What is the probability of winning in a game of chance?

[I_am_learning]

I friend of mine wondered, why on Earth do we have to learn different probability theories, afterall no one can ever be sure on anything, its only talk about, 'it can probably happen this than that' and so on.

Of course, I am sure, there is a lot of use of it particulartly when the no. involved is huge. But I am looking for a more satisfying answer with curde example for a newbiew, by the more knowledgeable like yourself.

 

[I_am_learning]

I meant, Give some interesting real life examples that are solved using the theories (concepts) of probability, which if solved by someone unfamiliar with those theories could have done very badly.

 

[mathman]

Insurance companies use them all the time to set rates. Also gambling casinos use probability to make sure the house will always come out ahead in the long run.

 

[zli034]

Probability can arm you.

 

[chiro]

I friend of mine wondered, why on Earth do we have to learn different probability theories, afterall no one can ever be sure on anything, its only talk about, 'it can probably happen this than that' and so on.

Of course, I am sure, there is a lot of use of it particulartly when the no. involved is huge. But I am looking for a more satisfying answer with curde example for a newbiew, by the more knowledgeable like yourself.

While its true that things that are random are unpredictable, there are results in mathematics (general results), that tells things that happen with regard to these systems.

Take for example the strong law of large numbers. It says that as the number of measurements gets larger and larger, taking the average of these numbers will converge to the mean value. It doesn't matter what kind of distribution we have (i.e. the probabilities can be whatever they want), but it still works.

There are other results along these kind of lines including the central limit theorem, where the theorem let's us use any general type of distribution.

There are more tools like this in probability and they have applications to many different areas.

 

[I_am_learning]

Thanks for those. I like the casinos example more (Real life one, not abstract things like mathmatical theorems). So, I can generalize,
The only reason the casino boss rides around in luxurios car is that he knows the theories of probabilities.

I also have this prespective. Everybody does have basic proability common sense. For example, when tossing coin twice, everybody knows that it is foolish to bet that both will be head than to bet that atleast 1 will be head.
The probability studies are just generalization and cascading of such things to such a huge magnitude that common sense seems useless. Am I right?

 

[chiro]

Thanks for those. I like the casinos example more (Real life one, not abstract things like mathmatical theorems). So, I can generalize,
The only reason the casino boss rides around in luxurios car is that he knows the theories of probabilities.

I also have this prespective. Everybody does have basic proability common sense. For example, when tossing coin twice, everybody knows that it is foolish to bet that both will be head than to bet that atleast 1 will be head.
The probability studies are just generalization and cascading of such things to such a huge magnitude that common sense seems useless. Am I right?

You are right, but one thing you should know about mathematics is that it really clarifies what is right under given assumptions, and in some cases our intuition does not match up with the mathematics, and in these cases, the math is right: not our intuition.

A real life example for you is the Monty Hall Problem:

http://en.wikipedia.org/wiki/Monty_Hall_problem

Also there have been mathematicians in the past that while very intelligent, have actually screwed up even simple probability calculations. Kolmogorov was the one (or at least one of the ones) that put probability on a solid footing. Again a real life example of this happening (by a real mathematician) is with Jean le Rond d'Alembert:

From wikipedia:

While he made great strides in mathematics and physics, d'Alembert is also famously known for incorrectly arguing in Croix ou Pile that the probability of a coin landing heads increased for every time that it came up tails.
http://en.wikipedia.org/wiki/Jean_le_Rond_d'Alembert

In a lot of cases most math does have a highly intuitive component, but in some cases its necessary to check our intuition with math that has proven useful in the past that seems to model the real world. Sometimes math is wrong, but when that happens, we reflect on that and change the assumptions and try and understand why our thinking was wrong.

 

[HallsofIvy]

Essentially, your friend is saying "because we can't be perfect, there is no point in even trying to do anything". That's the coward's theme song. Sounds like a loser to me.

 

[I_am_learning]

Thanks for all of those. I liked the monty hall, I am going to present this problem to that stupid friend. :)
After reading the quote from wiki, I remembered 1 question I used to have,
In a roll of a single Dice, Do I have any more chance of winning by consistently betting on single number than by say randomly betting on each throw?
I feel (this is mathmatical feeling BTW, intutive feeling tend to be opposite.) that the answer is no, beacuse like in the coin example, the chance of getting my no. in the next throw don't have anything to do with whether the no. has already appeared a lot of times or not even for once. But there is my another friend (not the former :) ) who consistently bets on single no. and goes on doubling his bet for hope that it will earn him back all which has been lost.
He has won quite a few times though.