HAND - The cards that a player holds.
HARD HAND - In blackjack, a hand that doesn't contain an Ace.
HIGH POKER - Standard poker (high hands win).
HIGH ROLLER - A player who places big bets.
HIT - In blackjack, to take one more card. The card that is taken is also called a hit.
HOLD YOUR OWN - To end up even, neither winning nor losing.
HOLE CARD - In blackjack, this is the facedown card that the dealer gets.
HONEYMOON PERIOD - In gambling, new players are usually on a winning streak when they start playing. This period is called Honeymoon Period.
HOT - A player that is on a winning streak or a slot machine that is paying out.
HOUSE - A casino.
HOUSE EDGE - The advantage that the casino has over the players.