Blackjack remains unique in that it is
the only game in which the cards can be considered to
have a form of “memory”. A player must remember
that one-third of each card deck used will always consist
of 10-value cards. Essential in the formation of Blackjacks,
it is these most abundant of cards that offer the greatest
value to a player.
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Because there are three times as many of these 10-value
cards in a deck, the odds that one will appear in favour
of any other card are much greater. It is through astute
analysis of which cards have been played previously,
that a player makes the correct strategical decisions
based upon the information they have received.
Depending on which cards are left to be dealt, the
odds will be in one of three states: 1. They will be
neutral. 2. They will be with the dealer. 3. They will
be with the player.
It is here that Blackjack sets itself apart from other
luck based card games. It is only an experienced counter
however, that can tell with whom the advantage lies
before any given deal.
The object of counting systems is simple; to inform
the player of which cards are likely to appear in the
next hand thereby allowing them to raise or reduce their
bet accordingly.
A counter can tell when the deck is obviously skewed
i.e., when it is impossible that they will be dealt
certain cards. For example, if, through analysing the
deal, a player was to correctly observe that all four
Aces had already been dealt in a single deck game, then
they will know that the chances of these cards appearing
again is impossible. The chances of receiving a straight
Blackjack are, therefore zero.
In this unfortunate situation, the player cannot receive
any soft hands, nor can they hope to split Aces. The
player’s advantage exists because they have noted
this fact, and are therefore less inclined to place
a large bet on the coming hand. The player may even
choose to bow out of that hand altogether, (in a casino
environment the player should always check the rules
pertaining to mid-shoe entry. If mid-shoe entry is forbidden,
they should stick with the game and simply place a smaller
bet.)
On the other hand, if towards the end of a game, a
player observes that no Aces have been dealt, they should
be inclined to place larger bets due to the probability
of them being dealt in the near future. Obviously the
dealer also stands an equal chance of receiving a Blackjack.
If this turns out to be the case, it is unfortunate
for him that he receives only even money while the player
is paid off at 3 to 2.
If the first ten cards to come out of a shoe have a
10-value, despite a player being unable to predict with
complete accuracy the likelihood of the next card being
of a 10-value, they can assume that the odds are against
it. Similarly, if the first ten cards to appear are
of a low rank, then the odds are smaller that the next
card to appear will also be of a low rank. The moral
of the story is simply this: A player should bet more
when their chances of winning are higher and less (or
nothing at all) when they are not.
The fact that counting diminishes the randomness of
the remaining cards may prove justification for a player
to slightly abandon basic strategy in favour of a “modified
basic strategy.” Although these systems will be
touched upon presently, they will be explained in full
later.
Thorp's five count strategy
Edward Thorp, you may remember, was the
author of the computer program that allowed the composition
of the remaining deck to be carefully analysed as certain
cards were removed from play.
He proved that the removal from the deck of all the
5s in a single-deck game resulted in a 3.6% player advantage
over the dealer. In a single-deck game, he suggested
that in order for a player to range their bets more
accurately, they should take note of how many 5s remained
to be dealt.
After all 5s have been removed, Thorp suggests that
a player should adopt a modified basic strategy. Modifications
include: standing with 15 against a dealer’s 9
and 10, and standing with 12 against all dealer’s
stiff cards. He recommended that in addition, a player
should stand with three or more cards that total 16,
against a dealer’s 7 or 8.
Despite it’s effectiveness, critics of this system
have noted that it fails to account for too many possible
changes. Firstly, when no 5s are left, a player must
range their bets far more drastically in order to take
full advantage of the situation.
Secondly, this system tends to be far less effective
in shoe games, since the removal of such an insignificant
number of cards, affects the composition of the deck
to a far lesser extent.
In addition, Thorpe’s system provides the player
with little insight into the order in which the 10-value
cards will arrive.
Thorp’s ten count strategy
Thorp later discovered that adding four
10-value cards to a deck further increased a player’s
chance of winning their next hand by 1.89%. He proved
that the greater amount of 10-value cards in a deck
the greater their chance of winning.
The 10-count system tracks only two types of cards:
the 10-values (of which there are 16,) and the non-10-values
(of which there are 36.)
The neutral condition of an un-played deck is calculated
by dividing 36 by 16, and equals 2.25. Once this value
drops to 1.0 i.e., an equal number of 10s and non-10s,
the player’s advantage is increased to 9%. By
ranging bets in accord with this advantage, a player
can make potentially huge profits. This system has the
additional advantage of informing a player when to take
insurance (whenever the ratio drops to 2.0).
Like its predecessor, Thorp’s-10 count system
unfortunately has major disadvantages. Not only does
it fail to account for he importance of the Aces, the
10-count system is extremely difficult to memorise,
and should therefore be adopted only by players with
considerable mathematical ability.
Although a potential money-spinner in the few single
deck games on offer today, the inherent difficulties
of learning and memorising the 10-point system make
it accessible to few players. The speed at which Blackjack
is played exerts too great a pressure on a player’s
mathematical skills to make this system viable.
Thorp’s point count system
This system, first published in Thorp’s
second edition of beat the dealer, has subsequently
formed the basis for the vast majority of all other
systems. With the aid of Braun’s sophisticated
computer programs, Thorp calculated that the player’s
advantage was greatest when the lower ranking cards
(2,3,4,5 & 6) had been removed from the deck.
To illustrate Thorp’s point, let us take a hypothetical
extreme in which the deck consists only of Aces and
10-value cards. The following is a list of potential
hands that a player may receive in such a situation.
1. A 10 & 10 against a dealers Ace is a no-lose
hand for the player. If a player takes insurance and
the dealer has a Blackjack, the player would win only
even money. If the dealer does not have a Blackjack,
the splitting potential of this hand means the player
will win big.
2. When a player has a Blackjack against the dealers
Ace, a sure win would be guaranteed by settling for
even money. If the player wishes to hold out far a 3
to 2 payoff the least they can expect is a push.
3. By taking insurance when the player has two Aces
against the dealers Ace, the player is guaranteed to
at least break even.
4. When split and re-split, a players two 10s against
a dealers 10 represents a number of potential 21s for
the player (providing the dealer does not draw another
Ace). If the dealer draws a Blackjack the player would
only lose their original wager.
5. If both the player and the dealer have a natural
it will result in a push, thereby costing the player
nothing.
The wisdom of risking more money in a situation like
this is obvious. Also obvious is the extent to which
Aces and 10-value cards are vital to a player’s
success.
On account of both its innovativeness and simplicity,
Thorp’s system remains relevant, practical and
attractive even today. The application of this system
involves counting each card as seen and giving it either
a positive or negative count i.e., the low cards (2,3,4,5
& 6) each count as +1, and the high cards (10,J,Q,K
& Ace) count as –1. The 7,8 & 9 are considered
neutral.
By memorising a single number at a time the player
will always know whom the odds favour. A positive point
count represents odds in favour of the player while
a negative point count favours the house.
It is when the odds favour the player that they would
be wise to play more aggressively. When high cards remain
to be dealt, the player should stand, double and split
more than they would when playing in accordance with
normal basic strategy.
Source www.blackjack-student.co.uk
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