MATHEMATICS OF BACCARAT

(Source: http://www.baccarat-instructions.com/baccarat-strategies/)

MATHEMATICS OF BACCARAT
The mathematics of baccarat strategies are also relatively easy to
understand. First, we must remember that $100 bet on the player hand
will yield $100 when it wins, but the same bet on a winning banker
hand yields only $95 because of the 5% commission. Now, let's consider
the effect of the fixed drawing and standing rules. Using a formula
from Allan N. Wilson's The Casino Gambler's Guide, we find that in the
long run the hands will break down like this:
Banker hand wins 45.84% of all hands 50.68% disregarding ties
Player hand wins 44.61% of all hands 49.32% disregarding ties
Neither hand wins
(a tie) 9.55% of all hands_______
100. % 100. %
44.61% of the time, bet on the banker hand will lose $100 or $44.61
45.84% of the time, $100 bet on the banker hand will win $95 or $43.55
9.55% of the time, bet on the banker hand will tie. ——
Casino advantage, banker hand: 1.06
45.84% of the time, $100 bet on the player hand will lose $100 or $45.84
44.61% of the time, $100 bet on the player hand will win $100 or $44.61
9.55% of the time, $100 bet on the player hand will tie ———-
Casino advantage, player hand: 1.23
There is only one other bet available on the Baccarat Strategies
layout, a wager that both hands will tie, paying 8 to 1. Knowing that
this will occur 9.55% of the time, let's see how good a proposition
this is:
90.45% of the time, bet on a tie will lose $100 or $90.45
9.55 of the time, $100 bet on a tie will win $800 or $76.40
Casino advantage, tie-hand bet: 14.05 From this we can see that if we
would like to lose our money ten times as fast in baccarat, the best
way to accomplish our goal would be to continually wager on a tie.
At one time, Las Vegas baccarat layouts provided for betting on a
natural 8 or 9, paying 9 to 1, and yielding the casino about 5%.
However, Edward O. Thorp, who published the first card-counting system
for blackjack, developed a baccarat card-counting strategy, enabling a
player to determine when the chance of a natural's being dealt from
the remaining decks increased. Based on the fact that a surplus of
8′s, 9′s, and 10-count cards would produce more naturals, the system
was described in Life magazine in 1964, and shortly after, all casinos
eliminated this option. Since then, no one has been able to devise a
card-counting strategy that would significantly alter the house edge
in baccarat.
If you would like to play a relaxed yet exciting, sophisticated casino
game without bothering to learn complicated rules or strategies,
baccarat may be the game for you. There are really only two places to
bet; the croupiers dictate the play of the cards, and your only major
decision is how much to wager. Unless you are foolish enough to bet on
a tie, there are no mistakes that can be made: more than any other
casino table game, Baccarat Strategies depends simply on pure luck.
Just remember the words of John Milton Hay, Teddy Roosevelt's
Secretary of State: "True luck consists not in holding the best cards
at the table. Luckiest is he who knows just when to rise and go home."
THE STREAK
Mr. K. is a high roller. There is no doubt about it. I got to know him
when he called me about participating in my Blackjack Clinic. He told
me that he had dropped $25,000 playing baccarat and he wanted to find
a way to win it back. I told him that I could teach him how to win at
blackjack, but that I couldn't guarantee how much he'd win.
Mr. K. took the Blackjack Clinic and became an excellent card counter
and a disciplined blackjack player. Or so I thought. It turns out that
he did win back his $25,000, although it wasn't just because of the
1.5% long-run advantage that I taught him how to achieve at blackjack.
He had a series of very lucky sessions where all the cards were going
his way. I told Mr. K. not to count on the same heavy winnings in
every session and, sure enough, his luck turned; he dropped about
$10,000. At that point he regressed to baccarat. He got lucky again
and won back his $10,000 and then began alternating his play between
blackjack and baccarat. Although he still plays an excellent game of
blackjack, Mr. K. is a gambler—he possesses the gambler's urgency to
play for high stakes. He seeks, as all true gamblers do, an
"adrenaline high."
Recently Mr. K. invited me down to observe his play at the baccarat
strategies tables. Agreeing to meet in front of the baccarat pit prior
to starting play, I arrived at the appointed time, only to find Mr. K.
already in the game, looking very distressed. He had arrived two days
earlier and was down about $10,000. Mr. K. expressed the usual
gambler's lament about not quitting when he was ahead; at one point he
had been up $5,000.
I sat down to play alongside Mr. K. Down to his last $500, he had used
up his $4,000 credit line, so there was nothing he could do if he
dropped that last $500. I watched it dwindle down to $50 and then
talked him into having lunch.
During lunch I attempted to talk Mr. K. into going home, licking his
wounds, and returning another day to play blackjack, where he could
enjoy a 1.5% positive advantage instead of the negative one-plus
percent at baccarat, but to no avail. In fact, he talked me into
cashing a check for him for $1,000. I agreed on the condition that we
would play blackjack. O.K. But we couldn't find a seat! Not even at a
$25 table.
Mr. K. suggested baccarat. I reluctantly acquiesced. One table was
full and one table was empty. Mr. K. chose the empty table with the
exclamation, "Let it [the recoup or the wipeout] happen fast!"
Now, Mr. K. is a streak bettor, looking for a long series of wins in a
row on either the bank or the players. He bets whatever has come up
last until it loses: For example, if the bank wins, he keeps betting
the bank until the play-ers win. Then he jumps to the players until
the bank wins, etc.
Well, it was Mr. K's lucky day, because we caught a shoe with a lot of
streaks, starting with 16 straight wins for the players. Mr. K's
betting progressed from $40 to $500. As I was willing to risk only
$100, my betting progressed from $20 to $200 in a conservative
progression as follows: 20-20-40-40-60-60-80-100-120-140-160-180-200.
This is one of the most amazing streaks I have ever seen in my
twenty-two years of playing casino games. The odds of getting a group
of sixteen wins in a row are about 65,000 to one. During the streak,
there were certain things prescribed by Mr. K. to keep it going: the
player's cards were turned over by the same person each time; the
banker's cards were always tapped against Mr. K.'s chips; the only
conversation allowed was in conjunction with the bet size; and
counting chips won was prohibited. But this streak was not the last
good thing to come out of this fantastic shoe; three or four other
streaks of five or six wins occurred, and at the end of the shoe, Mr.
K. had recouped his $10,000 and had won another $1,000 to boot. I had
multiplied my $100 by sixteen. Our play had begun at 3:00 P.M., and at
4:03 P.M. we were cashing in at the cashier's cage.
There is no moral to this story, but I will give you some advice on
baccarat. If you're feeling lucky, set aside part of your casino
bankroll for a fling at the baccarat tables— maybe you'll catch a
streak.

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