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.
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:
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?
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:
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.
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.
- 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:
- 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.
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.
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%
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%
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%
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.
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.
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.
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.