How to Beat
Super Fun 21
reprinted with
permission of the author, Orange County KO,
originally appeared on bj21.com, April 2002
For several months, counters have been intrigued by
Super Fun 21, generally falling into two groups. The vast majority of counters
believe SF21 is a circus game, to be avoided like timeshare salesmen. A few
daring souls, however, play this game and just wing it, intuitively believing
that a large spread will get the money. As you will see from the following
analysis, their intuition is correct.
An edge of over 1% can be achieved at Super Fun 21 with straight counting.
Call Ripley. With a healthy spread and aggressive ramp, this game can be as
lucrative as many traditional blackjack games.
Introduction
Super Fun 21 is a variation of single-deck blackjack with liberal rules, but
naturals pay even money. As counters, we hoped this game would disappear, but
apparently it's here to stay. For those living in the Yukon Territory, see the
Wizard of Odds for a detailed description of the rules:
http://www.thewizardofodds.com/game/superfun21.html
Eliminating the Guesswork
This analysis addresses the following questions:
What is the off-the-top house edge?
What is the basic strategy?
What are the effects of card removal?
What is each count worth?
At what count does the player have an edge?
Should the count be adjusted for the ace of diamonds and ten-valued diamonds?
Are play deviations worth the trouble?
Which play deviations are most important?
What spread is necessary to break even?
What is the player's expectation for various spreads?
How does the variance for SF21 compare to traditional blackjack?
House Edge
SF21 is a complex game and somewhat difficult to analyze. The multi-card rules
make playing decisions more complicated than a typical blackjack game. The basic
strategy chart that appears on the Wizard of Odds site is mostly accurate. The
Wizard's strategy results in a house edge of 0.9788%. By separately analyzing
all hand combinations based on the number of cards, an optimal strategy is
generated that results in a slightly smaller house edge of 0.9621%. These house
edge figures were generated using an approach similar to Cacarulo's Expected
Value Tables on bjmath.com and are based on 5 million rounds for each of the 550
2-hand versus dealer upcard combinations. Hey, 2.75 billion sims can't be wrong.
Optimal Basic Strategy
There are several playing decisions (all minor) that differ between the Wizard's
chart and the optimal chart. Most notably, do NOT surrender 17 versus Ace after
doubling down. (In fact, if basic strategy is to stand on 17 versus Ace with 3
or 4 cards, it stands to reason you would not surrender 17 versus Ace after
doubling down.) To be sure, I value and respect Shackelford's gaming expertise,
and all of these basic strategy differences are trivial in terms of overall EV.
Like any blackjack game, basic strategy forms the foundation for advantage play.
BS for SF21 is not necessarily intuitive. Do yourself a favor: print the chart
and bring it to the table with you. Unlike traditional blackjack, most playing
decisions for SF21 vary depending on the number of cards in the player's hand.
Key to Basic Strategy:
S: Stand
H: Hit
D: Double
P: Split
R: Surrender
S3: Stand, except hit with 3 or more cards
S4: Stand, except hit with 4 or more cards
S5: Stand, except hit with 5 cards
D3: Double, except hit with 3 or more cards
D4: Double, except hit with 4 or more cards
D5: Double, except hit with 5 cards
R4: Surrender, except hit with 4 or more cards
H*: Hit, except surrender with 3 cards
H**: Hit, except stand with 3 cards
R*: Surrender, except stand with 3 or 4 cards, and hit with 5 cards
S*: Stand, except double with 3 or 4 cards, and hit with 5 cards
Double Down Rescue
Surrender after doubling on any stiff hand (12-16) against a dealer 8, 9, 10, or
Ace.
Effects of Removal
2 3 4 5 6 7 8 9 10 A
0.27% 0.40% 0.61% 0.80% 0.48% 0.24% -0.09% -0.26% -0.53% -0.36%
EoR numbers are based on 110 million rounds for each card removed. As expected,
these EoR numbers are similar to traditional single deck. Aces are worth less to
the player because most naturals pay even money, while twos are worth more due
to multi-card bonuses.
Card Counting
Low-level, unbalanced counts are arguably the most appropriate for SF21. These
count systems have many advantages over the others: no true-count conversion, no
side counts, no remaining deck estimates, no fractions, no problems. These
practical considerations make KO and UBZII the most attractive choices.
Correlation Coefficients
Hi-Lo 0.942441
KO 0.944572
UBZII 0.969465
A more efficient counting system could be devised for SF21 as an academic
exercise, but I doubt anyone would want to learn a new count just for SF21. In
keeping with practical considerations, only KO and UBZII are considered.
