UPDATE (DEC 25, 2021): Energy is recharged twice daily. All players now receive the same amount of energy across all 6 ladders, according to the following.
10 energy recharge (per ladder): Players owning less than 3 on-chain mons (i.e., using 1-3 off-chain Mons to play for free) will be refueled to 10 maximum energy every 12 hours across ladders.
20 energy recharge (per ladder): Players owning at least 3 on-chain Mons will be refueled up to 20 maximum energy every 12 hours, plus bonus energy based on their additional Mon holdings (see below).
Each battle costs 2 energy and forming a new team in Tournament Mode costs 4 energy (except for the first time you join each ladder with a new account, in which the energy fee is waived.)
Your energy level is displayed on your Quests & Achievements and Battle dashboards and cannot accumulate beyond a maximum amount determined by your investment in the game.
Bonus energy system
For users who have at least 3 on-chain Mons, you can still further increase your maximum energy — recharging up to 30 every 12 hours.
For each additional on-chain Mon you own (excluding on-chain starter mons: Kyari, Omnom, Mintol, Hambrisk, and Snobbit), you can increase the amount of ENERGY you receive beyond the base of 20 according to the formula below. Please note that this will still only top you off to the following max energy counts based on your Mon holdings.
Since 1 battle requires 2 energy, the following table shows the bonus energy you will receive in intervals of 2, for quick reference. The column "on-chain Mons owned" shows the minimum number of Mons you must own to receive each energy bonus.