Tuesday, March 7, 2023

Odds are for the future: a brief chat about statistics

 

     Something happens. Something unexpected. A person near you says "what are the odds of that happening?" Well, since it has already occurred, the answer is 100%. Without a parallel universe, the chances of it NOT occurring no longer exists.

     In statistics, this situation is expanded by the concept that the past has no bearing on the future. If the odds of something occurring are 5 to 1, then after the event has occurred in the past then the NEXT odds of something occurring are still 5 to 1.

     Every time you flip a coin (with a fair, properly balanced, coin) the odds are 50% heads 50% tails (yes, with that very small possibility of landing on edge left out). If you toss a coin and get heads seven times in a row then the next time you toss it the odds are still 50% heads/50% tails.

     Now, if you anticipate the future, you can determine the odds of getting heads seven times in a row (1/2 * 1/2 * 1/2 * 1/2* 1/2 * 1/2 * 1/2 == 1/256) for the future. But every time you flip the coin, the odds for that flip remain the same.

     The phenomenon of people expecting the past to affect the future exists in many people -- good luck/bad luck. It exists in all addicted gamblers (the scientific gamblers are a different matter). That lucky streak just HAS to affect the future. (It doesn't.) I had an uncle who won the state numbers lottery (not a huge amount at that time -- but significant) and he put the money all back into the lottery system until he no longer had any net winnings.

     There are situations where the odds do change with time. This is true for actuarial tables. Your odds for living to a certain age changes with each year you live. If you live until you are 75, your odds of living until 85 (10 more years) are better than the odds of you living until 85 from the age of 55 (30 more years). But, be assured, the insurance company has it well planned out such that, on average, they are not going to lose money. Those tables require ignorance of the future to follow the actuarial odds. Robert A. Heinlein's story "Life-line" indicates a way to beat the system -- but it may be the only one.

     There are also situations where the perceived odds -- what we think exists -- are not the same as the statistical odds. Professional gamblers are aware of these situations and, by gambling calmly and without emotion, succeed in taking advantage of them -- over the long run. This also happens in other areas of investment and helps certain investors increase their likelihood of beneficial returns.

     All venture capital firms rely upon both experienced analysis and spreading their risks. Five investments of 10K still gives a good profit if two are totally lost, two give back 15K each, and one brings back 30K.

     "May the odds be ever in your favor."


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