In defense of the Bishop

I noticed some errors in criticism of Arnold Snyder's book, Blackbelt In Blackjack, posted some ways down the page.

I'm not sure if the original poster has an older edition of Blackbelt In Blackjack, but I have the 2005 edition and Snyder specifically says that getting 7 heads in 10 flips is within two standard deviations (not one) of the mean, with one standard deviation equal to approximately 1.58. If you multiply this by 2 that results correctly in the value of 3.16, which is greater than 7-5 of course.

With regard to a response by another poster, Snyder did not try to use the normal distribution to demonstrate the exact probability of 7,000 heads in 10,000 flips of a coin. He only pointed out how many standard deviations that event would be away from the mean. One cannot use the standard normal distribution for any particular numerical outcome since that is always equal to zero, by definition (not just for practical purposes). If a continuous distribution must be used to obtain the probability of an event, one must use the cumulative normal distribution, which requires the outcome in question to lie within a range of values.

Another poster mentioned that Snyder wasn't highly regarded as a theoritician. I think he's done ok for demonstrating a good count, especially since Peter Griffin has an error in one of his first tables in his famous book (and this was in a very late edition of the book).

In being a red-chipper?

Snyder made plenty of valuable, unique contributions to the blackjack world.

But he never made large sums of money playing Blackjack.

Don't get me wrong.I didn't intend to discredit Snyder in general whom I appreciate greatly as a BJ-researcher. But here he was clearly wrong. In the 1998 edition he really wrote that scoring only 3 tails in 10 was well within one standard deviation. The fact that he corrected this in a later edition is the best proof that my criticisme was justified.
But the way in which Snyder corrected his error is not very satisfactory. Saying that something is within 2 standard deviations is pointless. Being down by 2 sds or more has only a probability of 2.5% (1 in 40) and that's not what Snyder wanted to say.
In fact scoring only 3 tails or less out of 10 has still a probability of 17.2% and that's what he should have said to make his point.

Francis Salmon

It sounds like Snyder should have made a note in the new editions regarding the correction. Or at least mentioned it on Blackjack Forum (maybe he did?).

I do think though that he was trying to make a different point in the 2005 edition. The reason he said that 3 tails in 10 flips is within 2 standard deviations was to demonstrate that great fluctuations are common when using relatively few trials.
And to be precise, in this point he makes, he was not trying to give a probability at all when he wrote that. He was just saying that the event falls within an acceptable distance of the mean.