If you find yourself suddenly surrounded by a whole new batch of faces, you may have been seated at a new table -- don't worry, it's perfectly normal and usually it means players have been knocked out and you are nearer to the prizes!
During MTTs, there will be times that players need to be re-seated from one table to another in order to keep an even distribution of players on all tables. There are two scenarios in which tables are rebalanced and players are re-seated:
Breaking a table and reseating all players from that table
If a player being eliminated from a tournament means the remaining player can now be seated on one less table than is currently running, a table is selected for dissolving/breaking. Players from the broken table are moved according to their position relative to the button during the last hand played at the table being done away with.
The table for breaking is selected at random by the system. The player having paid the Big Blind is given highest priority (best empty seat), then anticlockwise from that seat, each player given a lower priority.
Empty seats at other tables are evaluated according to their position relative to the Big Blind in the current hand at their table. An empty seat which would receive a Big Blind next hand is given lowest priority and each seat clockwise around the table is given a higher priority until the seat having just paid the Big Blind is given highest priority.
Starting with the best empty seat amongst all empty seats in the tournament, the player with highest priority is seated. There may be more empty seats than players which will result in some empty seats not being filled, but these will be the ones which would be the worst ones for the moving players to take, because they will be facing a Big Blind the soonest.
Balancing by reseating a single player
It will be necessary to simply balance tables when a player getting eliminated results in a table having at least 2 fewer players than at least one other table in the same tournament. Provided the number of tables cannot be reduced by breaking a table, we follow these steps:
When a table has been recognised as short of players, a random player is chosen from players at all tables with too many players (all tables with highest # of players). This player will be moved at the end of the hand currently playing at their table. The player is relocated to the seat most beneficial to them (highest priority, according to rules above) at the table needing the player. This may mean they sit between the BB and Button and actually miss a hand at their new table.
In a 9-seat tourney with 26 players, the tables are seated with 9 players at one, 9 players at another, and 8 at a third. If one player is eliminated from the 8 player table, it leaves 25 players seated as such: 9, 9, 7.
We rebalance the tables, so that there is only a difference of 1 player (max) between the tables. Hence, a player is moved from a table with 9 players, to a table with 7 players, now seated: 9, 8, 8.