Casino poker games played against the house rather than other players, among them Three Card Poker, Ultimate Texas Hold'em and Caribbean Stud, give the dealer a threshold. If the dealer's hand falls below it, the dealer has not qualified: the ante is paid, usually at even money, and the play or raise bet is returned as a push whatever you were holding. Only when the dealer qualifies are the two hands compared and every bet settled.
In Three Card Poker the dealer needs queen high or better and gets there on 69.59% of hands, counted across all 22,100 three-card hands. The other 30.41% are free ante wins, which is why folding a marginal hand costs more than it looks: you are giving up three chances in ten that the dealer had nothing.
In Ultimate Texas Hold'em the threshold is a pair or better on the dealer's seven cards, and the dealer reaches it far more often. Of the 133,784,560 seven-card hands, 82.59% contain a pair or better and 17.41% are high card only; those are the frequencies enumerated for the Trips bet, read the other way round. A rule that sounds like a small concession in one game is a large one in another, and the number of cards is the reason.
The qualification rule is not a gift. It is part of how the house edge is built: when the dealer fails to qualify, a strong hand you raised into is paid on the ante alone, and the raise that carried most of your money earns nothing. The Ante and Play house edge of 3.3730% is the whole arrangement priced, qualification rule included, and the single strategy line it produces, play Q-6-4 or better, is the one that already accounts for the 30.41% of hands the dealer will not show down.
Caribbean Stud uses ace-king as its threshold. That game has not been enumerated on this site, so no figure is quoted for it.
Where the numbers come from
- Three Card Poker Ante and Play: the 69.59% qualification rate and the 3.3730% edge
- Ultimate Texas Hold'em Trips: every seven-card hand counted
Related terms in casino floor
- Ante, A small forced bet from every player, used alongside or instead of blinds.
- Push, A tie in which the bet neither wins nor loses and the stake is returned.
- House edge, The average share of each bet the casino expects to keep over the long run.
- Blind, A forced bet posted before the cards are dealt.
Where an entry quotes a number, that figure comes from the computed sections of this site rather than from another glossary, so the definition and the derivation cannot drift apart. Each entry links to the page where the number is worked out.