Letter Gift, Pickup, or Fate?

The gacha expected value is said to be 55 pulls for pickup (16,500 diamonds) and 37 pulls for fate (18,500 diamonds) for the 4-color case. For the 37 fate pulls, the actual number of pulls will be less than 37 because it doesn't account for the increased probability. Thanks to the increased probability, it's safe to say you'll never reach the pity with Fate pulls (it usually drops around 60-65 pulls). So, the actual expected value might not be that different. The advantages of each are: Pickup ・You get about 8 times more R rarity items than Fate. ・You get Witch's Invitation from milestone rewards. ・Including character coins, you get about 2.4 times more SR rarity items than Fate. Fate ・You can get magic crystals, equipment, red orbs, etc. (rarely, you can get 30,000 diamonds). ・The pity count carries over. Looking at the advantages, Pickup seems better... Disadvantages Pickup ・The pity count does not carry over. ・Since there's no increased probability, reaching pity isn't uncommon. ・N rarity items are basically trash, so if you get unlucky... it's a fatal blow to your heart. Fate ・The total diamond cost will be higher than Pickup (I'm not sure of the exact amount, but maybe a difference of 20,000-40,000 diamonds for 20 pulls?). To be continued

In short, the downside of Fate is just the high diamond cost, aside from getting fewer R and SRs. On the other hand, Pickup has the potential to be a huge miss with only Ns (given the rates, it's not unreasonable to get only Ns). Pickup's advantages are big, but so are its drawbacks... Considering the drawbacks... if R has low priority, it becomes Fate only, not Pickup. So, after Level Link is unlocked, isn't Fate enough instead of Pickup? In the long run, should we stop Pickup and Letter Gifts before and after Level Link is unlocked, and focus on limited banners... To be continued

Also, since Fate and Guidance have tickets, it's possible that the diamond cost will be lower than pickup if tickets are included. It assumes spending money, but for paying players, Fate and Guidance would be better than pickup. What about low spenders? Even if it's almost all diamonds, I think Fate and Guidance, which are easier to get stable results from, would be better in the long run. To be continued

It got long, but to get to the point: Before unlocking Level Link, it's fine to use diamonds on Pickups and Letters. After unlocking, it's better to use them on Fate and Guidance.