That's a very profound
statement, being that only 30% of all the cards are 10s. What on
earth could possess a 10 to find its way in between two more 10s
twice as often as the odds would dictate? This reader, and many
other gamblers say the cause is:
the drawing strategy
of the players combined with
imperfect shuffling by mere human dealers.
He explains that if you're dealt a 20, you won't take any cards
and those two 10s will go into the discard tray together. However,
if you're dealt a 4 and a 5, you will take a card, and if it's another
small one those small cards will go together into the discard tray
as well. Now if the dealer shuffles those discards less than perfectly,
he says there will still be clumps of high and low cards in the
newly shuffled pack.
At first blush it all
sounds reasonable, but let's ponder that concept for a minute. When
you're dealt a 20, I'll admit that two 10s go into the discard tray
back to back. When you hit a 5/4 and catch a 6, it's also true that
three low cards get stacked together.
But if you have a 10/5
then bust with a 10, a high/low/high formation goes into the discard
tray. And finally, if you have a 5/10 and hook a 4, a low/high/low
gets stacked together. So, let's see. That's a high/high, a low/low/low,
a high/low/high and a low/high/low. It seems like a pretty rounded
assortment of high and low cards to me.
This hazy concept could
be debated until we're all blue in the face. But nothing breaks
the deadlock like a little hard evidence. So I shuffled up my six-deck
shoe and dealt to four players plus the dealer for several hours.
I picked up the cards in the same sequence that they do in the casino
and used a standard, two pass casino shuffle.
I was looking for third
base's second card of his starting hand to be a 10, while the first
hit card of the first player to take a hit was also a 10. That would
leave the dealer's hole card in between those two 10s. According
to our reader and the blackjack manual that he referred to, the
dealer's hole card in this situation would be a ten 66% of the time.
But if the dealer's hole card was truly random, it would be a 10
only 30% of the time, since it could be any one of 94 other 10s
or 216 non-10s.
Well, the experiment
was going so slowly that I had to speed it up somehow. After I thought
about it, I realized that all we were trying to do was identify
any card that was flanked by a 10 on both sides. If clumping was
real, it wouldn't matter whether the card between two 10s was the
dealer's hole card -- or anybody else's card that happened to come
out between two 10s.
After testing 300 qualifying
cases, I'd seen enough. The card in the middle turned out to be
a 10 an even 100 times. That's 33% -- not the 66% that pro-clumpers
suggest, nor quite the 30% that total randomness would produce over
the long haul. For the mathematically inclined, the standard deviation
of this experiment is eight "tens in the middle". That
means there's roughly 1 chance in 700 that the next 300 tries will
produce more than 124 "tens in the middle". As for 200
tens in the middle out of 300 tries (66%) -- that's way off the
chart!
So then, what have we
learned? Are the card formations totally random, or merely "almost"
random? To be absolutely positive about it, I don't know. That would
take a much longer and more laborious experiment. But I'll tell
you this. For literally thousands of hours at the tables I've been
playing this game as though the cards are purely random, and things
haven't worked out too badly. How about you?
