Each challenge at the Battle Dome is a tournament between 16 Trainers.
Before each battle, the player can find out about their opponent, such as the Pokémon they use, their battle style, and how they train. Then, both Trainers choose two Pokémon from their three-Pokémon party to use in battle. Competitors can find out who was eliminated in each round by looking at the tournament bracket.
Seedings are determined by their ranking: the sum of the combined base stat totals of all Pokémon, plus 1/20 of the product of the number of different types represented by the Pokémon and the highest level among the Pokémon. If two Trainers tie in ranking, the higher internal Trainer number will win the tiebreaker; the player will always win the tiebreaker against any CPU Trainer, while Dome Ace Tucker will win any tiebreaker against other CPU Trainers. In the event of a tie battle, the higher seed advances and the lower seed is eliminated.
The battle style of a Trainer is solely determined by the effort values of all of the Trainer's Pokémon. A stat is considered to be emphasized if it makes up at least 30% of the team's EVs (taking Nature into account: for this calculation, EVs on a Pokémon with a beneficial Nature are worth 10% more, while EVs on a hindering Nature are worth 10% less), and neglected if there are no EVs in that stat among the entered Pokémon.
If there are any emphasized stats, they are shown (if there are three emphasized stats, only two are shown). Otherwise, if there are any neglected stats, they are shown (if there are more than two, only two are shown; the ones that are shown are further influenced by the number of entered Pokémon having a hindering Nature in the particular stat). Otherwise, the Trainer is said to "raise Pokémon in a well-balanced way."
Note that the game does not simulate battles between two CPU Trainers. Instead, the outcome between two CPU Trainers is broken down as follows: each Trainer is scored based upon the sum of the following:
The type affinity of damaging attacks: each attack dealing damage on the team is compared against each Pokémon on the opposing team. 4 points are awarded if the attack is normally effective, 12 if super effective, and 20 if 4× super effective. No points are awarded if the attack is resisted. 8 points are deducted if the attack is 4× resisted, and 16 points are deducted if the attack is ineffective. For the purposes of calculating this, Ground-type attacks are considered to be neutral against Pokémon with Levitate. Against Pokémon with Wonder Guard, type matchups that are not super effective do not award nor deduct points.
The sum of the base stats of all Pokémon, divided by 10
The seeding of the Trainer, minus 1
A random value from 0 to 31
The Trainer with the higher score advances; if this is a tie, then the higher-seeded Trainer advances. During tournaments in which he may be challenged by the player, Tucker always appears as the #2 seeded contestant, and will always win his battles against CPU opponents.
CPU Pokémon Selection
To determine the Pokémon sent out by a CPU Trainer against the player, each of the CPU Trainer's three Pokémon is given a score. There are two scoring methods, which are chosen at random: the offensive method and defensive method. Both methods compare the type affinity of the Pokémon's damaging attacks against each of the three Pokémon on the player's team. In the offensive method, 2 points are awarded if the attack is normally effective, 4 if super effective, and 8 if 4× super effective. In the defensive method, 2 points are awarded if the attack is resisted, 4 if 4× resisted, and 8 if ineffective. 2 points are deducted if super effective, and 4 are deducted if 4× super effective. No points are awarded or deducted in any other scenario. For the purposes of this calculation, type matchups that are not super effective against Pokémon with Wonder Guard are ignored (no points are awarded or deducted), and Ground-type attacks are considered to be neutral against Pokémon with Levitate.
If all three Pokémon tie in one method, the other method is used. If all three Pokémon tie in the second method, then two Pokémon and the order they appear are chosen at random. Otherwise, the two highest-scoring Pokémon is chosen (if there is a tie for the second selection, the second selection of Pokémon is chosen at random). There is a 40% chance that the CPU Trainer will lead off with the higher-scoring Pokémon, and a 60% chance of leading off with the lower-scoring Pokémon.
This section is incomplete. Please feel free to edit this section to add missing information and complete it.
