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 advantage. By now, most Players are probably used to most of these methods, that 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 3 cards, the game would be a 100% payback. Any game in which the Player and Dealer get the same number of cards and no decisions after the initial wager is made is simply one big push.
In the game of blackjack, the Player must act first. If he busts, he loses. It won't matter if the Dealer busts also. This is an advantage for the house. The Player's ability to double down, split and decide when to hit/stick are advantages for the Player. I've often be 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!
In the game of Three Card Poker, the Player and Dealer receive the same number of cards, so that's an even game. The Player, however, gets to decide when to Play/Fold so this is an advantage to him. He can take his really weak hands and walk away from them without making another wager. He can wait for his stronger hands and Play. In the background to this process is the fact that because the Dealer always gets 3 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 advantage, the Dealer must qualify with a Queen High Hand. As a result of this, 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 - by Playing 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 that the Player will lose.
Ultimate Texas Hold'em adds a twist to the idea of Dealer qualifying. In UTH, if the Dealer doesn't qualify, the Ante wager pushes, but the Play wager stays in Play. 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 wager would pay even money. In UTH qualifying, the Ante pushes and the Play wager is in play. The Player could be left with a Queen High hand. If the Dealer has an Ace High hand, the Ante will push and the Play wager will lose. This subtle difference in how qualifying is handled gives the casino just a smidge more edge. In the case of UTH, this is the difference between the game having no house edge and having just the right amount of house edge.
Moving on, we find ourselves at Four Card Poker. Four Card Poker has no Dealer qualifying. Every hand is in play. All wagers are in play (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 cards to make his best 4-card hand. The Dealer gets six cards to make his best 4-card hand. This little 'advantage' is enough to get rid of qualifying and to allow the Player to make a 3x Play wager if he so chooses. If the Dealer were to get 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 that he will win a larger percentage of the hands.
I'm sure that if I were to look 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 provide 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 you play him in a game where you are each dealt the same number of cards. There is no real correct answer. There is simply a variety of proven methods for doing this - and probably even more that haven't been thought of yet.