Virtually any credible book on the subject of beating the game of Casino Blackjack revolves their presented [playing] strategies around the dealer break-ratio; whether or not the author comes right out and says so. This is of course the problem with most "pure" progression systems, they are essentially ignorant of the current dealer break-ratio.

Why do we double down? We do so to either draw a stronger total than the dealer (more difficult to do these days) or (and this is more likely), because we are looking for the dealer to break and we want to increase our bet in anticipation of that breaking. In some cases, we split pairs for pretty much the same reason.

Statistics can often be
mis-leading. This was of course the central theme in the classic book __How
to Lie with Statistics__.
Unfortunately, MUCH of the information regarding playing-off the
dealer break-ratio is either mis-leading, or flat out WRONG. We can
break these inaccuracies into to TWO major categories: 1) An
incorrect understanding (or use) of statistical methods that allow us
to decipher the dealer break ratio; 2) Ignorance of the non-random
nature of most multi-deck games.

If you are a frequent visitor
to the **Boris on Blackjack**
Website on the Internet, you are familiar with the latter aspect. I
will have more to say on this aspect of the game in a future article
on this subject, to be entitled: __Minding
and Mining the Mode: Capitalizing on Dealer-breaking__.
However, to my knowledge, no one has written about the first item
mentioned above. I want to spend a considerable amount of time with
the first item. You may be surprised at what you learn.

In most books on Blackjack of any depth, you will read that on average the dealer breaks approximately 28.3% (28.23, but who's counting - heheheh). The Hit/Stand/Double/Split decisions of Basic Strategy are based on this GOSPEL; a Gospel, as it turns out, that is based on flawed computer simulations. While this Gospel contains many truths, there are situations where it simply doesn't apply to our play today; i.e. play in the real-world casino.

For starters, realize that the 28.3% number is based on computer simulations utilizing a million or more rounds of play. In the real world where you and I play, we will never SEE a million rounds of Blackjack. LARGE casino environments (like the MGM Grand in Las Vegas, Caesars in either Atlantic City or Vegas, Foxwoods or Trump Taj Mahal) will probably "see" a million rounds of Blackjack play in a months time; assuming an average of 50+ open Blackjack tables open continuously throughout the day.

Throughout your entire Blackjack play, and even MORE SO on any given play trip you make, you will encounter just a small-fraction of hands. I call this the short haul. Ironically, Basic Strategy and Card-counting (and yes, even my Basic Strategy II) base their approach on playing towards the long haul, ignoring the fact that if you continuously mis-play the short-haul, you will never MAKE it to the long haul. One of the major differences between clump-card play and card-counting, is that counting plays to the long haul and clump playing focuses on the short haul.

Because most
"experts" recommend that we play to the **Mean**,
we blindly follow their recommendations. Allow me to demonstrate to
you how flawed this advice can really be. To do this, I recorded the
break-ratio for 24 shoes of Boris
Simulation play at the Trump Taj Mahal in Atlantic City. At
approximately 6 shoes per hour, this represents about 4 hours of
play; the amount of time a typical tourist player will sit at the
table to drink and play.

Hour # |
Shoe #1 |
Shoe #2 |
Shoe #3 |
Shoe #4 |
Shoe #5 |
Shoe #6 |

1 |
18% |
25% |
28% |
50% |
40% |
30% |

2 |
18% |
18% |
25% |
20% |
18% |
50% |

3 |
30% |
18% |
25% |
18% |
33% |
18% |

4 |
30% |
30% |
18% |
30% |
40% |
50% |

MEDIAN: 34% MODE: 18% MEAN: 28.3% STD-Dev.: 10.55%

The above data provides us
with an interesting study. Notice that while the FIRST hour opened as
dealer-favorable, as the game marched on, the dealer break-ratio
increased CONSIDERABLY; especially in the 4th and 5th shoe. The
second and third hours were all but a DISASTER for the players.
Except for the shoes bridging Hours 2 & 3, and one shoe near the
end of hour 3, this table made a considerable amount of money for the
house. Finally, for the players who were strong enough (or maybe
stupid enough?) to survive to the fourth hour, the table once again
turned around.

