One ongoing method to beat baccarat is to use the knowledge of the rank of exactly one card in the shoe to gain an edge on one hand per shoe (see this post). One card out of 416 may not seem like a lot, but to the "known-card" AP it's a pot of gold. Millions have been taken from the tables using this method. A known-card AP patiently counts down the shoe until the known card reaches the window where it is eligible to be dealt in the following round, that is, the card is one of the next six in the shoe. The AP then follows a fixed strategy that tells him which wager to make to take full advantage of this information.

It recently came to my attention that some APs are engaged in using known-carding against the Knockout baccarat collection of side bets. This post gives the various edges and strategies based on the rank of the specific known-card and its location in the six-card window. As will be evident, there is an abundance of situations when the AP can get a substantial edge.

Knockout Baccarat is a variant of baccarat that offers a collection of seven (7) separate baccarat side bets. These side bets are described as follows.

  • Winning total of 1, 2, 3, 4. This side bet wins if the winning hand (Player or Banker) has a total of 1, 2, 3 or 4. This side bet is a push if the result of the hand is a Tie. Otherwise this side bet loses. A winning hand pays 7-to-1.
  • Winning total of 5, 6. This side bet wins if the winning hand (Player or Banker) has a total of 5 or 6. This side bet is a push if the result of the hand is a Tie. Otherwise this side bet loses. A winning hand pays 3.5-to-1.
  • Winning total of 7. This side bet wins if the winning hand (Player or Banker) has a total of 7. This side bet is a push if the result of the hand is a Tie. Otherwise this side bet loses. A winning hand pays 4.5-to-1.
  • Winning total of 8. This side bet wins if the winning hand (Player or Banker) has a total of 8. This side bet is a push if the result of the hand is a Tie. Otherwise this side bet loses. A winning hand pays 3-to-1.
  • Winning total of 9. This side bet wins if the winning hand (Player or Banker) has a total of 9. This side bet is a push if the result of the hand is a Tie. Otherwise this side bet loses. A winning hand pays 2.5-to-1.
  • Player Natural. This side bet wins if the winning hand is a Player natural two-card 8 or 9. This side bet is a push if the result of the hand is a Tie (regardless of naturals). Otherwise this side bet loses. A winning hand pays 4-to-1.
  • Banker Natural. This side bet wins if the winning hand is a Banker natural 8 or 9. This side bet is a push if the result of the hand is a Tie (regardless of naturals). Otherwise this side bet loses. A winning hand pays 4-to-1.

The "Tie is a push" rule should be interpreted in its most literal sense. For example, if the player wagers on "winning total of 1, 2, 3, 4" and the hand ends in a 9-9 natural Tie, then the "winning total of 1, 2, 3, 4" wager is a push. In other words, the final total does not matter when the hand is a push. Similarly, if the player wagers on the Banker Natural side bet and the hand ends in a three-card 2-2 Tie, then the Banker Natural wager is a push. 

The following table summarizes the basic statistical information about these seven bets:

Knockout Baccarat Combinatorial Alalysis Summary
Winning Total Pays H/A STD DEV HIT FREQ
1,2,3,4 7 -0.067231 2.434338 10.4702%
5,6 3.5 -0.075277 1.724266 18.4348%
7 4.5 -0.033009 1.988763 15.8515%
8 3 -0.035976 1.625204 21.7217%
9 2.5 -0.064628 1.470031 24.0062%
P Natural 4 -0.091899 1.826263 16.2589%
B Natural 4 -0.091899 1.826263 16.2589%

The following table gives the edge the AP can get if he knows the first or third card to be dealt from the shoe, that is, one of the Player hand's first two cards. The cells marked with green give the situations when the AP has an edge over the house. In the best possible situation, the AP can get an edge of 79.706% over the house if he knows the first/third card is a Nine. In this case the AP bets on "Player Natural."

