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 |
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.
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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