Genshin Impact 7.1 anniversary, as arithmetic. How the sign-in and mail convert to 20 pulls, what each invitation is worth in pulls saved, whether the build cost belongs in the total, and three cases where spending it loses.

Genshin Impact 7.1 anniversary: laying the accounts out
What the anniversary hands out splits into three kinds: plain currency, sign-in items, and invitations. Each converts differently, and mixing them up is how people get the total wrong.
Kind one: things that convert straight into pulls
Primogems in the mail and Intertwined Fate from the sign-in sit here. Primogems convert at 160 per pull; one Intertwined Fate counts as one pull.
Kind two: things that convert into resources, not pulls
Materials like Sanctifying Essence don't belong in the pull maths. Treat them as resin you didn't have to spend.
Kind three: invitations, which cost zero pulls
"Through Snowy Lands, Forging the Edge" invites any one standard 5-star on login, and "Tabletop Troupe: Adventure's Eve" invites one limited 5-star after its quest. These convert as pulls you didn't have to spend, not pulls you gained.
Genshin Impact 7.1: how the free side adds up to 20 pulls
Two free streams, and together they're exactly 20 pulls.
The sign-in stream: 10 Intertwined Fate
"Golden Journey, Blazing Stars" gives 10 Intertwined Fate for seven days of sign-in. One Fate equals one pull, so that's 10 pulls, or 10 × 160 = 1600 Primogems.
The mail stream: 1600 Primogems
"Letters of Good Fortune" delivers 1600 Primogems across four separate letters, and 1600 ÷ 160 = 10 pulls. Note it arrives in four drops, not one, so log in a few times to collect.
The two together: 10 + 10 = 20 pulls
Twenty pulls is 20 ÷ 90 ≈ 22% of a 90-pull guarantee line. If you were already planning to pull Vasnera, that's a fifth of the way there for free.

Genshin Impact 7.1: what each invitation is worth
An invitation isn't pulls, it's a character handed over. Convert it against what you would have spent.
Standard invitation: it removes the lottery
Standard banner 5-stars arrive at random. Inviting one on login deletes the "wait for it to drop" step, so you never budget for it.
Limited invitation: it saves the guarantee
The "Tabletop Troupe: Adventure's Eve" invitation saves you the cost of reaching the guarantee line. On the in-game cycle that line is 90 pulls, so this one is worth "up to 90 pulls", not a flat 90.
Using both together
The reason the limited invitation goes to your biggest gap: the standard pool is always there to roll against, and a limited banner isn't. Spend the standard invitation on a hole in your roster, and the limited one on whoever you were going to pull anyway. When both are missing, the limited invitation goes to your biggest gap.

Genshin Impact 7.1: three cases where spending the 20 pulls loses
Once the sums are done, three kinds of player lose by using them.
Case one: pulling just to fill the archive
If the two invitations already complete your collection, pulling further only buys duplicates. Keeping the pulls is worth more.
Case two: treating the sign-in pulls as compulsory
Intertwined Fate doesn't rot, but treating it as "must spend now" pushes you into banners you never wanted. That's the most common loss.
Case three: leaving the build cost out
Pulling is only the first sum. Artifacts, talents and Mora are the second. A character you can't afford to build means the maths isn't finished.

Genshin Impact 7.1: the questions left after the sums (FAQ)
Can I claim both invitations?
A: Yes. The standard invitation is on login; the limited one needs the "Tabletop Troupe: Adventure's Eve" quest completed .
How many pulls does the anniversary give for free?
A: 20. Seven days of sign-in gives 10 Intertwined Fate (= 1600 Primogems = 10 pulls), and mail adds 1600 Primogems
Where do the 1600 Primogems come from?
A: "Letters of Good Fortune" delivers them across four letters, so they arrive in stages rather than at once .
Is Vasnera worth pulling?
A: She lets the team trigger a star Swirl reaction, which pays off only with the right partners. Without them, spend the free 20 pulls first .
Standard invitation: new character or a constellation?
A: Missing a main DPS, take the DPS slot; one constellation short of a key breakpoint, take that. If neither is missing, fill the roster gap.

Scope note:The 160-Primogem conversion and 90-pull guarantee are in-game values and are marked as such; nothing is extrapolated. Day-by-day character material lives on gghubs.com's Genshin Impact section.