Knockout Baccarat Side Bet House Edge by Known First/Third Card (Player Card)
  Known First/Third (Player) Card
Side Bet A 2 3 4 5
Winning total of 1,2,3,4 3.874% 5.423% 5.928% 3.497% -7.548%
Winning total of 5,6 -4.018% -4.468% -5.301% -4.952% 0.157%
Winning total of 7 -5.264% -5.134% -5.071% -3.998% -4.072%
Winning total of 8 -6.625% -6.873% -6.524% -6.898% -5.832%
Winning total of 9 -10.031% -10.197% -10.089% -9.561% -9.556%
Player Natural -24.801% -24.679% -24.561% -25.134% -24.016%
Banker Natural -7.049% -6.970% -6.853% -6.330% -6.308%
  Known First/Third (Player) Card
Side Bet 6 7 8 9 T/J/Q/K
Winning total of 1,2,3,4 -27.152% -27.166% -28.133% -28.178% 3.014%
Winning total of 5,6 18.316% -26.209% -27.629% -27.183% -4.144%
Winning total of 7 -3.860% 50.571% -22.945% -22.824% -5.079%
Winning total of 8 -8.801% -8.751% 51.757% -23.455% -6.191%
Winning total of 9 -12.441% -12.486% -17.373% 48.038% -10.080%
Player Natural -23.147% -23.141% 69.630% 79.706% -24.831%
Banker Natural -5.438% -5.433% -17.844% -28.750% -7.123%

The following table gives the edge the AP can get if he knows the second or fourth card to be dealt from the shoe, that is, one of the Banker hand's first two cards. The cells marked with green give the situations when the player has an edge over the house. In the best possible situation, the AP can get an edge of 79.647% over the house if he knows the second/fourth card is a Nine. In this case the AP bets on "Banker Natural."
 
Knockout Baccarat Side Bet House Edge by Known Second/Fourth Card (Banker Card)
  Known Second/Fourth (Banker) Card
Side Bet A 2 3 4 5
Winning total of 1,2,3,4 3.669% 3.595% 5.852% 20.771% -25.270%
Winning total of 5,6 -6.397% -6.339% -7.051% -8.704% 18.521%
Winning total of 7 -4.085% -4.086% -4.441% -6.724% -7.350%
Winning total of 8 -5.769% -5.872% -5.865% -8.462% -8.305%
Winning total of 9 -9.560% -9.483% -9.690% -11.173% -11.951%
Player Natural -6.914% -6.964% -6.936% -6.669% -6.820%
Banker Natural -24.666% -24.672% -24.644% -25.473% -24.528%
  Known Second/Fourth (Banker) Card
Side Bet 6 7 8 9 T/J/Q/K
Winning total of 1,2,3,4 -25.091% -27.304% -28.111% -28.166% 3.164%
Winning total of 5,6 17.000% -25.681% -27.112% -26.687% -6.353%
Winning total of 7 -4.223% 50.350% -23.202% -23.078% -4.018%
Winning total of 8 -8.678% -8.846% 51.643% -23.570% -5.761%
Winning total of 9 -12.217% -12.625% -17.535% 47.895% -9.419%
Player Natural -5.525% -5.488% -17.903% -28.809% -6.860%
Banker Natural -23.233% -23.197% 69.570% 79.647% -24.568%

One important point to note from the previous two tables is that it doesn't matter which card the AP observes as the known-card. For any known-card in any of the first four positions, there is always a bet that gives the AP an edge. Moreover, if the AP knows one of the first four cards is a Seven, Eight or Nine, then he is going to thoroughly crush the house on that bet.

Knowing the fifth card to come out is an especially strong situation, regardless of the card in that position. The fifth card usually goes to the Player hand when it is played. Knowledge of this card gives good information about the final value of the Player hand when it draws. The following table summarizes these edges. Observe that when the AP knows the fifth card then there are always at least two side bets that give him the edge over the house. In fact, the AP can always get a double digit edge on at least one of the side bets:

