I don’t think this will shock any of you. Every table game has a house advantage.
Numerous mechanisms are used to build this house edge. By now, most players are probably used to so many of these methods they barely notice them.
If the game of Three Card Poker were played such that the player made a wager, got three cards and then simply went head-to-head against the Dealer’s three cards, the game would be a 100% payback.
Any game in which the player and dealer get the same number of cards with no decisions after the initial wager is simply one big push.
Blackjack makes the player act first. Bust and he loses. It won’t matter if the dealer later busts. This is an advantage for the house. A player’s advantages are the ability to double down, split and decide when to hit or stick.
I’ve often been quite amazed that the game of blackjack was developed centuries ago without the use of computers (obviously) and somehow managed to deliver a payback right where you would want it!
Three Card Poker sees the player and dealer receiving the same number of cards, so that’s an even game. The player, however, gets to decide when to play or fold so this is an advantage. He can take his really weak hands and walk away from them without making another wager.
The player can also wait for his stronger hands and continue. In the background to this process, because the dealer always gets three cards, the player knows what the average hand for the dealer is. In fact, he can know the frequency of every possible hand. This is what allows him to create the proper strategy for playing vs. folding.
If the game ended here, the player would have a significant advantage. To offset this and get back to a house edge, the dealer must qualify with a Queen High Hand. As a result, the dealer essentially surrenders 30% of his weakest hands and cuts the payout to the player in half.
For a small portion of these hands, a bad player might actually benefit from a hand below Q-6-4 and going against the right strategy. Despite these occasional wins, the casinos will more than gladly make up for this with all the Jack High hands the player will lose.
Ultimate Texas Hold’em adds a twist to the idea of dealer qualifying. If the dealer doesn’t qualify, the Ante wager pushes, but the play wager stays. If we were to use this rule in Three Card Poker, it wouldn’t make a difference to the overall payback because a player should fold every hand that would result in loss where the dealer does not qualify.
However, in UTH, players sometimes make a 4x wager or a 2x wager with something less than a Pair. If the hand doesn’t develop (usually you’re shooting for a Straight or a Flush), the player may be left with a very poor hand. If we used the TCP qualifying rule, the play wager might push and the ante bet would pay even money.
In UTH qualifying, the ante pushes and your wager is in play. The player could be left with a Queen High hand. If the dealer has an Ace High, the ante will push and the play wager loses. This subtle difference in how qualifying is handled gives the casino just a smidge more edge. This is the difference between this game having no house edge and having just the right amount of advantage.
Four Card Poker has no dealer qualifying. Every hand is in play as are the wagers (assuming the player doesn’t fold). So, where does the house advantage come from? The dealer gets an extra card. Despite the name of the game, the player gets five to make his best 4-card hand. The Dealer gets six to make his best 4-card hand.
This little advantage is enough to get rid of qualifying and allow the player to make a 3x wager if so choosing. Should the dealer acquire the same number of cards as the player, then each would win the same percent of hands. Even to allow an optional 1x player wager would require the adding of some sort of qualifying.
To allow a 3x play wager, the qualifying might not even be enough. Instead, the dealer gets an extra card, meaning he will win a larger percentage.
If I looked at all the games on the casino floor, I’d see a variety of other different methods for creating a house advantage. While each has a math component and provides different amounts of house advantage, the real impact of the methods is more psychological than mathematical.
How do you feel about the dealer having a stronger hand, on average, by being dealt more cards? If you beat the dealer, you might win more than you would if playing him in a game where each is dealt the same number of cards.
There is no real correct answer, simply a variety of proven methods for doing this. Probably even more that haven’t been thought of yet.
Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].