After the player has won five and ten championships, Dome Ace Tucker will challenge him or her. On his defeat, he awards the Tactics Symbol.
Tucker uses two of these Pokémon when battling the player.
In the Battle Dome, challengers have to defeat the Dome Ace in a Double Battle. They are given the possibility of swapping their party Pokémon with ones they have in storage after the Frontier Brain has revealed his Pokémon. After a tough match, Ash managed to defeat Tucker using his Corphish and Swellow. This victory gave Ash the Tactics Symbol, his third Frontier Symbol overall.
Pokémon used in the Battle Dome
The following is a list of Pokémon used in the Battle Dome:
Swampert was one of the two Pokémon that battled against Ash's Corphish and Ash's Swellow, and gave Ash a run for his money. Swampert and Arcanine seemed like a perfect combination, taking advantage of Arcanine's speed and its defense as stated by Brock in the episode. In the Double Battle, Swampert's main target was Corphish. Even though it looked bad for Ash, after Tucker used the Fusion of Fire and Water, Corphish and Swellow gained their fighting spirit and came back to win the match for Ash. Swampert was defeated by a devastating Aerial Ace from Swellow.
The other Pokémon Tucker used was Arcanine. Swampert and Arcanine were a perfect combination, taking advantage of Arcanine's speed and Swampert's defense. Even though it looked bad for Ash, after Tucker's Fusion of Fire and Water, Corphish and Swellow gained their fighting spirit and with the help of some strategy of Ash's, they were able to win the match. Arcanine was defeated by a devastating Crabhammer from Ash's Corphish.
The Battle Dome first appeared in Verily Vanquishing Vileplume I, where Emerald challenged it as his fifth Battle Frontier facility during the Battle Frontier's seven-day opening ceremony. Due to the tournament-style structure of the challenge, Trainers were shipped from the Hoenn mainland over to the Battle Frontier to participate in it to avoid endless battles between computer-controlled virtual Trainers. Amongst the participating Trainers were Ruby and Sapphire, who tried to make friends with Emerald, much to his annoyance.
During the semifinal battle between Ruby and Emerald, Ruby revealed that Emerald's Sceptile was the very same Treecko that Emerald had once been supposed to receive from Professor Birch. As Emerald defeated Ruby and Sapphire was defeated by Tucker, Emerald and Tucker were set to face each other in the finals. However, Emerald abruptly requested the permission to swap his party Pokémon with ones from Crystal. Although this was against the rules, Tucker allowed it. However, Emerald's borrowed Alakazam and Metagross both wound up getting defeated by Tucker's Charizard, resulting in Emerald's first loss at the Battle Frontier.
In Epilogue, after Emerald had managed to obtain all six other Symbols, he realized that he only had one day left to earn the Tactics Symbol. While the Battle Dome was still operable, despite the damage that Guile Hideout had caused to the Battle Frontier, the challenge required a group of Trainers to form a tournament. To everyone's surprise, Red suggested a tournament between the ten Pokédex holders, which Scott happily accepted. By the end of the round, Emerald was shown to have earned the Tactics Symbol, indicating that he had won the tournament and thus successfully completed his seven-day Battle Frontier challenge.
In Pokémon Adventures, the Trainer who wins the Battle Dome challenge always earns the Tactics Symbol, regardless whether Tucker makes it to the finals or not.
In the Pokémon Battle Frontier manga
The Battle Dome in Pokémon Battle Frontier
The Battle Dome appeared in Introducing the Frontier Brains!. After learning about Frontier Brains, Enta decided to challenge each of them, starting at the Battle Dome. After achieving a long-enough win streak, Enta came face to face with Tucker, who challenged him to a Double Battle. After a tough match, Enta was able to defeat Tucker with his Vulpix and Feebas. At first, Tucker was unwilling to admit that Enta could've beaten him with a Pokémon as ugly as Feebas, but he changed his mind when Feebas evolved into Milotic.