KEY ELEMENTS
Super Texas Hold'em™ occupies a unique space, featuring two progressively larger betting rounds while placing focus on the flop as the ultimate point of attack. Both features put Super Texas Hold'em™ in direct contrast to virtually every other casino poker game to hit the casino floor, particularly hold'em and hold'em-related adaptations.
Moreover, Super Texas Hold'em™ delivers an unrivaled level of action: The player is correct to max-bet (3x) pre-flop on 49.6% of hands and max-bet (5x) the flop on 46.0% of hands, placing a max-wager on at least one round on 66.9% of hands, while betting the max 10 units on both rounds on 28.7% of hands. As a result, the player averages 7.2 units wagered per hand.
No other game comes close.
Pre-Flop and Total Action
Let's say you're dealt A♠K♠. What any poker player wants to do with a hand like AKs is to bet the max (3x) pre-flop, and then make a bigger bet (5x) if he hits the flop, or otherwise call down (bet the 2x minimum) and hope either to improve his hand, or otherwise hope that AK-high is enough to win in a showdown.
This doesn't happen in other games.
In Ultimate Texas Hold'em, the player is correct to max-bet (4x) pre-flop on 37.7% of hands, but then is done betting in the hand. In Mississippi Stud, max-betting (3x) with AKs is not even the correct play on second street (the "Third Street" wager), as the player is only correct to max-bet (3x) with any pair, which only happens on 5.9% of hands.
In Criss Cross Poker, the player max-bets (3x) on the opening Across and Down rounds slightly more often, max-betting (3x) with any pair and QJs+, which works out to 6.2% of hands Across (6.7% of hands on the Down bet, as the player max-bets a few more hands given information gained from the Across cards being revealed); these opening rounds are followed by a single 1x-3x Middle wager.
As a result, Super Texas Hold'em™ is able to generate significantly more action within the same game space. In Super Texas Hold'em™, the player bets the full 10 units on 28.7% of hands and averages 7.23 units wagered per hand. In contrast, the payer only bets the max 11 units in Criss Cross Poker on less than 7% of hands, averaging 5.87 units wagered per hand. Meanwhile, the player only bets the max 10 units in Mississippi Stud on 4.1% of hands, averaging only 3.59 units wagered per hand in the same 10-unit game space.
Moreover, Super Texas Hold'em™ delivers an unrivaled level of action: The player is correct to max-bet (3x) pre-flop on 49.6% of hands and max-bet (5x) the flop on 46.0% of hands, placing a max-wager on at least one round on 66.9% of hands, while betting the max 10 units on both rounds on 28.7% of hands. As a result, the player averages 7.2 units wagered per hand.
No other game comes close.
Pre-Flop and Total Action
Let's say you're dealt A♠K♠. What any poker player wants to do with a hand like AKs is to bet the max (3x) pre-flop, and then make a bigger bet (5x) if he hits the flop, or otherwise call down (bet the 2x minimum) and hope either to improve his hand, or otherwise hope that AK-high is enough to win in a showdown.
This doesn't happen in other games.
In Ultimate Texas Hold'em, the player is correct to max-bet (4x) pre-flop on 37.7% of hands, but then is done betting in the hand. In Mississippi Stud, max-betting (3x) with AKs is not even the correct play on second street (the "Third Street" wager), as the player is only correct to max-bet (3x) with any pair, which only happens on 5.9% of hands.
In Criss Cross Poker, the player max-bets (3x) on the opening Across and Down rounds slightly more often, max-betting (3x) with any pair and QJs+, which works out to 6.2% of hands Across (6.7% of hands on the Down bet, as the player max-bets a few more hands given information gained from the Across cards being revealed); these opening rounds are followed by a single 1x-3x Middle wager.
As a result, Super Texas Hold'em™ is able to generate significantly more action within the same game space. In Super Texas Hold'em™, the player bets the full 10 units on 28.7% of hands and averages 7.23 units wagered per hand. In contrast, the payer only bets the max 11 units in Criss Cross Poker on less than 7% of hands, averaging 5.87 units wagered per hand. Meanwhile, the player only bets the max 10 units in Mississippi Stud on 4.1% of hands, averaging only 3.59 units wagered per hand in the same 10-unit game space.
