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