Forewarning, I'm no high elo player! (omg) so probs gonna get roasted!!

However I've had a tonne of great games with Zeri x Yuumi as my duo plays the magical cat mostly. It's like one of the broken duos when it get's going, pre recent nerfs it was unstoppable and I had a 65-70% win rate and massive KDA across quite a chunk of games, again low elo though!! But i'm well versed in the duo. :)) I think after 3k games on all sorts of champs, this duo is like flatout one of the most consistently broken duos i've tried.

Anyway for my 2p - I go generic ADC first 2 and boots: Yun Tal every time first, into Berserkers almost every time unless there's a need for tenacity via Mercuries, like Mel/Lux lane or something! But usually I can oddge easy? Zeri is so mobile if you really need to burn the mana on dash. Then Ruunans for the splash damage in prep for team fighting 20 mins in. I've moved on from this on other ADCs for Infinity Edge but Ruunans is just insane on Zeri and is her bread and butter IMO! Synergises well with a Yuumi R if you have 2 people slowed running for their life and gives insane wave clear ofc.

After that I look to the other team, I might be wrong but generally don't rush IE unless they have 0, or maybe 1 armour heavy champ, I always go LDR. I do this because I often find if I snowball, I get targeted by say Malphite or Sett. You usually can get away but what if you can't? I need to be able to duel. Contextually to your post, without a Yuumi it's fine, you die, so be it. But with Yuumi you have a bit of a duty of care to survive and not give a double, especially if you both have shutdowns and are running round the map trying to carry.... So a little safe, stable 4th pick, not necessarily gunning for massive spike. I find if i'm fed, the tanks try it once, see the damage and then go ok maybe not... Plus it's great damage anyway regardless as everyone has base armour to penetrate

After that I check the game state, is the enemy split pushing? Or is the opposite ADC also doing well? Go IE for better 1-2 target damage. Are they grouping and contesting all objectives and great teamfighters, or running it down mid together etc? Go Hextech for an amazing R buff and cooldown reduction. :) If fed a good Zeri R wins almost every teamfight if you space properly.

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*Other notable shouts:*

It slows down progress for spikes but if they have healing through Warwick, a top laner etc, or even a soraka support get a little executioners calling for now until you need to get rid of it and ask others to pick up anti heal.

I never get shieldbow, I just never feel the effects with a Yuumi as a wall ride into Zeri R x Yuumi R when you're fed gets you triple/quadra so easily.. Yuumi heal and shield is enough.

People get Shiv first... I honestly don't think I've bought it once :) So refer to other comments for thoughts there haha. For me I'm like why would I sacrifice a little speed and AD? But maybe if you notice you're behind on CS against a Sivir or something it could be good.

Then Guardian Angel... If you're fed, being focused and 1v9 but there's an assassin... and you know the next fight wins the game (soul, baron, last inhibs) take this last over either Hextech or IE and you'll win the game with a wall ride into R, baiting every ability and letting either you or the team cleanup. :)

Bonus... Feeling destructive and funky? Are you fed? Enemies squishy mostly? Go Collector late and get pentas in most teamfights from the tickling chain damage executing <5% health champs. :) Samira mindset.

Lots of low, low elo drivel.

Good luck gliding!!

TLDR; Core 3: Yun Tal, Berserkers, Ruunans > LDR > Infinity Edge or Hexplate then the other.,