One-pulling on Uma Banners: Brilliant Strategy or Utter Buffoonery?

One thing I’m considering for pull strategy is NOT doing 10-pulls on Umas. With any Uma banner, my strategy is to get one copy of the banner Uma I want, and then stop pulling.

With a 10-pull, we of course guarantee at least a 2 star uma on the 10th pull, but the chances of a 3 star are still 3%. The only benefit this provides over a 1-pull is more 2 star umas, which means 10 star pieces instead of 5, and 3 goddess statues instead of 1.

I think one-pulling may have greater advantages by saving carats, which are a much rarer and more valuable resource than 2 star uma star pieces. Here’s how one-pulling saves carats:

Say you’ve done 70 pulls already. Let’s just say for example, you pull the banner uma on the 73rd pull. If you do ten-pulls, then you’re doing pulls 74-80 despite having obtained the banner uma on pull 73. However, if you do single-pulls, you can stop after pull 73, thus saving 1,050 carats from not doing pulls 74-80.

With single pulls, you save potentially anywhere from 0-1,350 carats per banner (0 if you pull the banner uma on a pull number ending in 0, and up to 1,350 if you pull the banner uma on a pull ending in 1). The expected value of the number of carats saved from this method is 675.

Let’s compare this to the cost, which is forgone star pieces and godess statues. The expected value of number of pulls you must do to pull a banner uma is 1/.0075, ~133 or roughly 13 ten pulls. So the cost is roughly 26 goddess statues and 65 star pieces. 675 carats is 4.5 pulls, which averages to about 6 goddess statues (.80*1+.17*3+.03*0) and 34 star pieces (.8*5+.17*10+.03*60). So on average, you sacrifice 20 goddess statues and 31 star pieces for 4.5 additional opportunities to pull in the future.

One caveat though, is that this assumes that star pieces are created equal, which they are not. 2-star uma star pieces are inherently more valuable than 1-star uma star pieces because we will max star unlock 1 star umas prior to 2-star umas due to 2-star umas being much more rare to pull than 1-star umas.

So, is it worth it? It depends on your priorities. Do you value star-unlocking umas earlier, or do you value saving small amounts of carats more?