In the book "Blackbelt in Blackjack" by A.Snyder it is stated on p.59 that the standard deviation is equal to the square root of the number of trials. Not correct!Rather it is only equal to 1/2 of the stated value in a binomial trial with 1/2 probability of success.
his can be varified experimentally in Feller's book on probability on p.21. He tabulates the actual outcome for 10 trials of 100 coin tosses each . He obtained a range of 39-60 per 10 tosses, with a std. dev. of 15.74 for 1000 tosses or half of the claim in the book by Snyder.
A deviation of 2 from 5 in 10 tosses represents 2/1.58=1.265 std. dev., which covers 79+% of the time, while 2 std. dev. or 2-8 would cover 95%.
The book has conviced me to obey the KISS principle.
Have I misunderstood the book?
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