spins.
2 in a row in 10 spins or 5 in a row in 100 spins
This is simple, but there is a trap or two here that confuses non-mathematicians.
The answer that I will give you ONLY refers to predicting, in advance,
an occurrence of ANY 2 numbers appearing within a given series of spins.
The odds of a particular number coming up is the SAME as any other number.
e.g. You can be asking what is the probability of the numbers 36, 0, 1 appearing in succession.
That is the SAME as a repeating number, although it "feels" counter-intuitive.
Remember that you MUST note that we are speaking of a pre-defined set of spins.
If you want to know the probability of a particular string of numbers appearing within, let us say,
all of the spins that you will witness over the course of an hour, a day, a year or a lifetime the probability
must be multiplied by the total number of times such a set of 2 spins or 5 spins etc. will occur.
Each number will occur once in every 38 spins (American wheel with 0 and 00)
Thus the correct (odds) solve for [1/38 [-1] to 1
37/1 and the casino pays off at 35/1 where the real odds are 37/1
That gives the house an advantage of 2/38
Reducing to 1 in 19 yields a House Advantage of about 5.5%
Imagine that you have $100 and bet $1 on 100 spins of the wheel.
ON AVERAGE you will lose $5.50.
The longer you play the closer to 100% true that figure becomes.
But I digress. Back to the topic at hand.
To get the percentage probability of ANY spin we do the division as above.
[1/38 [-1] to 1 yielding 2.63%
If "predefined" as any particular 2 rolls in succession, the probability is the </u>product<u>:
2.63% X 2.63%
That equals .069%
That is odds of about 700 / 1
Try for 3 pre-guessed rolls in succession ?
Now the odds are almost 500,000 / 1
Understand, that if you try to guess THREE in a row, for the rest of your life, you will probably not succeed.
Having said all off the above, what I have said reverts to averages; which are completely accurate when it
comes to the probability of ANY occurrence within a very very very long timeframe, e.g. 100,000 spins at the least.
To explain how a small sample size MAY produce odd-seeming results would require a lesson in Standard Deviation and "Z-Scores"
Let it suffice to say that The roulette ball and the dice have "no memory." That is "key."
If Red comes up 5 or 20 times in a row, the odds of Red / Black occurring on the next spin will always be 50% - 50%.
If number 32 comes up twice or thrice in a row the same holds true.
Humans see PATTERNS where none exist. This was part of human evolution, as the "most fit" survived and reproduced because of that ability.
They could find patters in nature, e.g. the seasons are repeating patterns, babies take 3/4 of a year to be born, predators hunted us at
nightfall, enemies tended to attack in the same fashion, crops followed patterns of growth. etc. etc.
The ancient Greeks and Romans all believed that the Gods controlled what we call "LUCK."
The Greek God "Mercury, and later the Roman God, "Fortuna."
Note that "LUCK" cannot exist. It is a label that we apply to events that are in the past.
If I win a lottery, you may say I am lucky AFTER I win it.
If I am robbed of the money, you may say that I am UNLUCKY.
If I recover the money, somehow I am then LUCKY again.
That is, until my doctor informs me that I have liver cancer.
"Luck" is no more than a Label. It is a "construct" of the fallible human mind fishing around for patterns.
Without these non-existent patterns, casinos would not make any money, by offering us payoffs that do not approach the real odds.
Incidentally, scientists and mathematicians are trained early on to TEST for the reality of patterns, not to accept the illusions.