Probability - And Business Decisions!

Studying statistics is an interesting endeavor as business activities are so closely related to observation, formulation of strategies and extrapolation for analysis of data and implementation of new strategies. The behavior of large groups of people can be as random as coin tosses as mentioned in the previous post. In fact the entire life insurance business is based on this fact. We can't predict whether a specific person will die next year (except for my mother who can predict deaths through dreams...no pun intended she seriously can.) But if we observe millions of people, deaths are random. Hence make accurate prediction models for payouts. The proportion of men aged 25 to 34 who will dice next year is about 0.0021 say on the North American continent. When you have this data compared to the probability of death in women which about 0.0007 for the same range an insurance company tat sells many policies to people aged 25 to 345  will have to pay off on about 0.21% of the polices sold to men and about 0.07% of the policies sold to women.

So we see the law of large numbers applies as the mean of a fairly accurate sample moves towards the mean of the population (in this case the overall customers) very slowly. The law of large numbers is the foundation of such business enterprises like gambling casinos and insurance companies.The winnings (or losses) of a gambler on a few plays are uncertain - that's why gambling is exciting. If you take 100 gamblers and make 100 observations the mean of the sample is not very close to mean of the population, it is only in the very long run that the mean outcome is predictable. The house plays tens of thousands of times so the the house unlike individual gamblers can count on the long run-regularity described by the law of large numbers. Hence the average winnings the house on tens of thousands of plays will be very close to the mean of the distribution of winnings which translates effectively to say that the mean guarantees the house a profit and that's why gambling like insurance is usually a profitable business. At the end of the day the odds are always stacked up against the consumer. 

Thoughts, 

Sam Kurien

Randomness & Probability

The idea of probability is empirical. I chuckled when I twittered last night on Einstein's quote that- "God does not care about our mathematical difficulties. He integrates empirically". So probability is the art of observing a class of data closely and describing the data in several trials. Hence Randomness or "Random" behavior in statistics is not a synonym for "haphazard" but a description of a kind of order that emerges only in the long run.

The French naturalist Count Buffon (1707 - 1788) tossed a coin 4040 times. The results were 2048 times heads which means 0.5069 chances for the heads to occur. Around 1900 Karl Pearson heroically tossed the coin 24,000 times result was 12,012 heads, a proportion of 0.5005. John Kerrich while imprisoned in the German Nazi camp tossed the coin 10,000 times the result of which was 5076 heads, a proportion of 0.5067. So to make a point about randomness and probability we call a phenomenon random if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions, what I am interested in is under the density curve how this randomness can be plotted to make accurate assumptions. The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions.

I think gamblers and lay people always express this idea in terms of "What are the odds rather than probability?" Odds of A to B against an outcome means that the probability of that outcome is B/(A+B). So "odds of 5 to 1" is another way of saying "probability is 1/6". A probability is always between zero and one as per the laws of probability but odds range from to zero to infinity.

I wonder if some of the Vegas regulars apply laws of probability?

Thoughts.

Sam Kurien