Update: At the time of writing this article I made a mistake in the formula for the 10 sim which skewed the results and distribution to the left. I will re-write the article this week with the updated values.

I’ve seen it all. From streamers to Reddit to Discord the infamous question “should I do singles or tenfolds” appears regularly. The inevitable answer that comes up always, without a doubt, starts with “well I do….”

No longer do we need to preface our “answer” with this phrase. If I’m being honest, that’s not really an answer in the first place if it’s just what you do without understanding why you do it.

In this article, I’ll talk about the best way to roll if you’re optimizing for 5s pulls as well as a simulator and some theory behind it.

The Answer

If the only thing you came here for was the answer you won’t have to go any further, just don’t forget to check out my Discord, Twitch channel, and YouTube for all my discussions, tips, videos and more!

The answer you’ve been waiting for is that it is better to do 10 single to raise pity once and as soon as pity rate increases start with the tenfolds. If you’ve watched my streams in the past I’ve explained my reasoning and always did it for rolls. However, I’ve seen all sorts of answers ranging from “it doesn’t matter” to “do all singles” or “do all tenfolds” and maybe every other permutation. I’ve tested the following: doing all singles, doing all tenfolds, doing singles to raise pity once before tenfolds, doing singles to raise pity twice before tenfolds. In the end, raising pity once with singles was the ideal.

The Simulation

Using Excel I wrote a set of four formulas to apply a simulated rolling experience for 100,000 rolls. I was going to host it on Google Sheets and offer a link here but Google doesn’t seem to like having 100,000 instances of Rand with another 500,004 cells updating based on the new results. Due to that I just left everything in Excel and made use of the i9-9900k that I bought not too long ago to have a seamless experience for myself. You can click here to download a copy for yourself or visit the Discord. If you do find a mistake in the formulas let me know! I will post a correction as needed.

Here’s one result from 100,000 rolls on a base rate of 4%:

Base Rate 4.00% Average 5s Rate (tenfold only) 4.7062% Average 5s Rate (Singles only) 4.7032% Average 5s rate (using 10 singles before tenfold) 4.9452% Average 5s rate (using 20 singles before tenfold) 4.7839%

Here’s another result from 100,000 rolls but on a rate of 6% (such as for the current gala).

Base Rate 6.00% Average 5s Rate (tenfold only) 6.4724% Average 5s Rate (Singles only) 6.4736% Average 5s rate (using 10 singles before tenfold) 6.7034% Average 5s rate (using 20 singles before tenfold) 6.5519%

As you can see from both, doing singles only or tenfolds only gives about the same results. I will cover it in the theory section why one will be higher or lower than the other in any given test. That being said, the differences between 10 singles and the straight single/tenfold options is over 0.2%. While this might seem minimal upfront, keep in mind that we get an estimated 200 rolls per month or 2400 rolls per year. Losing 0.2% chance for a 5s per roll means about 5 5s that you would have given up.

Why did you do a test with 20 singles before tenfolds test?

The simple reason was that I was checking if there was a better possibility or if the 10 singles option was the best. To understand this, think of the input as delay. When you do tenfolds from the start, you are inputting a 0 delay while singles throughout is essentially infinite delay. These two are the extremes and are equal. Once the high point is found then the remaining outcomes should trend down to the rate of infinite singles. If 20 singles was better then I’d continute on and check 30, then 40, etc. However, the search ended so soon and we’ll talk about the theory in the next section. If you’re more visual, this might help:

The Theory

No simulations for this, just a bit of thinking. Let’s take the opening 10 rolls. Let’s say you will get a 5s on the first roll. In the case of a tenfold from the start, rolls 2 through 10 will be assigned the base rate but will not continue counting to your next pity increase. This delays your pity increase over using singles. Now, let’s say you have your pity rate. Let’s say on the 11th roll you will get a 5s (you just don’t know it). Using the strategy of singles straight through, you lose 9 rolls where you would have had pity increased (12 through 20) had that been a tenfold. The strategy of using 10 singles before tenfolds removes both of the above issues of losing with respect to pity rate. The section about simulation shows a rough 0.20%-0.25% improvement which is about half the pity rate from one increase, further supporting the theory.

The Conclusion

There’s somewhat significant value in raising pity once using singles before going in with tenfolds. Over the span of 1000 rolls you are looking at 2 more 5s than if you wouldn’t have done this strategy. That being said, there is somewhat of a time commitment to doing 10 singles every time you reset and you are not guaranteed any 4s from those singles. If you are an uber whale that doesn’t care about efficiency of wyrmite/dia to 5s and just needs mass volume then by all means go with the straight tenfolds.

I hope this was informative to you! Don’t forget to check out my Discord, Twitch channel, and YouTube for all my discussions, tips, videos and more!