Tournament Magic has a penalty that is applied when a player shows up to a match after the round has started. This penalty, called tardiness, falls under the Tournament Error section of the Magic Infraction Guide. It is in that category as being late does is not an infraction against the rules of the game but the rules that govern how tournaments work.
The penalty is applied immediately when a round begins and at competitive and professional the penalty comes with a game loss. But there a few mitigating factors and reasons that a head judge can use to not give the game loss. The first thing that the head judge can do is to be aware of activity in the room and make sure that the vast majority of players are aware that the round is about to start and have had adequate time to make it to their assigned match. As a whole, judges do not want to give out penalties for being late, and will try to help players get to their seats.
A second ‘tool’ that a head judge can use at competitive events is to allow players to be a bit late as long as they do in fact present their decks by the end of the time allowed for pregame actions; shuffling and presenting. This is pregame time limit is three minutes. Keep in mind that this is up to the head judge, and the head judge of an event does not have to allow this. Additionally, it is important to point out that this leeway is not allowed at professional level events.
At regular REL events it is the philosophy that it is OK to be a bit late, as the focus is on creating a fun environment. The only assumption regarding tardiness at regular events is one that applies at competitive and professional events as well. That being that once a player is 10 minutes or more late that they will lose the match. Additionally, unless a player that is this late talks to staff, that player will be dropped from the event. If you are this late for a round and do receive a match loss, it is possible to ‘undrop’ as long as the current round has not yet ended. Talk to the head judge or scorekeeper to ‘undrop’ from an event.
However the ultimate tip regarding tardiness is to make every effort to pay attention to the time limits and pacing of an event to make every effort to show up to your matches on time.