Max-Bet Frequency: Comparison Group
Game
|
Max-Bet Frequency
(First Two Cards) |
Max Total Wager
|
Betting Rounds
|
Max-Bet Frequency
(Max Units) |
Avg. Bet Per Hand
|
Super Texas Hold'em™
Ultimate Texas Hold'em Criss Cross Poker (Across/Down) Mississippi Stud Source: Data derived from Wizard of Odds |
49.6%
37.7% 6.2%/6.7% 5.9% |
10 Units
6 Units 11 Units 10 Units |
2
3/1 3 3 |
28.7%
-- < 7% 4.1% |
7.23 Units
4.15 Units 5.87 Units 3.59 Units |
Original Variation: Strategy Considerations and the Dealer Qualifier
In the first iteration of Super Texas Hold'em™:
There were a couple of primary motivations for this setup. The first was the desire to have a game with a single forced bet and two progressively larger betting rounds, with the emphasis on the flop as the ultimate point of attack. And the second key consideration relates to sculpting player strategy.
This second consideration is where the 2x-minimum flop bet and the flop dealer qualifier come in.
Recall first that the Blind and Pre-flop wagers always play. So if the player call 1x pre-flop and has to call a minimum of 2x on the flop to get to showdown, the player is only getting 2:1 or 3:1 to call (The one-unit Blind + the one-unit Pre-flop wager = 2 units which pay 2 units for a total of 4 units. The player must call 2 units, and only wins 2 units on the Flop wager if the dealer qualifies with a pair or better and the player can beat the dealer, and thus is getting 4:2 or 2:1, with a max of 3:1). Thus the intention was induce folds by making it harder for the player to call.
The flop dealer qualifier was also intended to keep the player from having to max-bet (4x) with marginal hands, like bottom pair or Ace-high on a paired board. Because the dealer will only pay the Flop wager if the dealer makes a pair, it is incorrect for the player to max-bet (4x) with bottom pair, as the dealer will likely only play against this wager if the dealer can make a pair, and thus is likely to beat the player. As such, the player is in effect laying odds with not only a hand like bottom pair, but is also laying odds on draws to bottom pair!
The sum of these rules was intended to both keep the player from max-betting (4x) the flop too often, and to fold more hands on the flop; and then by devaluing the flop, get the player to fold more often pre-flop as well. This would then both sculpt the player strategy and make the game solvent on a single forced bet as desired.
The game works -- which is to say that the game is solvent when structured this way, and with a single forced bet -- but not as intended.
What actually happens is that the player is correct to play 95% hands pre-flop, max-betting 49.3%, and only fold 5.4% of hands, while min-calling (1x) everything else. The pre-flop strategy below is perfectly solved.
Pre-flop Strategy: Original Version
In the first iteration of Super Texas Hold'em™:
- The player started with a single Blind wager, and could bet 1x-2x pre-flop or fold, and bet 2x-4x on the flop or fold.
- The Blind and Pre-flop wagers always played, while the 2x-4x Flop wager pushed if the dealer had less than a pair, or less than two pair if the board was paired.
There were a couple of primary motivations for this setup. The first was the desire to have a game with a single forced bet and two progressively larger betting rounds, with the emphasis on the flop as the ultimate point of attack. And the second key consideration relates to sculpting player strategy.
This second consideration is where the 2x-minimum flop bet and the flop dealer qualifier come in.
Recall first that the Blind and Pre-flop wagers always play. So if the player call 1x pre-flop and has to call a minimum of 2x on the flop to get to showdown, the player is only getting 2:1 or 3:1 to call (The one-unit Blind + the one-unit Pre-flop wager = 2 units which pay 2 units for a total of 4 units. The player must call 2 units, and only wins 2 units on the Flop wager if the dealer qualifies with a pair or better and the player can beat the dealer, and thus is getting 4:2 or 2:1, with a max of 3:1). Thus the intention was induce folds by making it harder for the player to call.
