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Repost: Bryce Carlson's Strategy Variation Study (long...)  Author:   Bryce Carlson <brycarlson@earthlink.net> Date:   1995/12/22 Forum:   rec.gambling.blackjack

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Several readers of r.g.b. have asked me to repost my
recent in-depth simulation study on strategy variation.

So, for those and others interested, here it is:   


                              WORK VS. REWARD
                             How Much is Too Much?


Several years ago, Don Schlesinger determined the 18 most
important plays in any valid card-counting based Blackjack
strategy.

These top 18 plays are as follows (not in order of importance):
Insurance, 16 vs 9, 16 vs 10, 15 vs 10, 13 vs 2, 13 vs 3, 12 vs 2,
12 vs 3, 12 vs 4, 12 vs 5, 12 vs 6, 11 vs A, 10 vs 10, 10 vs A, 9
vs 2, 9 vs 7, 10-10 vs 5, and 10-10 vs 6.

In Blackjack for Blood I state that with the usual bet-spread
schemes, Don's top 18 plays will get over 75% of the total
available gain from strategy variation based on the true count.

Considering that complete playing strategies are comprised of
upwards of 150, or so, variable playing decisions, the fact that
the indices for just these 18 plays will get over 75% of the total
available gain above Basic Strategy is remarkable.

Don has made a real, and very practical, contribution with the
determination of these "illustrious" 18 plays.

The question, however, is whether or not it is worthwhile to learn
a larger subset, or perhaps even all, of a sophisticated playing
strategy, such as my own Advanced Omega II Strategy.

Although I'll leave that determination up to each of you, the
computer study, below, should give you the necessary
information to make an informed decision based on the amount
of work you want to do and the rules and customs of the
Blackjack games in which you play.

Here is the methodology of the study: Using the Omega II
Blackjack Casino v1.2, I ran a series of computer simuations.
Each simulation consisted of 500,000,000 rounds. Given this
large sample size, and even taking bet spreads into account, the
percent standard deviation is only about .01% in each
simulation.

There were three sets of simulations. Set one was for single
deck; set two was for double deck, and set three was for six
decks.

In the single- and double-deck simulations Las Vegas Strip rules
were used (s17, doa, resplits to 4 hands, no das). For the six-
deck simulations the rules were the same except that das was
allowed.

The game was dealt head-up (only one player); penetration was
about 66% for single deck (6 rounds), about 75% for double
deck (14 rounds), and about 85% for six decks (46 rounds).

Betting was by the true count (based on 52 cards), and was
done as follows:

For the single-deck simulations, the bet was always 1 unit at true
counts < or = to +1, 2 units at +2, 3 units at +3, and 4 units at
+4, or higher.

For the double-deck simulations, the bet was always 1 unit at
true counts < or = to +2, 2 units at +3, 4 units at +4, and 8 units
are +5, or higher.

For the six-deck simulations, the bet was always 1 unit at true
counts < or = to +2, 4 units at +3, 8 units at +4, and 16 units at
+5, or higher.

Even though this study is designed to measure the gain from
strategy variation, a realistic bet spread is important so as not to
exaggerate the relative gain from strategy variation.

The count used was always the Omega II Count (2 =+1, 3=+1,
4=+2, 5=+2, 6=+2, 7=+1, 8=0, 9= -1, T= -2, Ace=0).  A side
count of Aces was kept and used for betting purposes, only.

All variable playing indices were those of the Advanced Omega
II Strategy (optimized for number of decks and rules), as
published in Blackjack for Blood. All fixed playing indices
were those of Basic Strategy (optimized for number of decks
and rules).

Each of the three study sets (1dk, 2dks, 6dks) were comprised
of five 500,000,000 round simulations, consisting of: 1) Basic
Strategy, no insurance. 2) Basic Strategy, with insurance. 3)
Don's Top 18 plays. 4) 68 indices of the Advanced Omega II
Strategy (insurance, hard stand/draw, hard doubling 9-10-11,
splitting 10-10 vs 5, 6). 5) The complete Advanced Omega II
Strategy.