A god pack is the best thing that can come out of a booster box, and the odds of one are the least reliable number in the entire hobby. Both of those facts are worth understanding before you go looking for a percentage.
What a god pack actually is
A normal booster gives you one card from the top of the rarity ladder and a lot of cards from lower down. A god pack replaces the whole pack: every slot comes out at the top rarity. Instead of one chase card you get a pack full of them.
The name is community slang rather than an official term, which is part of why there is no official number attached to it. The Pokémon Company does not describe god packs, so it certainly does not publish how often they happen.
Why these odds are the shakiest of all
Every pull rate online is a collector count rather than an official figure. God pack odds are the worst case of that problem, and the reason is pure arithmetic.
The rarer an event, the more attempts you need before your estimate means anything. To pin down a one in 200 card you want thousands of packs. To pin down a one in 1,000 event you want tens of thousands. Almost nobody opens tens of thousands of packs of one set, so the god pack rate for any specific set is being estimated from a handful of sightings.
What you can say honestly
Three things, and no more. God packs exist and are confirmed by plenty of people who have opened them. They are rare enough that most people who open several boxes will never see one. And the published per-set figures are estimates that should be read as "rare" rather than as a number.
That is genuinely all anyone outside the printer knows. Anything more precise is somebody being confident on your behalf.
Should you chase one?
Chasing a god pack is chasing a rare event whose probability you cannot look up, for a reward you can price exactly. That asymmetry should tell you something. You know precisely what the cards are worth, and you know nothing reliable about your chance of getting them.
Our set pages give you the half you can know. Look up what the top cards of the set are actually worth, and treat the god pack as the story rather than the plan.
Related: what a set is actually worth, what provably fair does and does not prove, and which set to open.
Questions people also ask
What are the odds of getting a god pack in Pokemon?
Unpublished. The figures circulating are collector counts, and because god packs are so rare those counts are built on very few sightings.
Do all Pokemon sets have god packs?
Not every set is reported to have them, and reports come from collectors rather than from any official source, so treat set-by-set claims carefully.
Are god packs worth chasing?
You can price the reward exactly and you cannot price the chance at all. That asymmetry is the argument for treating it as a story rather than a plan.
The short version
A god pack is a booster where everything hits top rarity. Nobody publishes the odds, and because the event is so rare the community estimates for any single set are built on a few sightings. Treat it as rare and unquantified, because that is what it is.