Using basic strategy, 5 billion rounds were played assuming head-up with Rule of
6 to generate the following tables:
KO - Count Frequency & EV Table UBZII - Count Frequency & EV Table
Count Freq EV St Dev Count Freq EV St Dev
> 9 0.3% 4.1% 1.04 > 14 0.6% 3.7% 1.04
9 0.4% 3.5% 1.05 14 0.3% 3.1% 1.06
8 0.8% 3.0% 1.06 13 0.5% 2.9% 1.06
7 1.5% 2.5% 1.07 12 0.7% 2.7% 1.07
6 2.5% 2.0% 1.08 11 0.9% 2.4% 1.08
5 3.9% 1.5% 1.09 10 1.3% 2.1% 1.08
4 5.8% 0.9% 1.10 9 1.7% 1.8% 1.09
3 7.9% 0.4% 1.11 8 2.3% 1.6% 1.09
2 9.9% -0.2% 1.12 7 2.9% 1.2% 1.10
1 11.0% -0.8% 1.13 6 3.5% 0.9% 1.10
0 31.0% -1.1% 1.14 5 4.2% 0.6% 1.11
-1 9.3% -2.1% 1.15 4 4.9% 0.3% 1.12
-2 7.2% -2.8% 1.16 3 5.5% -0.1% 1.12
-3 4.3% -3.7% 1.17 2 6.0% -0.4% 1.13
-4 2.4% -4.6% 1.18 1 6.4% -0.8% 1.13
< -4 1.8% -6.7% 1.21 0 26.4% -1.0% 1.13
Total 100% -0.96% 1.13 -1 6.0% -1.5% 1.14
-2 5.6% -1.9% 1.15
-3 5.1% -2.3% 1.15
-4 4.2% -2.7% 1.16
-5 3.2% -3.2% 1.17
-6 2.5% -3.7% 1.17
-7 1.8% -4.3% 1.18
-8 1.3% -4.9% 1.19
-9 0.8% -5.7% 1.20
< -9 1.4% -7.4% 1.22
Total 100% -0.96% 1.13
The key count for KO is 3 - this is the lowest count at which the player has an
advantage. Each running count for KO is worth roughly 0.5% in EV. The key count
for UBZII is 4, and each running count for UBZII is worth roughly 0.3% in EV. As
the tables above indicate, we will be playing at a disadvantage roughly 77% of
the time, using the minimum waiting bet. Our +EV will come from the remaining
23% of the time, when substantially higher bets are justified.
KO UBZII
Key Count 3 4
Initial Advantage 0.4% 0.3%
Advantage per RC 0.5% 0.3%
Surprisingly, standard deviation for SF21 is similar to traditional single deck
games. Higher variance caused by double on any number of cards is offset by
lower variance caused by surrender and even money naturals. However, the
standard deviation for SF21 is more volatile at varying counts than traditional
single deck. In particular, it drops significantly at higher counts, likely due
to double down rescue.
Diamonds Side Count
Any natural in Diamonds pays 2:1, all other naturals pay even money. A player's
natural always win, even against a dealer's natural. You can expect a blackjack
in Diamonds once every 336 hands. The Ace of Diamonds seems like a valuable card
along with the ten-valued diamonds, to a lesser extent. My hunch was that a side
count for the Ace of Diamonds would be worthwhile for adjusting the bet. This
hunch was wrong.
The EoR for Aces is -0.356%. This is small (in absolute terms) compared to
traditional blackjack because most naturals pay even money. The EoR for the Ace
of Diamonds is -0.591%, while the EoR for all other Aces is -0.278%, a
difference of -0.313%. The difference in EoR for the ten-valued Diamonds is even
more trivial (1/4 * -0.313%). A 4 or 5 has greater impact on EV than the Ace of
Diamonds. Side counting the Ace of Diamonds would put too much emphasis on a
card that really is not that important, and add very little to overall EV. It
would be more worthwhile to side-count nines, which have an EoR of -0.255% but
are considered neutral by both KO and UBZII. The bottom line is this: pass on
side counting the Ace of Diamonds.
Bet Spreads
Beating SF21 is all about the spread. We have to overcome a HUGE off-the-top
house edge of almost 1%. Many SF21 games are "no mid-round entry" and
besides, Wonging in and out of single deck games is generally ill-advised.
The bad news: We have to play lots of hands at a 1% or higher disadvantage.
The good news: Heat is usually minimal, and large spreads are tolerated.
If you can't spread like a madman, SF21 is not for you. This game is roughly
break-even with a 1:5 spread using basic strategy. Consider the following
tables:
KO 1:5 Spread UBZII 1:5 Spread
Count Units EV Count Units EV
> 5 5 2.51% > 8 5 2.41%
5 5 1.48% 8 5 1.56%
4 4 0.94% 7 5 1.25%
3 2 0.37% 6 4 0.95%
< 3 1 -1.62% 5 3 0.60%
Total 0.00% 4 2 0.28%
< 4 1 -1.65%
Total 0.03%
With a 1:10 spread, the game is still a sleeper with an edge of about 0.5%:
KO 1:10 Spread UBZII 1:10 Spread
Count Units EV Count Units EV
> 5 10 2.51% > 8 10 2.41%
5 8 1.48% 8 10 1.56%
4 5 0.94% 7 8 1.25%
3 2 0.37% 6 6 0.95%
< 3 1 -1.62% 5 4 0.60%
Total 0.44% 4 2 0.28%
< 4 1 -1.65%
Total 0.50%
Using a 1:20 spread, the game becomes interesting with an edge of almost 1%:
KO 1:20 Spread UBZII 1:20 Spread
Count Units EV Count Units EV
> 5 20 2.51% > 8 20 2.41%
5 15 1.48% 8 15 1.56%
4 10 0.94% 7 12 1.25%
3 3 0.37% 6 10 0.95%
< 3 1 -1.62% 5 5 0.60%
Total 0.91% 4 2 0.28%
< 4 1 -1.65%
Total 0.93%
Note: Spread charts are based on 2.5 billion rounds, assuming head-up play
with Rule of 6.
