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