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# The "10s Follow 10s" Theory

21 June 2003

A fellow who purchased my new Blackjack Bluebook II wrote me a letter. He wanted to know why the book didn't mention anything about "card clumping" and how to play such clumps. This fellow is nearly 80 years old and said he's been seeing the cards come out in clumps for decades. In fact, he quoted another blackjack manual which says the cards clump together so much that if third base's second card and first base's first "hit" card were both 10s, then the card in between them -- namely the dealer's hole card -- would also be a 10 two times out of three!

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:

1. the drawing strategy of the players combined with
2. 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?

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Fred Renzey
Fred Renzey is a high-stakes, expert poker player. On a daily basis he faces--and beats--some of the best players in the country in fierce poker room competition. Now for the first time, Renzey offers his perceptive insights on how to play winning poker. For Fred's 13-page blackjack booklet "Ace/10 Front Count", send \$9 to Fred Renzey, P.O. Box 598, Elk Grove Village, IL, 60009

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Fred Renzey
Fred Renzey is a high-stakes, expert poker player. On a daily basis he faces--and beats--some of the best players in the country in fierce poker room competition. Now for the first time, Renzey offers his perceptive insights on how to play winning poker. For Fred's 13-page blackjack booklet "Ace/10 Front Count", send \$9 to Fred Renzey, P.O. Box 598, Elk Grove Village, IL, 60009