Using a 1:20 spread is much easier than it sounds. The chips are denominated to
assist us: $500 = 5 * $100 = 4 * $25 = 5 * $5. Dismiss the typical counter's
notion about conservative bet ramps and betting cover. Regular gamblers jump
their bets all the time without consequence. SF21 is typically regarded by the
pit as a carnival game, which it is to some extent with its high house edge and
hokey rules. It is largely believed that experienced counters avoid this game at
all costs. As a result, erratic betting attracts far less attention than a
traditional blackjack game.
Play Deviations
While only basic strategy is necessary to get the money, additional gains can be
achieved with play deviations based on the count. Many SF21 games are face-up,
which is beneficial for count-based play deviations. To maximize these gains, a
separate set of indices must be used for each play depending on the number of
cards in the player's hand. This is neither practical nor necessary. Count-based
deviations for 2-card hands can add 0.095% to a player's expectation using KO
(slightly higher for UBZII: 0.109%). Play deviations for hands containing more
than 2 cards would add significantly less and are not considered in this
analysis.
Each 2-hand player total versus dealer upcard was summarized at various counts
for both KO and UBZII. KO counts were limited to the range -5 to +10, while
UBZII counts were limited to the range -10 to +15. Six billion sims were run for
each of KO and UBZII. These plays were then ranked by frequency, gain in EV, and
size of bet (bearing in mind that play deviations at higher counts are more
important due to larger bets).
From this analysis comes the Fun 14, that is, the 14 play deviations that reap
the vast majority of the gains. Using KO, the Fun 14 achieves 88% of the total
gain available from all 2-card play deviations.
Fun 14 - KO Fun 14 - UBZII
Player Dealer RC Play Player Dealer RC Play
15 9 5 R 15 9 7 R
15 10 2 R 15 10 3 R
16 9 4 R 16 9 6 R
12 2 5 S 12 2 7 S
12 3 3 S 12 3 4 S
17 1 2 S 17 1 2 S
9 7 4 D 9 7 6 D
s19 4 4 D s19 4 5 D
s19 5 2 D s19 5 2 D
9 2 -1 H 9 2 -1 H
10 10 -1 H 10 10 -1 H
12 4 -1 H 12 4 -1 H
13 2 -1 H 13 2 -2 H
16 10 -1 H 16 10 1 H
If you remember only one play, make it 15 versus 10. By surrendering instead of
hitting at KO +2 (UBZII +3) you get 45% of the Fun 14 gain. Also, note that with
17 versus Ace, another important play, you should stand instead of surrendering
at KO +2 (UBZII +2). Many of the Catch-22 plays are excluded from this
list due to their decreased importance as a result of SF21's liberal rules (eg,
DOA) and increased spread.
Using the Fun 14 for play deviations adds 0.083% in expectation using KO and
0.096% in expectation using UBZII.
Acceptable Conditions
Like any single deck game, a counter's expectation will vary dramatically
depending on several factors including number of rounds per shuffle, number of
other players, speed, bet spread, and ramp. Since SF21 is generally considered
unsusceptible to counting, penetration tends to be better than traditional
single deck games. Some casinos as a policy never deal more than 3 rounds per
shuffle regardless of the number of players - avoid these casinos. Other
casinos give their dealers a lot of leeway at deciding when to shuffle. RO7 is
more common with SF21 than traditional single deck games. SF21 is worthwhile if
you receive at least 4 rounds per shuffle and are getting RO6 or better. Avoid
casinos and dealers that give less than RO6, and avoid crowded tables that get
less than 4 rounds per shuffle. Of course, playing head-up with RO6, getting 4
rounds on 2 spots is better than 5 rounds on 1 spot.
Occasional Wonging out and spreading to two hands can increase expectation.
Other lucrative opportunities can sometimes be found on SF21. New dealers will
sometimes pay 3:2 for blackjacks, although this typically does not last very
long, especially at higher stakes. If a casino has SF21 but does not offer
surrender on any of its other BJ games, you might find dealers and/or PC's that
mistakenly allow early surrender.
Final Thoughts
My motivation for analyzing this game was not counter-related. Anyone interested
in more advanced analysis can email me. If I know you and you're in the know
(think J Morgan), I'll send you the charts that end the guesswork. I know a few
GC members were researching this game as well, and I welcome your comments and
further analysis.