Wizard Of Odds Baccarat Game

admin  4/1/2022
  • Appendices
  • Baccarat Analysis
  • Miscellaneous

Introduction

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 image--leftolumn.

Number

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Card
Removed
Banker WinPlayer WinTie Win
122592662028147202198201626637560468838163231312
222593903474394802198279181695870468636463548240
322594153369551302198240411263230468650244465232
422595656395608302198132965463160468607387659600
522590565407134702198626760121850468622691848272
622592306298549702198942636434940468132726393680
722592886254717402198847351781120468170015430736
822588808772148402198299582316670469125533152080
922590132111123202198292198535290469000583035984
1022590946490869702198163195365880469048148230736

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.

Probability

Card
Removed
Banker WinPlayer WinTie Win
10.4586130.4462170.09517
20.4586380.4462330.095129
30.4586430.4462250.095132
40.4586730.4462030.095123
50.458570.4463030.095127
60.4586050.4463670.095027
70.4586170.4463480.095035
80.4585340.4462370.095229
90.4585610.4462350.095203
100.4585780.4462090.095213

The next table shows the house edge of each bet by card removed.

House Edge

Card
Removed
BankerPlayerTie
10.0105350.0123960.143467
20.0105270.0124050.143836
30.0105140.0124180.14381
40.0104630.012470.143889
50.0106620.0122670.143861
60.0106920.0122380.144756
70.0106620.0122690.144688
80.0106290.0122980.142942
90.0106020.0123260.14317
100.010560.0123690.143083

The next table shows the effect on the house edge of each bet according to the card removed. A negative number indicates removal is bad for the player, positive indicates removal is good.

House Edge

Card
Removed
BankerPlayerTie
00.000019-0.0000180.000513
10.000044-0.0000450.000129
20.000052-0.000054-0.000239
30.000065-0.000067-0.000214
40.000116-0.000120-0.000292
5-0.0000830.000084-0.000264
6-0.0001130.000113-0.001160
7-0.0000830.000082-0.001091
8-0.000050.0000530.000654
9-0.0000230.0000250.000426

The next table multiplies the above numbers by ten million.

Count Adjustment

Card
Removed
BankerPlayerTie
0188-1785129
1440-4481293
2522-543-2392
3649-672-2141
41157-1195-2924
5-827841-2644
6-11321128-11595
7-827817-10914
8-5025336543
9-2312494260
Average000
How do you play baccarat

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 opposite 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 image--leftolumn indicates the ratio of cards dealt before the cards are shuffled.

Positive Expectation

PenetrationBankerPlayerTie
90 percent0.0001310.0000240.000002
95 percent0.0010620.0003810.000092
98 percent0.0058760.0037000.002106

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.

Expected Profit

PenetrationBankerPlayerTie
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.

For your further consideration I would recommend this baccarat odds calculator. You can put in any deck composition and it will give the house edge on all three bets.

Go back to baccarat
Go to baccarat appendix 1
Go to baccarat appendix 3
Go to baccarat appendix 4
Go to baccarat appendix 5
Go to baccarat appendix 6
Go to baccarat appendix 7


Written by: Michael Shackleford

On This Page

Introduction

7 Up Baccarat is a baccarat variant offered at the Marina Bay Sands casino in Singapore. The rules and play of the game are mostly the same as conventional baccarat, except the Player hand always starts with a seven as the first card. This affects the probabilities, so the pays are different as well.

Rules

The rules are the same as conventional baccarat, except as noted. To avoid confusion, I capitalize Player and Banker when referring to the bets. When referring to the person playing the game, I use player in lower case.

  1. Six decks are used, with a continuous shuffler.
  2. The first card to the Player is always a seven. This is indicated with a seven printed on the felt.
  3. The Player receives one card to make his hand along with the seven, and the Banker receives two cards.
  4. Drawing rules are exactly the same as in conventional baccarat.
  5. Wins on the Player bet pay even money, except a Player win of 7 pays 1 to 2. Ties are still a push, and Banker bets result in a loss.
  6. Wins on the Banker bet pay even money, except a Banker win of 7 pays 9 to 5. Ties are still a push, and Player wins result in a loss.
  7. Tie bets pay 7 to 1, except a 7-point tie pays 9 to 1.
  8. There is also a side bet titled 'Super Sevens,' which pays according to the number of sevens between the Player and Banker hands, including the Player's first seven. The wins are indicated separately below.

Odds

All analysis in this report is based on six decks of cards.

The following table shows all the possible outcomes of the Player bet. The lower right cell reflects a house edge of 2.60%.

Player Bet

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EventPaysPermutationsProbabilityReturn
Player win (other than 7)1818,970,471,3600.2860770.286077
Player win on 70.5561,338,904,3840.1960830.098041
Tie0308,245,281,9840.1076740.000000
Loss-11,174,211,488,5120.410167-0.410167
Total2,862,766,146,2401.000000-0.026049

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The following table shows all the possible outcomes of the Banker bet. The lower right cell reflects a house edge of 2.56%.

Banker Bet

EventPaysPermutationsProbabilityReturn
Banker win on 71.8166,043,860,9920.0580010.104402
Banker win (other than 7)11,008,167,627,5200.3521660.352166
Tie0308,245,281,9840.1076740.000000
Loss-11,380,309,375,7440.482159-0.482159
Total2,862,766,146,2401.000000-0.025592

The following table shows all the possible outcomes of the Tie bet. The lower right cell reflects a house edge of 4.05%.

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Tie Bet

EventPaysPermutationsProbabilityReturn
Tie on 79140,427,142,2720.0490530.441477
Tie on any other total7167,818,139,7120.0586210.410347
Banker or Player win-12,554,520,864,2560.892326-0.892326
Total2,862,766,146,2401.000000-0.040503

The following table shows all the possible outcomes of the Super Sevens bet. Remember, this includes the given Player seven, so there will always be at least one. The lower right cell reflects a house edge of 8.86%.

Super Sevens Bet

SevensPaysPermutationsProbabilityReturn
67005,100,4800.0000020.001247
570208,099,5840.0000730.005088
4175,689,804,0320.0019880.033788
3581,285,488,6400.0283940.141970
22666,866,329,3440.2329450.465889
1-12,108,711,324,1600.736599-0.736599
Total2,862,766,146,2401.000000-0.088616
Odds

Strategy

My general advice to baccarat players is if you like the Player and Banker bets, the odds are better in conventional baccarat. However, if you like the long odds on the side bets, 7 Up Baccarat is a better value. If you don't have the choice, and must play 7 Up, then the Banker is the best bet, at a house edge of 2.56%.

Wizards

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Comparison to Baccarat

Bet7 Up
Baccarat
Conventional
Baccarat
Player2.60%1.24%
Banker2.56%1.06%
Tie4.05%14.38%
Super Sevens8.86%
Player/Banker Pair11.25%

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Written by:Michael Shackleford