The flop dealer qualifier was also intended to keep the player from having to max-bet (4x) with marginal hands, like bottom pair or Ace-high on a paired board. Because the dealer will only pay the Flop wager if the dealer makes a pair, it is incorrect for the player to max-bet (4x) with bottom pair, as the dealer will likely only play against this wager if the dealer can make a pair, and thus is likely to beat the player. As such, the player is in effect laying odds with not only a hand like bottom pair, but is also laying odds on draws to bottom pair!
The sum of these rules was intended to both keep the player from max-betting (4x) the flop too often, and to fold more hands on the flop; and then by devaluing the flop, get the player to fold more often pre-flop as well. This would then both sculpt the player strategy and make the game solvent on a single forced bet as desired.
The game works -- which is to say that the game is solvent when structured this way, and with a single forced bet -- but not as intended.
What actually happens is that the player is correct to play 95% hands pre-flop, max-betting 49.3%, and only fold 5.4% of hands, while min-calling (1x) everything else. The pre-flop strategy below is perfectly solved.
Pre-flop Strategy: Original Version
Action
Fold Max-bet (2x) Min-bet (1x) |
Frequency
5.4% 49.3% 45.3% |
Hand Range
82o, 72o, 62o, 52o, 42o, 32o 22+, Ax, Kx, Q2s+, Q5o+, J6s+, J8o+, T7s+, T9o Everything else |
The above is not in itself a bad result -- in fact quite the opposite, as it is good to be able to play most every hand while making a raise on half of hands. The problem is what the player folding only 5% of hands says about the flop strategy.
The flop strategy is close to optimal but not perfectly solved due to the underlying complexity of hold'em, and is based on a randomized sampling of 16,900 flops -- 100 flops for each of the 169 starting hands in hold'em.
On the flop, as it turns out, the player is correct to max-bet (4x) on 21% of flops seen. This is a healthy number, and more or less in line with expectations: The player max-bets (4x) with top pair or better, plus stronger middle pair hands or better (basically if you can beat middle pair -- with say 99 on a K-7-2 rainbow flop), such as with an overcard kicker or with flush draw.
What's surprising -- or surprising to me, anyway -- is that the player is only correct to fold on 5.3% of flops seen. This is, again, despite laying odds on bottom pair hands and draws to bottom pair hands, while getting only 2:1 to call when the player bets the 1x minimum pre-flop. And basically what it takes to fold is something like 10-high or less with at least one undercard to the board and no backdoor draws; and even then, this turns out to be a close decision as some of the same types of hands that show up as folds also show up as calls, so it's really hard to say what the actual cutoff is.
And the reason this happens is because of the dealer qualifier. Recall that the dealer only plays against the 2x-4x Flop wager with a pair or better (or two pair on a paired board), which again was intended to limit action. But what happens as a function of the qualifier is that while the player is laying odds with bottom pair and draws to bottom pair, the player is also getting a partial freeroll.
Let's say you have 8♠7♠, and call 1x pre-flop. The flop comes A♠6♦4♥, giving you a gutshot with a backdoor flush draw. You bet the 2x minimum, and the dealer turns up the K♠Q♠. The board runs out 9♠2♦; you missed your draw(s) and the dealer wins with his KQ-high (technically ace-high with KQ-kickers, but whatever).
But the end result is that you only lost your 1-unit Blind and 1-unit Pre-flop wagers, while your 2x Flop wager pushed: Even though you missed your draws, you also didn't lose the Flop wager because the dealer didn't qualify, as the dealer didn't make a pair.
And so, as a consequence of the partial freeroll, you wind up getting far better than 2:1 to call, and justify calling with far worse hands than you'd ever want to call with.
Flop Strategy: Original Version
The flop strategy is close to optimal but not perfectly solved due to the underlying complexity of hold'em, and is based on a randomized sampling of 16,900 flops -- 100 flops for each of the 169 starting hands in hold'em.
On the flop, as it turns out, the player is correct to max-bet (4x) on 21% of flops seen. This is a healthy number, and more or less in line with expectations: The player max-bets (4x) with top pair or better, plus stronger middle pair hands or better (basically if you can beat middle pair -- with say 99 on a K-7-2 rainbow flop), such as with an overcard kicker or with flush draw.
