KEY ELEMENTS
In stark contrast to traditional blackjack, Super Blackjack™ is very much a betting game that plays on the player’s desire to bet the crap out of favorable situations, much the same way that a card counter waits for favorable situations in which to put as much money on the table as possible.
Super Blackjack™ borrows from the original “bet 1x-4x-or-fold” betting structure of Super Omaha Poker™ – only instead of having to fold the bad hands, the player can stand and check the hand down. The obvious drawback to taking away hitting is that without any other rule changes, the player would be doing a lot of standing around; a natural solution is to let the player split any two cards in order to increase player activity, while allowing the player to create more situations in which to max-double (4x).
That said, there are really six key elements to Super Blackjack™:
All figures that follow are based on an infinite deck model created by Charles Mousseau of Total Gaming Science.
Doubling for Up to 4x and Splitting Any Two Cards
The ability to “double” for up to 4x and split any two cards are both powerful rules individually, but the combination of the two rules packs an extra punch.
The table below shows the gain from doubling at various max-doubling sizes. As we can see from the column on the left, the raw gain to the player from being able to double for up to 4x is 6.01%. But when we also allow the player to split any two cards to create additional max-doubling situations, the player gains an additional 7.91% from the ability to double for up to 4x, resulting in a total gain of 13.92%.
Note: Note that the figures in the following tables are raw figures relating to the original version of Super Blackjack™ (in which there is no surrender, the Ante pays when the dealer busts based on the dealer's final hand total, and the Ante does not pay for blackjack).
Super Blackjack™ borrows from the original “bet 1x-4x-or-fold” betting structure of Super Omaha Poker™ – only instead of having to fold the bad hands, the player can stand and check the hand down. The obvious drawback to taking away hitting is that without any other rule changes, the player would be doing a lot of standing around; a natural solution is to let the player split any two cards in order to increase player activity, while allowing the player to create more situations in which to max-double (4x).
That said, there are really six key elements to Super Blackjack™:
- Doubling for up to 4x
- Splitting any two cards
- Taking away hitting
- The Ante (V1)
- House advantage and adj. house advantage (element of risk)
- The Ante (V2): Surrender and Super Blackjack™
All figures that follow are based on an infinite deck model created by Charles Mousseau of Total Gaming Science.
Doubling for Up to 4x and Splitting Any Two Cards
The ability to “double” for up to 4x and split any two cards are both powerful rules individually, but the combination of the two rules packs an extra punch.
The table below shows the gain from doubling at various max-doubling sizes. As we can see from the column on the left, the raw gain to the player from being able to double for up to 4x is 6.01%. But when we also allow the player to split any two cards to create additional max-doubling situations, the player gains an additional 7.91% from the ability to double for up to 4x, resulting in a total gain of 13.92%.
Note: Note that the figures in the following tables are raw figures relating to the original version of Super Blackjack™ (in which there is no surrender, the Ante pays when the dealer busts based on the dealer's final hand total, and the Ante does not pay for blackjack).
Gain from Max-Doubling
|
Max-Double Size
|
Max-Double Raw Gain
(No Split Any Two) |
Max-Double Added Gain
From Split Any Two |
Max-Double
Total Gain |
|
1x
2x 3x 4x |
0.00%
1.91% 3.93% 6.01% |
0.00%
2.16% 4.88% 7.91% |
0.00%
4.07% 8.81% 13.92% |
On its own, splitting any two cards is actually the stronger of the two rules. In regular blackjack, allowing the player to split any two cards is worth nearly 15% to the player. But when we take away hitting – as is the case in Super Blackjack™ – the impact of splitting any two cards is reduced to 12.63%.
The result is a total gain to the player of 26.55% from splitting any two cards and doubling for up to 4x.
The result is a total gain to the player of 26.55% from splitting any two cards and doubling for up to 4x.
Total Gain from Split Any Two and Doubling for Up to 4x
|
Max-Double Size
|
Max-Double
Raw Gain |
Max-Double Added Gain
From Split Any Two |
Gain from Split Any Two
|
Total Gain
|
|
1x
2x 3x 4x |
0.00%
1.91% 3.93% 6.01% |
0.00%
2.16% 4.88% 7.91% |
12.63%
12.63% 12.63% 12.63% |
12.63%
16.70% 21.44% 26.55% |
This requires adjustments in the other direction.
