Baccarat Appendix 2
In either blackjack or baccarat a good first step in developing a card counting strategy is to
determine the effect of removing any given card from the game. The following
table shows the number of banker, player, and tie wins resulting from the
removing of one card in an 8-deck shoe. The card removed is indicated in the
left column.
Card
Removed |
Number |
| Banker Win |
Player Win |
Tie Win |
| 0 |
2259094649086970 |
2198163195365880 |
469048148230736 |
| 1 |
2259266202814720 |
2198201626637560 |
468838163231312 |
| 2 |
2259390347439480 |
2198279181695870 |
468636463548240 |
| 3 |
2259415336955130 |
2198240411263230 |
468650244465232 |
| 4 |
2259565639560830 |
2198132965463160 |
468607387659600 |
| 5 |
2259056540713470 |
2198626760121850 |
468622691848272 |
| 6 |
2259230629854970 |
2198942636434940 |
468132726393680 |
| 7 |
2259288625471740 |
2198847351781120 |
468170015430736 |
| 8 |
2258880877214840 |
2198299582316670 |
469125533152080 |
| 9 |
2259013211112320 |
2198292198535290 |
469000583035984 |
| Average |
0 |
0 |
0 |
The next table puts these number is some perspective by indicating the
probability of a banker, player, and tie win according to the card removed.
Card
Removed |
Probability |
| Banker Win |
Player Win |
Tie Win |
| 0 |
45.8578% |
44.6209% |
9.5213% |
| 1 |
45.8613% |
44.6217% |
9.517% |
| 2 |
45.8638% |
44.6233% |
9.5129% |
| 3 |
45.8643% |
44.6225% |
9.5132% |
| 4 |
45.8673% |
44.6203% |
9.5123% |
| 5 |
45.857% |
44.6303% |
9.5127% |
| 6 |
45.8605% |
44.6367% |
9.5027% |
| 7 |
45.8617% |
44.6348% |
9.5035% |
| 8 |
45.8534% |
44.6237% |
9.5229% |
| 9 |
45.8561% |
44.6235% |
9.5203% |
| Average |
45.8594% |
44.6253% |
9.5154% |
The above table shows slight differences in the probabilities according to
the card removed. The next table shows the probability according to the given
card removed less the average probability, multiplied by ten million.
Card
Removed |
Point Value |
| Banker |
Player |
Tie |
| 0 |
188 |
-178 |
5129 |
| 1 |
440 |
-448 |
1293 |
| 2 |
522 |
-543 |
-2392 |
| 3 |
649 |
-672 |
-2141 |
| 4 |
1157 |
-1195 |
-2924 |
| 5 |
-827 |
841 |
-2644 |
| 6 |
-1132 |
1128 |
-11595 |
| 7 |
-827 |
817 |
-10914 |
| 8 |
-502 |
533 |
6543 |
| 9 |
-231 |
249 |
4260 |
| Average |
0 |
0 |
0 |
The table above shows the relative effect of removing one card according to
the future probability of a banker, player, and tie win. The greater the number
the more beneficial it is to remove that card. For example when betting on the
banker it is best when 4's leave the deck, and when betting on the player is
best when 6's leave the deck.
To adapt this information to a card counting strategy the player should start
with three running counts of zero. As each card is seen as it leaves the shoe
the player should add the point values of that card to each running count. For
example if the first card to be played is an 8 then the three running counts
would be: banker=-502, player=533, tie=6543. Of course the player does not have
to keep a running track of all three counts. In fact the point values for the
banker and player are nearly oposite of each other. A high running count for the
banker would mean a corresponding low count for the player, and vise versa.
In order for any given bet to become advantageous the player should divide
the running count by the ratio of cards left in the deck to get the true count.
A bet hits zero house edge at the following true counts:
- Banker: 105791
- Player: 123508
- Tie: 1435963
Assuming you were able to actually play this strategy perfectly you would
notice that the true counts seldom passed the point of zero house edge. The next
table shows the ratio of hands played, based on a sample of 100 million, in
which the true count passes the break even points above. The left column
indicates the ratio of cards dealt before the cards are shuffled.
| Penetration |
Positive Expectation |
| Banker |
Player |
Tie |
| 90 percent |
0.000131 |
0.000024 |
0.000002 |
| 95 percent |
0.001062 |
0.000381 |
0.000092 |
| 98 percent |
0.005876 |
0.003700 |
0.002106 |
The final table indicates the expected revenue per 100 bets and a $1000 wager
every time a positive expected value occured. Please remember that this table
assumes the player is able to keep a perfect count and the casino is not going
to mind the player only making a bet once every 475 hands of less.
| Penetration |
Expected Profit |
| Banker |
Player |
Tie |
| 90 percent |
$0.01 |
$0.00 |
$0.00 |
| 95 percent |
$0.20 |
$0.06 |
$0.15 |
| 98 percent |
$2.94 |
$1.77 |
$11.93 |
I hope this section shows that for all practical purposes baccarat is not
a countable game. For more information on a similar experiment I would
recomment The
Theory of Blackjack by Peter A. Griffin. Although the book is mainly devoted
to blackjack he has part of a chapter titled 'Can Baccarat Be Beaten?' on pages
216 to 223. Griffin concludes by saying that even in Atlantic City, with a more
liberal shuffle point than Las Vegas, the player betting $1000 in positive
expectation hands can expect to profit 70 cents an hour.
Go back to baccarat
Go to baccarat appendix 1
