Activate Bartolomé del Presidio by sacrificing Gollum.
When Gollum dies, it and Ratadrabik trigger.
Resolve the Ratadrabik trigger, creating a  nonlegendary token copy of Gollum that is a 2/2 Zombie in addition to its other types.
Resolve the Gollum trigger from step 2, causing the Ring to tempt you, and for the Gollum token to become your Ring-bearer, thus making it legendary.
Resolve the Bartolomé del Presidio ability from step 1, putting a +1/+1 counter on it.
Repeat.

Infinite +1/+1 counters on a creature

Infinite death triggers

Infinite ETB

Infinite LTB

Infinite sacrifice triggers

Ratadrabik of Urborg

Gollum, Patient Plotter

Bartolomé del Presidio

Activate Skirge Familiar by discarding Gollum, adding {B}.
Bone Miser's first ability triggers, creating a 2/2 Zombie creature token.
Activate Gollum by paying {B} and sacrificing the Zombie, returning it from your graveyard to your hand.
Repeat.

Infinite self-discard triggers

Bone Miser

Skirge Familiar

Activate Skirge Familiar by discarding Gollum, adding {B}.
Activate Gollum by paying {B} and sacrificing a creature, returning Gollum from your graveyard to your hand.
Tormod triggers, creating a creature token.
Repeat.

Tormod, the Desecrator

Activate Mind over Matter by discarding Gollum.
Bone Miser's first ability triggers, creating a 2/2 Zombie creature token.
Resolve the Mind over Matter ability, untapping a mana-producing permanent.
Activate the permanent by tapping it, adding at least {B}.
Activate Gollum by paying {B} and sacrificing the Zombie, returning it from your graveyard to your hand.
Repeat.

Mind Over Matter

Activate a permanent by tapping it, adding at least {B}.
Activate Mind Over Matter by discarding Gollum, untapping the permanent.
Activate Gollum by paying {B} and sacrificing a creature, returning Gollum from your graveyard to your hand.
Tormod triggers, creating a creature token.
Repeat.

Activate Hardened Academic by discarding Gollum.
Activate Gollum by paying {B} and sacrificing a creature, returning Gollum from your graveyard to your hand.
Kheru Goldkeeper and Kheru Goldkeeper trigger, creating a creature token and a Treasure token.
Activate the Treasure by tapping and sacrificing it, adding {B}.
Repeat.

Combos with "Gollum, Patient Plotter"