Taking Away Hitting
In regular blackjack, the player’s disadvantage is that the player must draw first, and he loses if he busts. But in Super Blackjack™, we’ve given the player the opposite problem, and deny the player the chance to make a hand by taking away hitting: In this game, if the player wants to draw, he must pay for it.
Essentially, the reason why this works is because the dealer is never a favorite to bust, regardless of the up card.
Taking Away Hitting
In regular blackjack, the player’s disadvantage is that the player must draw first, and he loses if he busts. But in Super Blackjack™, we’ve given the player the opposite problem, and deny the player the chance to make a hand by taking away hitting: In this game, if the player wants to draw, he must pay for it.
Essentially, the reason why this works is because the dealer is never a favorite to bust, regardless of the up card.
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You see, the dealer shows a 7-A on 61.5% of hands, but busts only 21.6% of the time on these hands on average (given six decks, and dealer hits soft 17). Moreover, the concept of a dealer “bust card” is widely misunderstood – the dealer still only busts 39.8% of the time on average when showing a 2-6. Consequently, the burden is still on the player to make a hand, or otherwise be a dog against any dealer up card.
Unfortunately, this rule alone is not as strong as I would have liked it to be. As it turns out, the raw deficit to the player from taking away hitting is only a little over 6%, which is just enough to allow the player to double for 4x while blackjack pays 3 to 2; however, the game would be unplayable, as the player would just be standing much of the time. My first impression was that the 6% figure seemed extremely light, considering that in regular blackjack, hitting and standing basic strategy rules come into play on about 67% of hands. But as Peter A. Griffin notes in his discussion of “The World’s Worst Blackjack Player” in The Theory of Blackjack (1979), the cost of a player failing to a hit stiffs (12-16) against high cards (dealer 7-A) is only 3%. Moreover, the cost of not being able to hit on 9, 10, or 11 is slight where the player can – and is often correct to – double anyway. |
Dealer Bust Frequency, 6 Decks H17
Source: Wizard of Odds, 6 Decks, Dealer Hits Soft 17
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And then the cost of not being able to hit small hands like (3,2) or (4,3) vs. 10 is not terribly large due the relative infrequency of such hands, combined with the strength of the up card.
But in addition to the raw deficit of a little over 6%, taking away hitting also reduces the impact of splitting any two cards. When hitting is allowed, the impact of splitting any two cards is nearly 15%; but as we saw earlier, this number is reduced to 12.63% when taking away hitting. What this means is that when the player can split any two cards but can only double for 1x (as in regular blackjack), taking away hitting reduces the player advantage by over 8%.
In short, taking away hitting is strong, but not strong enough to cover splitting any two cards, much less cover both splitting any two cards and doubling for more than the standard 1x.
The Ante: A Second Forced Bet (Version 1)
So we’ve taken away hitting, but we still have a problem. When the player can double for 4x and blackjack pays 3:2, but the player can’t split any two cards, the game is solvent (0.74% house advantage assuming infinite decks and H17); but as we’ve noted the game would also be unplayable, as the player would be doing a lot of standing. On the other hand, even when the player can split any two cards, but only double for 1x while blackjack pays 1:1, the player has a 3.62% advantage.
Essentially, there is no version of this game in which the player can split any two cards with a single forced bet. There are alternatives – for example, we can limit non-pair splitting to splitting any ace; with a max-double of 3x and blackjack paying 3:2, this yields a house advantage of 0.30%. It’s also conceivable that the player could split any ace or deuce if blackjack pays even money.
Both of those alternatives are covered under the patent application, and it’s possible that a single-bet variation (Version Y) along those lines may be developed. But for maximum playability, the split any two cards rule is key, and the solution is to force a second initial bet with a bad paytable – a technique made prominent in Roger Snow’s Ultimate Texas Hold’em and Crazy 4 Poker games.
In Super Blackjack™, this second forced bet is termed the “Ante”.
