A light stick-on-stick tap during a battle is usually fine. But when a player takes a swing at someone stick, hands, or body, that is slashing. Slashing the hands is the most common call because it can break fingers even through gloves. It is a two-minute minor penalty.
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Cross-checking
Shoving a player with your stick held in both hands. Cross-checking is when a player holds their stick with both hands and shoves it into another player. Imagine holding a broomstick horizontally and pushing someone with it. This penalty gets called a lot in front of the net where defensemen are trying to clear attackers out of the crease area. A little stick contact is usually allowed, but when a player uses their stick to deliver a forceful push, the referee calls it. It is a two-minute minor and can be a major if it causes injury.
Delay of game
Intentionally slowing down play. The most common version today is when a player in the defensive zone shoots the puck over the glass and out of play. That is an automatic two-minute penalty. Other examples include a goalie freezing the puck when there is no pressure, a player intentionally knocking the net off its pegs, or a team taking too long to set up for a faceoff. The rule exists to keep the game moving and prevent teams from stalling.
High-sticking
Hitting another player with your stick above the shoulders. High-sticking is when a player hits another player with their stick above the shoulders. If the high stick draws blood, it is a four-minute double minor instead of the normal two minutes. If a player scores by deflecting the puck with a high stick above the crossbar, the goal does not count. This happens a lot accidentally. A player will follow through on a shot or lose control of their stick, and the blade catches someone up high. Intentional or not, it is still a penalty.
Tripping
Causing another player to fall using your stick, knee, or foot. The most common version is when a player reaches out with their stick and clips the skates of the puck carrier, causing them to go down. It is a two-minute minor. If a player is on a breakaway and gets tripped from behind with no defenders between them and the goalie, the referee may award a penalty shot instead.