Lucky 8 (L8) is a baccarat side bet I first heard about on the Wizard of Vegas website in this thread. As the name implies, a Player/Banker final total of 8 is key to winning this bet. It should therefore come as little surprise that L8 is highly vulnerable to card counting, with 8's being the key-card for a counting system. For the interested reader, here is a reference to L8 in the UK, and here is a document from the State of Washington.

The player can wager on L8 from both the Player side and from the Banker side. L8 wins if the corresponding hand has a point total equal to 8, with bonuses for three-card suited totals of 8.

Following are descriptions of the winning outcomes. In case more than one description applies to the hand, the player wins only the highest paying outcome:

  • Double suited 3-card 8. The hand ends in an 8-8, where both the Player and Banker hands consist of three cards of the same suit (note, the Player and Banker hands can be the same or different suits from each other).
  • Suited 3-card 8. The hand consists of three suited cards with total of 8. In this case, the value of the other hand does not matter.
  • Double 8. The hand ends in an 8-8 tie.
  • Unlucky 8. The hand value is 8, the other hand has value 9.
  • Lucky 8. The hand value is 8, beating the other hand.

There are three pay tables given for L8, as follows:

lucky 8 pay tables


Note that both a suited 8 and double suited 8 require that the hand have three cards. The Player hand is more likely to require three cards than the Banker hand. Intuitively it follows that the house edge for the Player side of L8 should be lower than the house edge for the Banker side. As we will see, this is the case.

Here is the combinatorial analysis for L8 for PT #1:

lucky 8 baccarat side bet, player & banker side -- combinatorial analysis, PT #1


In particular, for PT #1, the house edge for the Player side is 6.1493% and the house edge for the Banker side is significantly higher, at 9.7224%.

The following table summarizes the house edge and standard deviation for both the Player and Banker bets for each pay table.

lucky 8 baccarat side bet, combinatorial analysis summary


On to card counting. Before I give the EORs and a counting system, this is a good chance for you to use your well-developed intuition to puzzle out the system in advance. I offer these clues:

  • Obviously, 8's are very important. As a counter, you should be very sad every time an 8 is played.
  • The premium payouts require 3 cards. 9's often give a natural that stops the hand after two cards. It follows that you should be happy to see 9's leave the shoe.
  • Once a third card is going to be drawn, in order to get a total of 8 the counter needs to draw a card that is large enough to get that total. For the Player hand, if the draw is a T, J, Q, K, A or 2 then the total can't be 8 (Player draws on 5 or less). For the Banker hand, the same list works, except that very rarely, if the Banker draws a 2 to a two-card total of 6, he can get a three-card 8.  In either case, the counter should be happy to see T, J, Q, K, A and 2 leave the shoe.

Ok, got that? Glad to see 2, 9, T, J, Q, K and A leave the shoe. Sad to see 8 leave the shoe. 3, 4, 5, 6, 7 are neutral.

The following tables give the EOR's for both the Player bet and the Banker bet for PT #1, together with a counting system for each:

lucky 8 player, EORs, PT #1

 

lucky 8 banker, EORs, PT #1


That is, the recommended card counting system for both the Player and Banker sides of L8 is:

  • 3, 4, 5, 6, 7 = 0
  • A, 2, 9, T, J, Q, K = +1
  • 9 = +2
  • 8 = -8

This system is very accurate. The betting correlation for the Player side is 0.99604. For the Banker side the betting correlation is 0.99635. This system is also  a nearly optimal choice for PT #2 and PT #3.

The following tables give card counting summaries for using the system above against L8, assuming the usual burn card rules and that the cut card is placed 14 cards from the end of the shoe:

lucky 8 baccarat side bet, player side count system

 

lucky 8 baccarat side bet, banker side count system


For example, if an AP was card counting at a game using PT #1, then he would play the Player side of L8 whenever the true count was 6 or higher, and he would play both the Player and Banker sides whenever the true count was 10 or higher. In this way, the AP will earn 1.166 units per 100 hands against the Player side and 0.743 units per 100 hands against the Banker side, for a total of 1.907 units per 100 hands.

The following table summarizes the total profit possible from card counting L8:

lucky 8 baccarat side bet, count system, units won per 100 hands


Because of the very high house edges associated with PT #3, the counter will probably not be too interested in playing against this version. However, both PT #2 (1.421 per 100) and PT #1 (1.908 per 100) are significant card counting opportunities. In my opinion, L8 with PT #1  poses a high risk to card counting.

Here's a quick lesson -- any time a side bet has the rank of a card in its name, it's very likely that card counting will be highly effective against that side bet.

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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