Epic Seven rate-up summons: guaranteed on summon 121, typically about 70
The featured 5★ hero is 1% a summon and guaranteed on summon 121. Half of players have the hero by summon 69; 29.9% ride all the way to the guarantee.
An Epic Seven rate-up summon takes about 70 summons on average to land its featured 5★ hero, and never more than 121. At 5 Covenant Bookmarks a summon, the average is 352 Bookmarks and the worst case is 605. Both figures follow from the two rules below.
Two rules
On a Drop Rate Up or Limited Summon, the featured hero is the only 5★ hero in the pool. The 5★ hero rate is 1% a summon, and all of it goes to the featured hero. There is no 50/50, and no off-banner 5★ hero can take the slot. The 4★ hero rate on the same summons is 4.5%, and the featured 5★ artifact has its own 1.05%.
The second rule is the guarantee. If 120 summons go by without the hero, summon 121 gives it to you. The rate does not climb on the way there. Summon 1 and summon 120 both have the same 1% chance. That makes Epic Seven's rate-up easy to plan for: a flat chance with a hard ceiling.
A flat rate also means a dry streak does not make the hero "due". After 60 summons with nothing, your next 60 have the same 45.3% chance of landing the hero as your first 60 did. The only thing the streak changes is how far away the guarantee is: it is now 61 summons off instead of 121.
How the odds build
The median is summon 69: half of players have the hero by then, which costs 345 Bookmarks. After that the flat rate makes progress slow. Each extra summon still has only a 1% chance, so the curve flattens instead of accelerating. By summon 120, 70.1% of players have the hero. The other 29.9% get it from the guarantee on summon 121.
29.9% of players pay the full 605 Bookmarks. Save for the guarantee and expect to spend about 352.
That is the practical rule. The average is what a rate-up costs over many banners, but your cost on any one banner can fall anywhere up to the ceiling. If you must have the hero, only a full 605 makes it certain. If you are saving across several banners, the average of about 70 summons per hero is the better budget. Some banners will come in well under it and some will run to the ceiling.
Why the rate-up matters so much
The Covenant Summon has a higher 5★ hero rate, 1.25% a summon, but it spreads that rate evenly across its whole 5★ pool. Each specific 5★ hero gets 0.0147%. At that rate one particular hero averages about 6,803 summons. A rate-up summon makes its featured hero 68 times likelier on every summon, and then caps the wait. For any one 5★ hero, their rate-up is by far the cheapest place to summon them.
Each hero's own rate on the Covenant and Moonlight summons is listed on the hero summon rates page. Every grade's rate on every summon type, including Mystic and Custom summons, is on the summon rates page.