Based SOLELY on the mean, we
would NEVER be able to deduce these fluctuations. Even examining the
MEDIAN is mis-leading. The Median, combined with the Mean suggests
that this table has been player favorable throughout, when in fact,
the MAJORITY of the time, the dealer has been cleaning up.

If you evaluate the game on
the basis of the Mode, you will see a different profile of this
table. From the profile of this table it becomes CLEAR that this
Blackjack table is dealer favorable; and, barring any major
disruptions (change in player number, shuffle alterations, new cards,
etc.), will continue to be so. To understand why this is so, let's
review some statistical fundamentals; like the definition of
important terms.

**Mean:**
This is what is also known as the average. This average is computed
by summing all the values in a list and then dividing that sum by the
total of ENTRIES in the list. So, extremely low values and extremely
high values tend to cancel each other out. If you could manage to
play to the long haul, this will more-or-less happen for you too.
Unfortunately, most of us never reach the long haul. I will have more
to say about this later.

**Median:**
The median is essentially the CENTER-POINT in a group of numbers.
Like the mean, this can be VERY misleading to us. While it is
normally not very useful to track the Median, it appears on Boris'
Table-Statistics screen in case some statistics-genius wishes to put
the information to use.

**Mode:**
When you play to the short haul, the MODE is arguably more important
information than the Median and the Mean, COMBINED. The Mode is the
value in a list which occurs most often. From the table above, the
top 4 frequent values in the list are: 18, 30,25 & 40. Yet, even
THIS can be misleading when we look at the data itself:

Break-Ratio |
18% |
30% |
50% |
25% |

Occurances |
8 |
5 |
3 |
3 |

Even in the top 4 values, the low break-ratios outnumber the high break-ratios by a factor of 11 to 8. Comparing the number of shoes with a break-ratio of under 28% to those with a break-ratio of 28% and above, we find them split evenly. Again, that does not tell us the whole story. However, the Table Hold% DOES give us quite a picture, being that it showcased a 16.6% profit for the house, at this one table, containing a mix of Typical-Tourists and Basic Strategy Players.

As the debate over random
.vs. non-random cards enters into its 5th year, what amazes me the
most is that the critics of clump-card playing are virtually
unwilling to spend time in a dozen casinos monitoring the ACTUAL
Dealer break-ratio in real-world play. We can theorize about why this
is so, but my most educated guess is that these people are afraid to
see how LOW the break-ratio REALLY IS in the real world.

In hand-shuffled single and
double deck games, the break-ratio Mode is considerably closer to the
mean than we find it in the multi-deck shoes games. In this
comparison I exclude the ShuffleMaster shuffled games because the
shuffles produced by these machines do not fit the definitions of
randomness as we use them in the evaluation of today's games.

Playing methods like Target,
Universal Confirmation Procedure (UCP), and even the old B.I.A.S.
system give considerable attention to monitoring the dealer
break-ratio. Ellis Davis' World Class Blackjack (WCB) has devised a
complete approach to tracking and responding to dealer-breaking.
There must be a reason for all this effort.

The bottom line is that if
the dealer is not breaking, then s/he is making their hand. It is
well known that in non-random [shuffle] games (most of today's shoe
games), the dealer's ending total has risen from under 19 to over 19.

This means that in games
where the dealer is not breaking the players are having an even
greater difficulty overcoming the dealer advantage.

If you look into it, you will
notice that the above-mentioned playing methods all spend their time
essentially examining the MODE with regarding to dealer-breaking.
This is because the MODE and the short-haul are often closely allied.
This should tell you something.

I don't care WHAT kind of
method you use, if the dealer is not breaking, unless you are
consistently winning (which is rare in non dealer-break games), you
should get out of those games and in the future avoid playing them to
begin with. You may think you have a HOT playing strategy, however
unless the dealer is breaking at or greater than the 28.3% minimum,
overall you will be wasting your time. In that case, you have nothing
but your carelessness to

blame for your losses.

If you would like more
information on this subject..........

The next installment in this
series on dealer-break analysis will look at how the shuffles and
washes in use with most multi-deck games affect the dealer
break-ratio. The casinos no longer need to cheat; nor are smoke and
mirrors necessary. All that is necessary is to carefully construct
and control the card washing and shuffling procedures. The rest will
be done by the players themselves. Stay tuned - the best is yet to come.

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