The “Lucky Lucky” (LL) blackjack side bet has payouts based on the player’s two cards
and the dealer’s up-card. After 8️⃣ the player makes the LL bet, the values of the player’s
two cards and dealer’s up card are summed. Hands 8️⃣ that total 19, 20 or 21 are winners,
with bonuses for suited hands and for the hands 6-7-8 and 7-7-7. 8️⃣ All other hands lose.
As usual for blackjack, an Ace counts as 1 or 11. From 2009 through early 2012, 8️⃣ this
wager was licensed through Gaming Network, Inc. Unfortunately, Gaming Network dissolved
in April of 2012. This wager is currently 8️⃣ licensed through Aces Up Gaming.
There are
versions of the bet for both a double-deck game and a six-deck shoe. Here 8️⃣ are the most
common pay tables and the house edge for each:
The following table gives the effect of
removal (EOR) 8️⃣ for each card for the double-deck version of LL. This table shows the
importance of the 6’s, 7’s and 8’s 8️⃣ to player side. The Aces are also good for the
player, mainly because of their dual role as a value 8️⃣ of 1 or 11. This table also shows
that the cards 2, 3 and T benefit the house so that 8️⃣ the edge moves towards the player
as they are played from the deck. The reason for this is intuitive. First, 8️⃣ the 2’s and
3’s are too small; it is hard to get a total up to 19 after being dealt 8️⃣ these cards.
Next, if the player is dealt a ten-valued card, then most likely his three-card total
will exceed 21. 8️⃣ The card counter likes it when there are a lot of A’s, 6’s, 7’s and 8’s
in the deck. He 8️⃣ doesn’t like it when there are a lot of 2’s, 3’s and T’s in the
deck.
By looking at the column 8️⃣ for EOR, I created a card counting system that assigns
the 7’s a card counting value of -2 (negative two). 8️⃣ To do this, I multiplied each value
in the EOR column by 115.81 to get “System 1” with card counting 8️⃣ tags (-0.98, 0.90,
0.70, 0.47, 0.37, -1.21, -2.00, -1.46, 0.29, 0.73). As usual for card counting systems,
these tags are 8️⃣ given in the order (A, 2, 3, 4, 5, 6, 7, 8, 9, T).
System 1 in not meant
as a 8️⃣ practical system. However, as a baseline counting system, it is worthwhile to see
how it performs. In an effort to 8️⃣ simplify this system, I also considered the balanced
card counting system with tags (-1, 1, 1, 0, 0, -1, -2, 8️⃣ -2, 0, 1). I’ll refer to this
system as “System 2.” This system is easily used by a card counter 8️⃣ of average skill
level.
I wrote a computer program to simulate using these two systems in live play. My
baseline simulation 8️⃣ assumed a double-deck version of blackjack. For convenience, I’ll
refer to the double-deck game as a “shoe.” After the cards 8️⃣ in the shoe were shuffled, I
assumed that the cut-card was placed after the 75-th card in the shoe. A 8️⃣ burn card was
dealt and the shoe was played out until the cut card came out. The shoe was then
8️⃣ shuffled and the next shoe was simulated.
The following table gives the results of a
simulation of one billion (1,000,000,000) shoes 8️⃣ for each system
These simulations show
that the card counter should make the LL wager whenever the true count is +2 8️⃣ or higher
for the indicated system. With System 1, the player would have an average edge over the
house of 8️⃣ 6.33% whenever he made the bet and he would make the bet on 26.44% of the
hands he played. The 8️⃣ player would then win about 1.674 units per 100 blackjack hands.
With System 2, the player has an average edge 8️⃣ over the house of 5.57% whenever he makes
the LL bet, and he would make the bet on 28.48% of 8️⃣ the hands. The player would then win
about 1.586 units per 100 blackjack hands.
As these results show, System 2 performs
8️⃣ remarkably well compared to the nearly optimal System 1. To put this in perspective, if
a person is playing head’s 8️⃣ up double-deck, he may get as many as 200 rounds per hour.
If the maximum allowed wager on LL isR$100, 8️⃣ then an advantage player will earn 1.586 x
2 xR$100 =R$317.27 per hour from card counting the LL wager.
The following 8️⃣ table shows
the player edge as a function of the true count for the double-deck version with the
cut card 8️⃣ placed at 75 cards, using System 2. The purpose of this analysis is to show
how the player edge is 8️⃣ correlated to the true count. These results are based on a
simulation of one billion (1,000,000,000) shoes.
Compared to ordinary blackjack 8️⃣ card
counting, where the player edge reaches a theoretical maximum of about 5%, playing
against LL can lead to some 8️⃣ very large advantages. The player gets an edge in excess of
10% on about 4% of his hands and an 8️⃣ edge in excess of 20% on about 1% of his hands. On
about 5 hands per 10,000, the player will 8️⃣ have an edge in excess of 40%.
The natural
defense a casino has towards a card counting form of advantage play 8️⃣ is to position the
cut card so that fewer cards are dealt between shuffles. The following table gives the
EV 8️⃣ per bet, bet frequency, and units won per 100 hands for cut card placements from 50
to 80 cards. Each 8️⃣ row was arrived at by a simulation of one hundred million
(100,000,000) shoes with the cut card placed at the 8️⃣ indicated depth. As is evident from
this table, the double-deck version of the LL wager is vulnerable to card counting,
8️⃣ even at modest cut card placements. It follows that decreasing deck-penetration is not
a viable way of protecting this wager.
It 8️⃣ is worthwhile comparing these results to the
six-deck version of the wager. For the six-deck game, a similar nearly perfect 8️⃣ “System
1” was developed after computing the EOR for each card. It was then compared to the
results from using 8️⃣ System 2 (the same system as for two decks). System 2 once again
performed exceptionally well. The following table gives 8️⃣ the six-deck results for a cut
card placed at 260 cards (1 deck cut off):
As can be seen from this 8️⃣ table, the six-deck
version is vulnerable and System 2 is a powerful system to use against it. However,
even with 8️⃣ a very deep cut card placement of 260 cards (52 cards cut off), the player’s
edge is about the same 8️⃣ as a mediocre placement of the cut card at 54 cards in the
double-deck version. For this reason, a player 8️⃣ who is targeting the LL side bet is much
more likely to attack the double-deck version than the six-deck game. 8️⃣ Because of this,
I did not pursue the analysis of the six-deck version any further.
The Lucky Lucky side
bet is 8️⃣ extremely popular. However, it has a significant vulnerability to card counting
and that vulnerability needs to be addressed. Because an 8️⃣ expert player will be giving
up very little to the house on the main blackjack game, such a player can 8️⃣ have great
longevity flat betting and staying under the radar, while selectively betting LL on
about 28% of his hands. 8️⃣ Such a player can easily produce a profit in excess ofR$200 per
hour at a fast game with a limit 8️⃣ ofR$100 on the LL bet.
The following are my
recommendations for protecting the Lucky Lucky side bet:
