Kit PvP was made custom because we didn't want to just copy other servers and say to our players 'our kit pvp is better', we made it custom for 1 reason only; so that it would be fun.
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Every time you kill a player, you will earn 3 Souls and 1 Kill will be added to your stats. Souls can be used to buy Kits and Combat Upgrades in the lobby. You don't lose Souls when killed, you just get 1 Death added to your stats.
Combat Upgrades are upgrable features that can be added to your character, for example you can buy the ability to earn double souls when you kill a player, or you can buy the portable shop which allows you to buy items like food and potions half way through battle. Check out the Lobby Shop in Kit PvP when you next login and you can check out the available Combat Upgrades.
Killstreaks are for players when they reach a kill target, for example if you get 25 kills without dying, you unlock the 'Nuke' Killstreak which kills every other player on the map you are playing on. You will earn the souls and kills per player you kill with the 'Nuke' Killstreak.