Now there are two parts to this equation. The first part is the main game, and if we are going to force a second bet, then there’s no short-arming it – we’re going to go all the way and use the rules we want to use, and take them to their practical limits. Namely:
This results in a player advantage of 22.06% in Charles Mosseau’s infinite deck model, assuming dealer hits soft 17 (22.05% for S17).
The second part of the equation is the Ante. This Ante wager comes with three requirements and two preferences:
The most natural outcome to wager on is the dealer busting. We all root for the dealer to bust anyway; it’s a singular outcome that everybody at the table can bet on, much the same way that everybody at the craps table can bet the Pass Line, and everybody at a baccarat table can bet on the Banker or Player; it doesn’t interfere with the main game, as is the case in blackjack sidebets that pay on the initial cards; and it doesn’t affect the main game, as the wager does not affect player decision-making.
Moreover, the Ante wager is not resolved until the last card is dealt, which: (a) heightens anticipation and (b) means that even a player who is dealt blackjack has a stake in the hand for the duration of the hand.
The next trick is to figure out a suitable bust wager that hasn’t been done before and is not patent protected. My first idea was to have a paytable with a variable payoff depending on the dealer’s up card when the dealer’s bust; the idea is that the wager would pay even money if the dealer busts with a bust card (2-6) showing, with the highest payoffs coming when the dealer has a 10 or A showing. Unfortunately, that’s been done before.
The other preferred idea was to have the paytable vary depending the dealer’s final hand total when the dealer busts. Not only has this not been done before, but also – at least as far as I could tell – nobody’s ever calculated the dealer’s final hand total on bust hands before!
That makes sense in that there was never a practical application for it before. Well, I present here – published for the first time – the frequencies for the dealer’s final hand total when the dealer busts, as calculated by Charles Mousseau.
But in addition to the raw deficit of a little over 6%, taking away hitting also reduces the impact of splitting any two cards. When hitting is allowed, the impact of splitting any two cards is nearly 15%; but as we saw earlier, this number is reduced to 12.63% when taking away hitting. What this means is that when the player can split any two cards but can only double for 1x (as in regular blackjack), taking away hitting reduces the player advantage by over 8%.
In short, taking away hitting is strong, but not strong enough to cover splitting any two cards, much less cover both splitting any two cards and doubling for more than the standard 1x.
The Ante: A Second Forced Bet (Version 1)
So we’ve taken away hitting, but we still have a problem. When the player can double for 4x and blackjack pays 3:2, but the player can’t split any two cards, the game is solvent (0.74% house advantage assuming infinite decks and H17); but as we’ve noted the game would also be unplayable, as the player would be doing a lot of standing. On the other hand, even when the player can split any two cards, but only double for 1x while blackjack pays 1:1, the player has a 3.62% advantage.
Essentially, there is no version of this game in which the player can split any two cards with a single forced bet. There are alternatives – for example, we can limit non-pair splitting to splitting any ace; with a max-double of 3x and blackjack paying 3:2, this yields a house advantage of 0.30%. It’s also conceivable that the player could split any ace or deuce if blackjack pays even money.
Both of those alternatives are covered under the patent application, and it’s possible that a single-bet variation (Version Y) along those lines may be developed. But for maximum playability, the split any two cards rule is key, and the solution is to force a second initial bet with a bad paytable – a technique made prominent in Roger Snow’s Ultimate Texas Hold’em and Crazy 4 Poker games.
In Super Blackjack™, this second forced bet is termed the “Ante”.
Now there are two parts to this equation. The first part is the main game, and if we are going to force a second bet, then there’s no short-arming it – we’re going to go all the way and use the rules we want to use, and take them to their practical limits. Namely:
- Double for up to 4x
- Split any two cards
- Blackjack pays 2 to 1
This results in a player advantage of 22.06% in Charles Mosseau’s infinite deck model, assuming dealer hits soft 17 (22.05% for S17).
The second part of the equation is the Ante. This Ante wager comes with three requirements and two preferences:
- The forced Ante must have a house advantage > 22.06%.
- Whatever outcome the Ante is tied to, it cannot affect the main game.
- Ideally, the Ante would be tied to a community feature in which every player is wagering on the same outcome.
- Ideally, the Ante wager would not interrupt the main game, and would not be resolved until the final card is dealt.
