Here is a pet-by-pet mob guide to having pets, From Cats to Creepers!

Blaze

Pros- Cool, Someone a light source, Intimidates intruders
Cons- Makes annoying noises, Can attack you randomly, Hard to get into a cage without attacking it, Other players can trick it into attacking you.
Gives you- Blaze rods, Gunpowder (?Needs proof?)

An blaze is an hard pet to have. You will have to keep it in the neither ( In-less you have /spawnmob or you have eggs ). The best environment to keep an blaze in is an steel bar cage with an soul sand floor. The roof of the cage should be neither brick. You should have an iron door on it. The only known way to get an Blaze into an cage without pushing it, Is, Of course, Attacking it and running into the cage. It will run after you and come into the cage with you. Get out of the cage, And wallah, You have yourself an pet Blaze. Also, The blaze will end up forgetting about you attacking it over time! (? Needs Proof?)


Creeper

Pros:Looks extremely awesome, If you build the cage like I say you can have a chance to get an ligning creeper, Can blow up intruders.
Cons:Can blow you up, Extremely dangerous to have.
Gives you:Gunpowder

Creeps are easy. Just make any type of cage with an floor and wall, And you're good to go. I recommend
iron doors with buttons. Just attack the creeper and it will follow you, But be sure to keep a safe distance!

Spider/Cave Spider

Pros-Looks pretty cool
Cons-Can escape using glitches, Can climb, Makes annoying noises, ETC
Gives you-String, Spider eye

Spiders are as easy as the creeper but I don't recommend having one. Use the same method you use with the creeper to get it in its cage. I Recommend that the cage be an solid block cage with an glass roof. An good thing to use with spiders as an cage is something made out of glass or sand.

Ghast

Pros:Most awesome thing you can get as a pet
Cons:Makes noises, Hard to capture, Can fireball itself out of the average cage.
Drops:Ghast Tear

To capture a ghast, Make an big 50x50 platform in the neither, Then build the walls up with obsisian to 50 blocks tall. Use a fishing rod to reel an ghast into the cage, Then close the top off with glass. I also recommend putting water barriers on the obsidian walls from the inside to prevent the ghast from making an big hole with its fireballs.

Slime/Magma cube

Pros: You can break them up into little guys, They are really cool looking
Cons: They sound like an fat guy masturbating, Can glitch through corners of walls.

Drops: Slime balls

To capture an slime, Use the same Creeper way of getting in his cage ( Attacking him and he will follow you there ). The cage can be made out of anything. Use an iron door, with a lever, And I recommend it being at least 5x5. Also, I recommend making hollow corners ( Like putting pillars on the corners )

Zombie

Pros:This cage can be used as a trap for rotten flesh
Cons:They make an extremely annoying sound.
Drops:Rotten flesh, Leather armor, Iron armor (? Needs proof ?)

Zombies are easy to capture, Just put an NPC villager in an creeper-styles cage ( Iron bars without a roof ) And the zombie will come running to it. It will kill the NPC villager unless you con-seal it.

Skeleton

Pros:Can use as a protection system ( It will shoot arrows at impostors, And you ), Looks really cool, Can use as a skeleton model.
Cons: It will attack you if you leave an hole in the cage.
Drops:Bones

To get the skeleton, Just attack it and it will come after you. Lure it into your cage, That should be an cobblestone cage with an hole in it ( So it can shoot arrows at impostors ) With an wooden door.

( Ender dragon is impossible to capture, Thus it can fly through walls.



--NOTICE--

*The ones with (? Needs proof ?) are the ones i'm not sure about. Please comment with proof of this being true or untrue.

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