Infinity Tower

The Infinity Towers are a set of incredibly challenging Dungeons in which your pets climb different elemental towers to gain Infinity Points and tier 3 and tier 4 Crafting materials. To unlock the Infinity Towers, your total Pet Dungeon Levels need to exceed 3,000 for your top 36 pets.

Tower Types
On each trip to the Infinity Towers, your pets may select which tower to visit, and how many hours to spend there.

On your first expedition to a given Infinity Tower, your pets will begin on floor 0, and will require 1 hour to complete that floor. If the trip lasts more than 1 hour, and if your pets don't fall in battle, then the second hour will be spent exploring floor 1, the third hour on floor 2, and so on.

On subsequent trips, your pets may choose to start on any floor number they have previously completed. E.g. if you begin a 4-hour trip starting on floor 5, your pets will attempt to complete floors 5, 6, 7 and 8. If you have purchased Infinity Repeat for 300k pet stones then you may choose to stay on your starting floor, rather than advancing to a more difficult floor each hour.

Enemies in the Infinity Towers receive an additive 40% bonus to their HP, defense and speed, and an additive 50% bonus to attack, per floor. For example, an Ice Queen on floor 0 has 1600 HP and 100 attack. On floor 1, she would have 40% more HP and 50% more attack (2240 HP and 150 attack); on floor 2, 80% more HP and 100% more attack (2880 HP and 200 attack); and so on.

It is important to note that while pet special abilities work in the Towers, Undine's special does not work if Hourglass is on the same team.

Strategy Guide
One of the top players made a small guide about what teams to use:

https://docs.google.com/spreadsheets/d/1W-66_97GUJevWRhvEmMc8W_wO1ZTC9aaXPBq-BnkKqE/edit#gid=818485860

Each Tower (other than Elemental) has a single type of enemy. You can customize your team to counter that specific foe.

Neutral Tower: Damage reflection is rough. Optimize your damage-dealers for HP (blue gems) so they don't die from the reflection, and lean on Supporters for much-needed healing. Succubus (self-healer when attacking) is especially useful.

Water Tower: Enemies heal each other and freeze you. High water element will resist the freezing a bit. You need to hurt them more than they heal, or you risk going to round 51 and losing that way. Emphasize damage output first, and water element protection a distant second.

Fire Tower: Enemies hit you very hard. Kill them as quickly as possible (emphasizing attack, speed and non-fire offensive element). If you can't kill them in one hit, you'll want a strong fire defender.

Wind Tower: Enemies are very fast, so you'll be taking a lot of speed damage. Emphasize HP (defense doesn't work against speed), and use good Defender(s) and Supporter(s). Elephant is quite useful.

Earth Tower: Enemies have extremely high defense, and they heal each other. You need to hurt them more than they heal, or you risk auto-losing on round 51. Virtually all of your damage will come from Speed, so prioritize that. Mages are preferred, because they get the Speed damage bonus to each enemy they hit.

Infinity Points
Each Tower will give Infinity Points of its corresponding type. Each Floor of the towers will give points equal to the Floor #. This is currently capped at a max of 50 points.

For example:
 * Floor 0 = 0 points.
 * Floor 20 = 20 points.
 * Floor 50 = 50 points.
 * Floor 60 = 50 points.

Infinity Points may be spent to purchase the following:

After Purchasing the 6th Dungeon Team, you can convert Elemental Points into the other elements at a rate of 5:1 of each. For example:
 * 500 Elemental Points will become 100 of every element.
 * 5000 = 1000 of each.
 * 50000 = 10000 of each.

Drops
Monsters in the Infinity Towers have a chance to drop T3 and T4 materials. The drop chance is (floor #)% per enemy for T3 mats and (floor # / 20)% for T4 mats. Rogues or other dungeon drop increase effects have no influence on the drop rate. Like with other dungeons, the drops are lost if you die.

For example:
 * Floor 20 ⇒ T3 = 20% and T4 = 1% per monster
 * Floor 40 ⇒ T3 = 40% and T4 = 2% per monster
 * Floor 60 ⇒ T3 = 60% and T4 = 3% per monster
 * Floor 80 ⇒ T3 = 80% and T4 = 4% per monster