- The wager must be something that hasn’t been done before and is not patent protected.
The most natural outcome to wager on is the dealer busting. We all root for the dealer to bust anyway; it’s a singular outcome that everybody at the table can bet on, much the same way that everybody at the craps table can bet the Pass Line, and everybody at a baccarat table can bet on the Banker or Player; it doesn’t interfere with the main game, as is the case in blackjack sidebets that pay on the initial cards; and it doesn’t affect the main game, as the wager does not affect player decision-making.
Moreover, the Ante wager is not resolved until the last card is dealt, which: (a) heightens anticipation and (b) means that even a player who is dealt blackjack has a stake in the hand for the duration of the hand.
The next trick is to figure out a suitable bust wager that hasn’t been done before and is not patent protected. My first idea was to have a paytable with a variable payoff depending on the dealer’s up card when the dealer’s bust; the idea is that the wager would pay even money if the dealer busts with a bust card (2-6) showing, with the highest payoffs coming when the dealer has a 10 or A showing. Unfortunately, that’s been done before.
The other preferred idea was to have the paytable vary depending the dealer’s final hand total when the dealer busts. Not only has this not been done before, but also – at least as far as I could tell – nobody’s ever calculated the dealer’s final hand total on bust hands before!
That makes sense in that there was never a practical application for it before. Well, I present here – published for the first time – the frequencies for the dealer’s final hand total when the dealer busts, as calculated by Charles Mousseau.
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Bust Frequency: Dealer’s Final Hand Total
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Based on the dealer’s final hand total frequencies, Super Blackjack™ employs the Ante paytables below for 6 decks, H17 and 6 decks, S17, which are sufficient to clear the 22.06% player advantage in the main game assuming infinite decks. For reference, Mousseau’s billion-hand simulation yielded a 22.05% player advantage for six decks, H17, and a 22.06% player advantage for six decks, S17.
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Paytable
|
Dealer’s Final Hand Total
26 25 24 23 22 House Advantage |
6 Decks, H17
4 to 1 2 to 1 3 to 2 1 to 1 1 to 1 23.08% |
6 Decks, S17
3 to 1 3 to 1 3 to 2 1 to 11 1 to 1 23.24% |
House Advantage and Adj. House Advantage (Element of Risk)
There are three basic driving forces behind the targeted house advantages:
- Casino operators have been making a concerted push to raise house advantages. This is noticeable particularly in blackjack games on the Strip, where depending on the joint, you might need to be a $25 or $50-minimum bettor in order to play traditional 3:2 blackjack at 0.50% or so, even at multiple decks. For everybody else looking to play blackjack at more reasonable stakes, it’s often either 6:5 blackjack or nothing.
- Intelligent gamblers and millennials demand lower edge games. The fact is that as house advantages rise and 3:2 games are increasingly disappearing, there are fewer and fewer games for smart people to play.
- Blackjack is fundamentally a flat game, and modern variants to date have done little to change that – until now. As such, the term and concept of element of risk (adj. house advantage) has not been widely used when referring to blackjack or blackjack variants.
In contrast to every blackjack variation to date, Super Blackjack™ is tremendously scalable. A single split and two max-doubles (4x) puts 11 units on the table (including the Ante); and as I’ve mentioned elsewhere on this site, at one point in Mousseau’s billion-hand simulation, the player had a whopping 41 units on the table stemming from a single hand, presumably after seven splits and eight max-doubles!
This action enables Super Blackjack™ to change the nature of the discussion entirely and appeal to the interests of both the casino operator and the intelligent (but not advantage) gambler alike. With a house advantage of 1.22% on the base Game wager (6 decks, S17), Super Blackjack™ delivers the slightly higher house advantage that the casino operator is seeking; but with an average bet of 3.91 units per hand, the game also delivers an adjusted house advantage of 0.31% per unit wagered, making Super Blackjack™ one of the fairest games around, while delivering a lower house edge per unit to the basic strategy player than even traditional multi-deck blackjack paying 3:2 on blackjack.
Play the demo for the original version of Super Blackjack™ below.
Super Blackjack™ Demo: Original Version (V1)
Ante V2: Surrender and Super Blackjack™
To be continued...
To be continued...
