The Hold 'Em Family
H is for Hold 'Em
Pretty much just good ol' as-seen-on-TV Texas Hold 'Em, except it's played as Limit (as are the other four games) leading up to the final table, when the format is planned to switch from standard HORSE to No-Limit Texas Hold 'Em only.
O is for Omaha, Eight or Better
Similar to the Texas version, there's a flop, turn, and river. The biggest difference in Omaha is that players start with four cards in their hands and make their best five by using exactly two from their hands and three from the board. That means the board has to pair for a potential full house or quads, or show three to a straight or flush for either of those to be possible.
"Eight-Or-Better" refers to the fact that it's a "High-Low" split game with an eight qualifier. That is, if at least three cards eight or smaller appear on the board, a "Low" hand is possible. To vie for that Low, a player must have two cards in their hand eight or smaller that don't pair three cards on the board also eight or smaller. The Low winner (with the lowest five cards) splits the pot with the "High" winner (based on regular hand ranking). If the board doesn't have three qualifying cards eight or smaller, a "Low" isn't possible and it reverts to "High-only" (normally, biggest hand wins the whole pot).
In this game, it's possible to "scoop" both sides of the pot, winning both High and Low. Let's say you have As-2c-7s-7c in your hand and the board comes 3s-5h-8s-Jd-Ks. You can make both the nut High (using your A-7 for the best possible spade flush) and nut Low (with your A-2, the smallest two cards possible to add to the 3-5-8 on the board). Unless another player has both an ace and deuce in their hands, you'll win both halves of the pot.
Putting The Horse To Stud
Each of the last three HORSE games is a version of Seven-Card Stud. Unlike Hold 'Em, Stud is not a community card game. That is, each player uses only the cards in their hand, ultimately three face-down and four face-up. With more cards visible, players have additional information upon which to base their decisions throughout the five betting rounds.
R is for Razz
In this version, only the best Low hand wins. In figuring the best Low, straights and flushes are ignored. It's all about having the highest card in the hand be as low as possible. Since it's based on five cards, a 5-high (A-2-3-4-5 with any suits, known as a "bicycle" or "wheel") is the best hand possible here (since aces are considered low).
S is for Seven-Card Stud
In this "regular" version, only the best five-card hand wins the pot. A royal flush is the stone-cold nuts, but a mere two pair is often enough to get the job done.
E is the Eight-Or-Better Seven-Card Stud
Played just like regular Seven-Card Stud, but if at least one player has five cards in their hand all eight or smaller, it becomes High-Low split. If no Low qualifies, it's High-only.

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