What's surprising -- or surprising to me, anyway -- is that the player is only correct to fold on 5.3% of flops seen. This is, again, despite laying odds on bottom pair hands and draws to bottom pair hands, while getting only 2:1 to call when the player bets the 1x minimum pre-flop. And basically what it takes to fold is something like 10-high or less with at least one undercard to the board and no backdoor draws; and even then, this turns out to be a close decision as some of the same types of hands that show up as folds also show up as calls, so it's really hard to say what the actual cutoff is.
And the reason this happens is because of the dealer qualifier. Recall that the dealer only plays against the 2x-4x Flop wager with a pair or better (or two pair on a paired board), which again was intended to limit action. But what happens as a function of the qualifier is that while the player is laying odds with bottom pair and draws to bottom pair, the player is also getting a partial freeroll.
Let's say you have 8♠7♠, and call 1x pre-flop. The flop comes A♠6♦4♥, giving you a gutshot with a backdoor flush draw. You bet the 2x minimum, and the dealer turns up the K♠Q♠. The board runs out 9♠2♦; you missed your draw(s) and the dealer wins with his KQ-high (technically ace-high with KQ-kickers, but whatever).
But the end result is that you only lost your 1-unit Blind and 1-unit Pre-flop wagers, while your 2x Flop wager pushed: Even though you missed your draws, you also didn't lose the Flop wager because the dealer didn't qualify, as the dealer didn't make a pair.
And so, as a consequence of the partial freeroll, you wind up getting far better than 2:1 to call, and justify calling with far worse hands than you'd ever want to call with.
Flop Strategy: Original Version
Action
Fold Max-bet (4x) Min-bet (2x) |
Frequency (% of Flops Seen)
5.3% of Flops Seen 21.0% of Flop Seen 73.7% of Flops Seen |
Hand Range
If you miss the flop completely; generally if you bet 1x pre-flop, and have 10-high or less, and likely have one or two undercards to the board. Big hands and big draws. Big hands: If you can beat middle pair, plus stronger middle pair hands (middle pair of tens or better, or sevens or better with an overcard kicker or with a combo draw). Big draws: The nut flush draw with a gutshot, an open-ended straight draw with a flush draw, or pair plus nut flush draw. Everything else. |
And then there's another aspect of the Flop qualifier that I wasn't happy with. While in theory -- and in poker reality -- it makes sense that the dealer would only play a bigger pot with stronger hands, and thus only play against the Flop wager with a pair-or-better, it is not necessarily ideal to have the player make this big 4x wager on the Flop and not only have to beat the dealer, but also hope that the dealer makes a pair so that the wager plays.
You can play through the original version below. The ultimate result, in my mind, was OK, but not necessarily what I wanted.
You can decide if you like this version better.
You can play through the original version below. The ultimate result, in my mind, was OK, but not necessarily what I wanted.
You can decide if you like this version better.
Super Texas Hold'em™ Demo: Original Variation
Sacking the Ante and Removing the Dealer Qualifier
There are four main methods typically used to make a game solvent (that is, to give the house an advantage):
To be continued...
Driving Max-Bet Frequency
All High Variance Games have one thing in common, which is perhaps a secret and perhaps not. We'll get back to this some other time.
There are four main methods typically used to make a game solvent (that is, to give the house an advantage):
- Dealer qualifier. Restrict the hands the dealer will pay off a bet with, so that the dealer will only play a bigger pot when the dealer has a bigger (minimum qualifying) hand. Sometimes used on the Play wager, sometimes used on the initial Ante wager. See Caribbean Stud, Three Card Poker, UTH, Crazy 4 Poker, High Card Flush.
- 2nd forced bet. Have the player start the hand with two two antes rather than one. See UTH, Crazy 4 Poker, Criss Cross Poker.
- Player qualifier. The player plays against a paytable, and only gets paid on a minimum qualifying hand. Typically used when there is no dealer hand to play against. See Mississippi Stud, Criss Cross Poker, or video poker.
- Sacking the ante. A form of player qualifier where all of the value is taken out of the ante, for example pushing on wins less than a straight. See Texas Hold'em Bonus.
To be continued...
Driving Max-Bet Frequency
All High Variance Games have one thing in common, which is perhaps a secret and perhaps not. We'll get back to this some other time.