Is random number predictable? I knows it sounds stupid, but...?

Question

somethings we are pretty sure that...
1. all number carry the same probability to be occured;
2. In long run, all number appear with same frequency.

So, if we observe some number are seriously under played, does it means this number is going to appear much more frequent than other number?

Anyway, one more phenomena ( I call it random number distribution) is that, given a game with 100 option (100 number), after 100 plays, almost 33% of the number will not be played, and slightly more than 41% of the number will be played once, 20.5% plays twice, 5% plays three times, 0.6% plays 4 times, 0.03% plays 5 times.

It can be proved easily, however, I feel upset that with such a distribution, we still can't predict the probability a random number will be played next time.

Hope any brilliant guy could share their insights here - to predict a random number. :o)

Answer 1

I think the key here is the words "long run". In statistics, it's called the law of large numbers where a VERY large sample set can be used to make predictions or correlations in a smaller sample set. But, the smaller the sample set the more deviation from the probabilities set by the large sample set. In the case of predicting a random number, how large does the sample set need to be before every number has a equal probability of coming up? If your talking about a die or roulette wheel, each numbers' probably isn't equal for each roll or spin. It's only over a very large sample set that you may approach this equality; and I bet this would be in the millions if not more. Many other factors may have affect on what number will come up each time. Thus, you have the gambler's fallacy; just because a number hasn't come up in the past doesn't mean it will or will not in the future and each roll or spin has no affect on the next. So, unless you're using a computer to generate a random number, which is a whole different topic, I don't think you can accurately predict a random number.

Answer 2

You ask: "So, if we observe some number are seriously under played, does it means this number is going to appear much more frequent than other number?"

Generally, no. This is commonly called the "Gambler's Fallacy" -- the false notion that if two events have an equal chance of occurring, then a streak of one increases the chances of the other. (For instance, if a balanced coin flips heads 9 times in a row, the chance that the next coin flip will be heads again is perceived to be pretty small.)

But it's not true, and it comes down to something called "conditional probability." The short description is: the chance of flipping heads 10 times in a row is 1 in 1024... but the chance of flipping heads 10 times in a row *once you've already achieved the first 9 of those heads* is 1 in 2. Sometimes you'll hear this expressed as "The coin (or dice, or whatever) have no memory."

Of course, this assumes a truly random distribution -- imperfect machines and pseudo-random number generators are not truly random, but in a properly operating system, the chances of any divergence from true randomness being detectable is slim to none. Especially when all the pit bosses in Vegas are on the lookout for such divergence. ;-) And in situations like a deck of cards, where the chance of drawing an Ace decreases as other Aces are drawn from the deck, the rules are much different.

For more info, see the link below. Hope that helps!

Answer 3

The short answer is no...

and yes.

In theory "random" means that future numbers are in no way effected by previous history. If you toss a coin 1 million times you should expect 500,000 heads. However, there is a probability that you will get 1 million heads in a row. On the next toss it is still 50/50.

But now we get to practical situations. If you are using a computer to generate a random number then there is an algorithm behind it.This means that there will be a sequence of numbers that approximates the definition of "random" If the sequence is short or the numbers that you look at is a significant percentage of the complete sequence then you could predict the probability change for the remainder of the sequence (as you described). If you can see enough of the sequence to guess the algorithm and seed then you can predict the next number with 100% accuracy. That's the downside of using machines to generate random numbers.

Why does this matter? Because many encryption codes rely on pseudo-random number sequences to make the codes hard to crack. As computers get more and more powerful, the code crackers get the tools to examine longer and longer sequences and crack the codes. This is why encryption keys keep getting longer - 32 bit keys were adequate 10 years ago, now we have to use 128 bit keys (and they are getting cracked more often).

Answer 4

It depends a little on how you think of randomness.

A series of random numbers is one in which each number occurs with precisely equal probability. There are algorithms for computers that will produce such series of numbers given a seed number, but they will always produce the same series given the same seed. Statistically, the number are random but they are predictable, and this means a random sequence on a computer is only as random as the seed.

A truly random number has equal probability of occurence AND is not predictable. Such numbers are generally hard to create.

Answer 5

Yes if you know the distribution function you can 'predict' the next random number. For instance given a big black hat with 100 numbered papers in it. Select randomly a paper . Chances that the random number you get is 1, is 1/100. I see no problem....

Answer 6

The assumption, and the reason, is that a given random number is non-deterministic. That is to say, it has no dependance on the numbers chosen before it, if it is truly random. The most common example:

If you flip a coin 100 times, and it lands on heads all 100 times, what is the chance that the 101st flip will land on tails? Answer: Exactly 50%.

Answer 7

a computer generated random number is not random, the r.n.g. runs off of a program, made by a person, and is written in a language written by a person, so numbers may seem to be random by the shear amount of number combination possibilities but it is not truly random.

for example if you ask a person to pick random numbers for an hour or so and don't let them see the numbers they picked then they will start re picking numbers over and over, unknown to them.

the same principle will work on a computer program. after a number is picked the information that was used to pick that number is dumped and it become possible for the program to pick the same number over and over depending on how good the program was writ en.

Answer 8

Learn about statistics...

And, yes, it does not matter at all which numbers were played in the past. Even if in roulette, the black colour appeared 10 times in a row - the next play the probability is the same as if there was no "history".

Answer 9

A game involving "100" events is far too little for a base 10 mathematical probability to be attempted. Thats only 1/10. Make it more like 100 billion events, involving base 10, then you'll be much more accurate.

Answer 10

Quite predictable to accuarcy (as stated significance level)

random nos generated by a computer algorithm has to comply

uniformity,convergence,Regression,recursive

and many more tests