Rob McGarvey
Well-Known Member
One of the previous versions of Eric's program was featured in my newletter found at:
http://groups.yahoo.com/group/blackjack_pro_newsletter/
Posted By: Eric Farmer <[email protected]>
@ http://www.bjmath.com (Archive copy)
Date: Monday, 30 December 2002, at 1:48 p.m.
(Dead link: http://mywebpages.comcast.net/erfarmer201/)
Hello all,
Having recently stumbled on some extra free time, I have been working
on a substantial revision of my combinatorial analyzer, primarily to
improve my pair-splitting algorithm. For those not familiar with
previous versions, my original design goal was to compute exact
probabilities and expected values as efficiently as possible, but
with an interface that allowed users to do their own analysis of a
wide range of situations, including arbitrary distributions of cards
in the shoe, most of the common rule variations, different playing
strategies such as total-dependent vs. composition-dependent basic
strategy, "mimic the dealer," etc., and card-counting systems (from
evaluation of existing systems to regression-fitting your own).
One aspect of my resulting design which I consistently ignored was
the inaccuracy of my pair-splitting algorithm. The latest version 5.0
(for which the associated game and basic strategy calculator have
been rebuilt) contains two significant changes:
1. The interface for resplitting rules is more general, allowing
specification of a maximum number of split hands for each individual
pair, including no splits at all. (Not sure how useful this really
is, except for not resplitting aces, but it was easy to do.)
2. The pair splitting algorithm has been improved, at a cost of some
increased memory and computation time; in particular, expected values
are exact when no resplits are allowed, assuming that playing
strategy is the same for both halves of the split.
I am posting here for a couple of reasons. First, check out the
software (source code and Windows executables included) at
(Dead link: http://mywebpages.comcast.net/erfarmer201/blackjack/) if you're
interested, and let me know if you find it useful; that's why I enjoy
writing programs like these. I will copy Mr. Reid as well if he would
like to post the software on bjmath.com.
Second, I have done a lot of testing of the new version myself (*),
including scouring posts here and on usenet for (mostly anecdotal)
exact results from Mr. Jacobs, Cacarulo, etc., with which to confirm
my calculations. Any additional input is appreciated. For my own
additional checking, are there expected value tables similar to those
generated by Cacarulo with no resplits allowed (RSP=2, if I read the
notation correctly)?
Let me know what you think,
Eric Farmer
(*) As an interesting "sanity check" of my new algorithm, recall the
discussion some time ago about Thorp's result on basic strategy EV
and its independence of number of hands dealt or of strategies of
other players at the table (see the above web site for a perspective
on this as a simple and neat generalization of the true count
theorem).
We may compute the overall expected value for a hand with an ace
removed from the shoe; repeat with a 2 removed, etc. Average these
expected values, weighted by the probability of each removal.
The "extended" true count theorem states that this average should
equal the expected value for the full shoe (note that this does not
follow from the true count theorem).
With no resplits allowed, the overall expected value is exact, and
equality holds. As before, however, my algorithm for resplitting is a
(better) approximation which is not of the appropriate form (namely,
an expected value of a function of a shoe arrangement, averaged over
all possible arrangements), and so the average is not equal to
the "full shoe" value. (It's closer than it used to be, though, only
differing in the sixth decimal place in my test case.)
(Dead link: http://mywebpages.comcast.net/erfarmer201/)
http://groups.yahoo.com/group/blackjack_pro_newsletter/
Posted By: Eric Farmer <[email protected]>
@ http://www.bjmath.com (Archive copy)
Date: Monday, 30 December 2002, at 1:48 p.m.
(Dead link: http://mywebpages.comcast.net/erfarmer201/)
Hello all,
Having recently stumbled on some extra free time, I have been working
on a substantial revision of my combinatorial analyzer, primarily to
improve my pair-splitting algorithm. For those not familiar with
previous versions, my original design goal was to compute exact
probabilities and expected values as efficiently as possible, but
with an interface that allowed users to do their own analysis of a
wide range of situations, including arbitrary distributions of cards
in the shoe, most of the common rule variations, different playing
strategies such as total-dependent vs. composition-dependent basic
strategy, "mimic the dealer," etc., and card-counting systems (from
evaluation of existing systems to regression-fitting your own).
One aspect of my resulting design which I consistently ignored was
the inaccuracy of my pair-splitting algorithm. The latest version 5.0
(for which the associated game and basic strategy calculator have
been rebuilt) contains two significant changes:
1. The interface for resplitting rules is more general, allowing
specification of a maximum number of split hands for each individual
pair, including no splits at all. (Not sure how useful this really
is, except for not resplitting aces, but it was easy to do.)
2. The pair splitting algorithm has been improved, at a cost of some
increased memory and computation time; in particular, expected values
are exact when no resplits are allowed, assuming that playing
strategy is the same for both halves of the split.
I am posting here for a couple of reasons. First, check out the
software (source code and Windows executables included) at
(Dead link: http://mywebpages.comcast.net/erfarmer201/blackjack/) if you're
interested, and let me know if you find it useful; that's why I enjoy
writing programs like these. I will copy Mr. Reid as well if he would
like to post the software on bjmath.com.
Second, I have done a lot of testing of the new version myself (*),
including scouring posts here and on usenet for (mostly anecdotal)
exact results from Mr. Jacobs, Cacarulo, etc., with which to confirm
my calculations. Any additional input is appreciated. For my own
additional checking, are there expected value tables similar to those
generated by Cacarulo with no resplits allowed (RSP=2, if I read the
notation correctly)?
Let me know what you think,
Eric Farmer
(*) As an interesting "sanity check" of my new algorithm, recall the
discussion some time ago about Thorp's result on basic strategy EV
and its independence of number of hands dealt or of strategies of
other players at the table (see the above web site for a perspective
on this as a simple and neat generalization of the true count
theorem).
We may compute the overall expected value for a hand with an ace
removed from the shoe; repeat with a 2 removed, etc. Average these
expected values, weighted by the probability of each removal.
The "extended" true count theorem states that this average should
equal the expected value for the full shoe (note that this does not
follow from the true count theorem).
With no resplits allowed, the overall expected value is exact, and
equality holds. As before, however, my algorithm for resplitting is a
(better) approximation which is not of the appropriate form (namely,
an expected value of a function of a shoe arrangement, averaged over
all possible arrangements), and so the average is not equal to
the "full shoe" value. (It's closer than it used to be, though, only
differing in the sixth decimal place in my test case.)
(Dead link: http://mywebpages.comcast.net/erfarmer201/)