 
Knockout Baccarat Side Bet House Edge by Known Fifth Card
  Known Fifth Card
Side Bet A 2 3 4 5
Winning total of 1,2,3,4 9.412% -18.481% -38.212% -54.982% -68.234%
Winning total of 5,6 23.652% 9.711% -6.101% -25.119% -18.219%
Winning total of 7 -3.886% 23.873% 11.461% -0.486% -0.611%
Winning total of 8 -20.400% -17.257% 15.893% 14.111% 14.730%
Winning total of 9 -22.597% -19.659% -19.888% 11.305% 11.300%
Player Natural -8.684% -7.331% -7.560% -7.981% -7.874%
Banker Natural -8.684% -7.331% -7.560% -7.981% -7.874%
  Known Fifth Card
Side Bet 6 7 8 9 T/J/Q/K
Winning total of 1,2,3,4 -41.350% -17.526% 6.291% 16.816% 29.716%
Winning total of 5,6 -36.436% -57.609% -35.804% -17.665% 16.432%
Winning total of 7 -0.107% 10.710% -38.227% -24.371% -5.316%
Winning total of 8 15.527% 15.145% 27.540% -24.737% -21.830%
Winning total of 9 12.743% 12.123% 4.204% 22.565% -24.028%
Player Natural -7.634% -8.145% -12.234% -11.570% -10.114%
Banker Natural -7.634% -8.145% -12.234% -11.570% -10.114%

The sixth card is the weakest position for the known-card. This card, when it is played, always goes to the Banker hand. The following table summarizes the edges on the various side bets when the AP knows the sixth card:
 
Knockout Baccarat Side Bet House Edge by Known Fifth Card
  Known Sixth Card
Side Bet A 2 3 4 5
Winning total of 1,2,3,4 25.883% 6.268% -15.614% -36.469% -68.583%
Winning total of 5,6 -7.283% 0.526% 7.944% 4.580% 7.798%
Winning total of 7 -7.373% -6.378% -5.241% 7.433% 7.625%
Winning total of 8 -9.518% -7.457% -6.295% -4.212% 5.642%
Winning total of 9 -13.042% -12.925% -10.925% -9.146% -6.446%
Player Natural -8.664% -8.571% -8.748% -9.067% -9.526%
Banker Natural -8.664% -8.571% -8.748% -9.067% -9.526%
  Known Fifth Card
Side Bet 6 7 8 9 T/J/Q/K
Winning total of 1,2,3,4 -62.115% -40.818% -18.339% 0.388% 30.500%
Winning total of 5,6 -6.575% -29.570% -24.438% -17.565% -8.319%
Winning total of 7 7.226% 19.248% -16.127% -13.326% -9.000%
Winning total of 8 5.787% 5.542% 15.171% -12.929% -9.625%
Winning total of 9 1.918% 3.076% 3.381% 12.720% -13.151%
Player Natural -10.017% -9.901% -10.102% -9.783% -8.772%
Banker Natural -10.017% -9.901% -10.102% -9.783% -8.772%

Finally, the following tables summarizes each combination of side bet and card location where the AP can get an edge over the house:
 
Knockout Baccarat Known Card Strategy
Side Bet Known 1/3 Known 2/4 Known 5 Known 6
Winning total of 1,2,3,4 A,2,3,4,T A,2,3,4,T A,8,9,T A,2,9,T
Winning total of 5,6 5.6 5.6 A,2,T 2,3,4,5
Winning total of 7 7 7 2,3,7 4,5,6,7
Winning total of 8 8 8 3,4,5,6,7,8 5,6,7,8
Winning total of 9 9 9 4,5,6,7,8,9 6,7,8,9
Player Natural 8,9 - - -
Banker Natural - 8,9 - -

In the U.S. market, side bets often have severely restricted maximum wagers. These low maximums will discourage known-card play. Internationally, where limits on side bets are often much higher, there is no doubt that known-card play has occurred and will continue to occur whenever opportunities arise.

The key to defending against known-carding in baccarat is to carefully inspect the shuffle procedure. If a single card is exposed at any point during the shuffle procedure then known-card play becomes a real possibility. Known-card play is one of the most sought after opportunities in baccarat. If it is possible to known-card your game, then it's probable that it is already taking place. 
About the Author
By

received his Ph.D. in Mathematics from the University of Arizona in 1983. Eliot has been a Professor of both Mathematics and Computer Science. Eliot retired from academia in 2009. Eliot Jacobson

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