 XP Math - Forums - View Single Post - LAW OF AVERAGES, odds , probability,?
 View Single Post 08-04-2007 #3 Player Guest   Posts: n/a Right then we'll get down to it, ah by the way how many "Pro's" do you know. I'm a casino manager and have worked with table games for 22 years and been all over the world, I don't know any!The law of averages is a lay term used to express the view that eventually, everything "evens out."This concept must be regarded as misleading at best. Future random events are not influenced by past random events. The odds of getting heads by flipping of a fair coin are not influenced by the number of tails obtained previously. Even if there have been 100 tails in a row obtained previously, the odds of obtaining heads in the next flip are still 50%. Things do not tend to even out in the sense that a run of good or bad luck influences future results. What can be predicted is that after 100 tail results further flipping of the coin can be expected on average to yield 50% heads; the average percentage of tails can be expected to decrease. However after flipping 100 tails the result expected after 200 flips is 150 tails and 50 heads, not 100 tails and 100 heads.The formal mathematical result that supports this is called the law of large numbers. It states that a large sample of a particular probabilistic event will tend to reflect the underlying probabilities. For example, after tossing a fair coin 1000 times, we would expect the result to be approximately 500 heads results, because this would reflect the underlying 0.5 chance of a heads result for any given flip.Note, however, that while the average will move closer to the underlying probability, in absolute terms deviation from the expected value will increase. For example, after 1000 coin flips, we might see 520 heads. After 10,000 flips, we might then see 5096 heads. The average has now moved closer to the underlying 0.5, from 0.52 to 0.5096. However, the absolute deviation from the expected number of heads has gone up from 20 to 96.There are common ways to misunderstand and misapply the law of large numbers:"If I flip this coin 1000 times, I will get 500 heads results." This is false; while we expect approximately 500 heads, it is very seldom the case that we will get exactly 500 heads results. If the coin is fair the chance of getting exactly 500 heads is about 2.52%. Similarly, getting 520 heads results is not conclusive proof that the coin's true probability of getting heads on a single flip is 0.52 "I just got 5 tails in a row. My chances of getting heads must be very good now" is an example of a false perception. It was unlikely at the beginning that one would get six tails in a row, but the probability of six tails was the same as five tails followed by a head: 1/64 (see statistical independence). Looking forward after the fifth toss, these probabilities are still equal. The only difference is that there are no other possibilities, so the probability of either outcome is 1/2. This error can be devastating for amateur gamblers. The thought that "I have to win soon now, because I've been losing and it has to even out" can encourage a gambler to continue to bet more. This is known as the gambler's fallacy. There are situations in which a very small imbalance in probabilities can lead to a large imbalance in outcomes, contrary to the usual notion of the law of averages. The gambler's ruin is one such scenario.Probability theory is the branch of mathematics concerned with ****ysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative ****ysis of large sets of data. Methods of probability theory also apply to description of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.