Fred Renzey: Theoretical Card Clumping question

[Fred Renzey]

A player wrote me and asked why my book doesn't address something as important as "card clumping strategy" (primarily for shoe games). He further quoted an expensive piece of blackjack literature which stated that if third bases's second card of his starting hand was a 10, and the first hit that anybody took was also a 10, then the dealer's hole card (the card sandwiched between those two) would also be a 10 two times out of three.

That's an incredibly profound statement since only 94 tens vs. 216 non-tens would be available as the dealer's hole card from a six deck shoe.

Now I know that computer studies have been done in an effort to simulate human shuffles, and I've read that the shuffled cards were found to be "almost" random.

Still, I decided to perform a manual experiment. Using a physical six deck shoe and employing a prevalent, two pass casino shuffle, I dealt four handed rounds looking for cases which fulfilled the scenario described above so that I could check and record the dealer's hole card. The data came so slowly (a "test" situation arose only once every 10 or 12 rounds) that I decided to speed things up by merely checking the value of the card between any two 10's that had just one card in between them.

I'm assuming that the proper "random" frequency of a "sandwiched" 10 there ought to be 30.3%, the same as if it were the dealer's hole card that was being checked.

Quickly verifying that 66% was a totally unrealistic claim, I suspended the fun after a sample size of 300 cases. The sandwiched card was in fact Ten 100 times, with a non-ten being there the other 200 times. This result was 1.1 standard deviations to the right of purely random -- not significant. But my question to all is, did I overlook anything in substituting any two "one space" 10's for the original more specific scenario??????

[Norm Wattenberger]

The 'expensive piece of blackjack literature' is a well known fraud. To think that anything can be determined from an unknown shuffle is nutty.

BJStats

[humble]

As I understand it, you will have observed some 30 or so instances of the original test situation in your little experiment. Did you indeed find in about 20 of these 30 cases that the holecard was a 10 (now there's variance for you), and is that why you ask your question?

Regards,
h

[Fred Renzey]

> As I understand it, you will have observed
> some 30 or so instances of the original test
> situation in your little experiment. Did you
> indeed find in about 20 of these 30 cases
> that the holecard was a 10 (now there's
> variance for you), and is that why you ask
> your question?

> Regards,
> h

Reply: No, I don't really know what percentage of the originally qualified test cases revealed a 10 in the dealer's hole. I only know that all 300 test cases, most of them the modified hybrid produced 33% Tens. My concern was whether I could have corrupted the test by admitting other evidence that should seem to produce the same results.