By Jeff Hwang

A distinguishing feature of poker-based casino table games is that the vast majority are multi-stage games requiring multiple wagers to get to showdown (with Pai Gow being the most notable exception as a single-bet game). These games typically start with an initial ante (or blind) wager – a forced bet – which drives the action in the game, much the same way that the antes and blinds effectively drive the action in real poker games.

The ante is essentially dead money. Assuming optimal play, the entirety of the house advantage is derived from the ante, while all wagers that come after are made in attempt to recover the lost value from the ante.

In Three Card Poker, for example, the player starts with an Ante wager and is dealt three cards. Optimal strategy is to make the 1x Play bet with Q-6-4 or better, which happens on 67.4% of hands. This strategy is enough to recover all but 3.37% of the initial ante.

That 3.37% is the house advantage.

Multiple Forced Bets
While most games start with a single forced bet, some games start with multiple forced wagers as a means of achieving certain gameplay characteristics – chiefly scalable betting, and higher betting and max-bet frequencies (see The Two Kinds of Hit Frequency and Betting Frequency and Max-Bet Frequency) – by creating more dead money.

Both Crazy 4 Poker and Ultimate Texas Hold’em – both designed by Roger Snow of SHFL Entertainment (now part of Scientific Games) – require two initial wagers to start the game. In Crazy 4 Poker, the player starts with an Ante wager and a forced Super Bonus wager, the latter of which pays according to a paytable; the player is dealt five down cards, and can bet 1x-3x the Ante, with the stipulation that the player must have a pair of aces or better in order to bet 3x. In Ultimate Texas Hold’em, the player starts with an Ante wager and a Blind wager, with the Blind wager paying according to a paytable; the player is dealt two cards, and can either bet 3x-4x the ante pre-flop, or 2x on the three-card flop, or 1x on the river.

It should be noted that no player wants to make multiple initial wagers – if the player wants to bet more, he can raise the stakes on his own. Consequently, if you are going to force the player to make multiple wagers, the player must get something back in return.

In Crazy 4 Poker, the player gets playability (betting frequency) and the ability to bet more on his good hands with a relatively high frequency (max-bet frequency). Overall, the player can bet at least 1x on 76.5% of hands, which is materially higher than the 67.4% betting frequency of Three Card Poker. The player can also bet the 3x maximum on 18.6% of hands, which compares favorably to a game like High Card Flush, in which the player can only bet more than the 1x minimum on 3.1% of hands.

In Ultimate Texas Hold’em, the benefits are even stronger.

1.     The player gets to see the river on 100% of hands without having to make another bet.
2.     The player can correctly bet and thus get to showdown on 80.8% of hands.
3.     The player can bet the max (4x pre-flop) on 37.7% of hands.

In these games, the second forced bet is used to create the house advantage. As Eliot Jacobson notes in his book Contemporary Casino Table Game Design, the main game in Crazy 4 Poker has a 31.36% player advantage; the Super Bonus bet has a house advantage of 34.78%, yielding an overall house advantage of 3.42%. Similarly, the Wizard of Odds shows the main game in Ultimate Texas Hold’em having a 29.28% player advantage; this is offset by a 31.47% house advantage on the Blind wager, yielding an overall house advantage of 2.19%.

By Jeff Hwang

The two most basic elements of betting structure are betting scalability and payoff scalability. These two elements are closely intertwined, and are as fundamental to profiling a casino poker variant as VPIP/PFR stats (essentially the percentage of hands a player plays, and how often a player enters the pot with a raise before the flop in hold’em or Omaha) are to profiling a poker player.

Betting Scalability
Betting scalability refers to how flexible player bet-sizing is in a given betting structure. There are three basic categories of betting scalability:

1.     Fixed
2.     Variable
3.     Semi-variable

A fixed betting structure is a flat betting structure with a single – fixed – bet size on the play/raise/bet wager. In Three Card Poker, for example, the player places an ante wager and receives three down cards; the player can bet 1x the ante or fold. In Caribbean Stud, the player gets five down cards and can bet 2x the ante or fold. The player can bet 1x – and only 1x – in Three Card Poker, and only 2x in Caribbean Stud.

In a variable betting structure, the player can bet within a range of bet sizes. In Four Card Poker, the player can bet 1x-3x the ante after receiving his five down cards. In Mississippi Stud, the player places an ante wager and receives two down cards, and can bet 1x-3x the ante or fold on three successive betting rounds for each of the three community cards to come. And in Ultimate Texas Hold’em, the player has three opportunities to bet once: The player can bet 3x-4x the ante on his two cards before the flop, or 2x on the flop, or 1 on the river.

Meanwhile, a semi-variable betting structure offers some betting flexibility, but generally with restrictions dictated by game rules. For example, in Crazy 4 Poker, the player can bet 1x-3x the ante, but can only bet 3x if he has a pair of aces or better.

The Three Categories of Betting Scalability
1.     Fixed: Flat betting structure, with one bet size

• Three Card Poker (1x ante)
• Caribbean Stud (2x ante)

2.     Variable: Player can bet within a range of bet sizes

• Four Card Poker (1x-3x ante)
• Mississippi Stud (1x-3x ante on 3rd, 4th, and 5th street)
• Ultimate Texas Hold’em (3x-4x pre-flop, or 2x on flop, or 1x on river)

3.     Semi-variable: Some betting flexibility, often dictated by game rules

• Crazy 4 Poker (bet 3x with A-A-x-x+, min-bet K-Q-8-4+)
• High Card Flush (bet 2x with 5-card flush, bet 3x with 6- or 7-card flush)

Payoff Scalability
Payoff scalability reflects the nature of the payoffs on the bet/play/raise bet. Are there flat payoffs, or is does the game pay according to a paytable?

In a game with flat payoffs, there is one, fixed payoff size – typically even money (1 to 1) – on the bet/play/raise bet. This is the case in most games featuring a player vs. dealer competition, including Three Card Poker, Ultimate Texas Hold’em, Crazy 4 Poker, Four Card Poker, and High Card Flush.

In a game with scalable payoffs, the player receives bigger payoffs for making bigger hands. Payoffs in these games are made according to a paytable. Mississippi Stud (played strictly against a paytable, with no player vs. dealer competition) and Caribbean Stud (played against a dealer, but with a paytable) both feature scalable payoffs.

The Two Categories of Payoff Scalability
1.     Flat payoffs: One payoff size on the bet/play/raise bet, typically even money

• Three Card Poker
• Ultimate Texas Hold’em
• Crazy 4 Poker
• Four Card Poker
• High Card Flush

2.     Scalable payoffs: Bigger payoffs for bigger hands, with wagers paid according to a paytable

• Mississippi Stud
• Caribbean Stud

Currently, only one prominent game on the market (Mississippi Stud) features both scalable betting and scalable payoffs. Given some thought, it makes sense that this is the case: It is quite difficult to let the player bet more, and win more when he wins, and still have the casino have the house advantage. 

Next: Forced Bets

Jeff Hwang is President and CEO of High Variance Games LLC. Jeff is also the best-selling author of Pot-Limit Omaha Poker: The Big Play Strategy and the three-volume Advanced Pot-Limit Omaha series.

By Jeff Hwang

Going back to the first proprietary table games developed three decades ago, virtually all poker-based table games developed since employ betting structures derived from the original smash hit, Caribbean Stud. In Caribbean Stud, the player starts with an initial ante wager and is dealt five cards, while the dealer is dealt four down cards and one up card. At this point, the player can either bet 2x his ante wager – the “raise” wager – or fold.

In some games, the “ante” wager may be called a “blind” wager, while the “raise” wager might be variously referred to as a “play” wager (as in Three Card Poker), a “call” wager, or simply a “bet” wager. In some games, the size of the play/call/raise/bet wager may be a single fixed amount; for example, in Caribbean Stud, the player can bet 2x the ante, and only 2x the ante. In other games, such as Crazy 4 Poker and High Card Flush, the player can make a range of wagers, but can only make a larger wager if he has a certain qualifying hand (A-A-x-x+ in Crazy 4 Poker, or a five-card flush or better in High Card Flush).
 
In still other games, the player can bet any amount within a certain range without any other restrictions.

Most games award the play/call/raise/bet wager a fixed amount (typically even money) on all wins when beating a dealer hand, while other games such as Mississippi Stud pay all wagers according to a paytable, and award higher payouts for bigger hands, as in video poker.

In most games, the player starts with a single initial wager, while in other games the player must start with two initial wagers (Ultimate Texas Hold’em and Crazy 4 Poker), or even three (Let It Ride). In most games, there is a single betting round after the initial ante wager; in Ultimate Texas Hold’em, the player has three opportunities to bet once (the player can bet 3x-4x pre-flop, or 2x on the flop, or 1x on the river), while Mississippi Stud features three distinct betting rounds.

Regardless, virtually all poker-based table games have distinct signatures, and can be analyzed and categorized according to at least eight basic sets of elements of betting structure:

1.     Betting scalability and payoff scalability. Is it a flat-betting game with a single fixed bet size, or can the player bet more on his good hands? Do wagers pay even money, or is it a paytable game?

2.     Number of forced bets. How many initial bets is the player forced to make to start the game?

3.     Number of betting rounds. After the initial blind/ante bet, how many betting rounds are there?

4.     Max-betting frequency and total betting frequency. What percentage of hands are playable under optimal strategy? And for games with scalable betting, how often can the player bet the maximum?

5.     Win frequency and payoff frequency. How often does the player receive money back (payoff frequency), and how often does the player win outright (win frequency)?

6.     Average bet per hand (units). How many bets per hand does the player have to make to get to showdown using optimal strategy? What is the true table minimum accounting for all units wagered under optimal strategy?

7.     House advantage and element of risk. What does it cost the player to play this game? And what is the house advantage per unit wagered?

8.     Qualifiers. Does the game use a dealer-based qualifier?

Let’s talk in greater depth about each of these elements, as well as the impact that these elements have on both game play and – by extension – game design. Click on the link below to continue the discussion.

Next: Betting Scalability and Payoff Scalability

Jeff Hwang is President and CEO of High Variance Games LLC. Jeff is also the best-selling author of Pot-Limit Omaha Poker: The Big Play Strategy and the three-volume Advanced Pot-Limit Omaha series.