Normal Combos: Should You Do 3N or 5N?

I studied five hundred normal combos to figure out which you should do. Posted: May 20 '20

For a long time, I've wanted to study the different combos in the game, to get a better idea of the cards each combo type yields. This is the first data-dive in that project. My goal in this experiment was to figure out the rate of Bronzes from 3N and 5N combo types and figure out which is the best to do.

**Tl;dr:** Do 5N combos... but it doesn't really matter.

Previous Data And How My Methodology Differs

My main motivation for this research was the lack of data available. The only source of information I'd found for this was this video. While quite helpful in ballparking the yield rates, I wasn't satisfied with their methodology. Namely, the sample sizes are too small. They only did fifty 3N combos and just thirty 5N combos. This impacts the accuracy of the data, since random variations are more pronounced with small sample sizes.

With that in mind, here's how I planned out my experiment:

What? Why?
I would do a fixed number of Normal combos (250) for each type This should be a large enough sample size to have statistically significant results.
After the fact, I would normalize for the number of cards used. I would use the yield rates to simulate however many of each combo type I could do if I started with the same very large number of Normals. This would tell me if the increased Bronze yield of 5N combos would actually be worth more, given that I can do more 3N combos (because they use 2 fewer cards).
Normalizing the results is important because at the end of the day, what we really care about is how we can get the most Bronzes for the same amount of Normals.

Side note: I also made sure to track every single Normal combo I did until I reached 250, to prevent any personal bias from accidentally creeping in (i.e. ignoring results I didn't like).

Bronze Acquisition Rates

Ok, here's what I found. In 250 combos of each type I found the chances of getting a Bronze were:

Combo Type Bronze cards yielded in 250 combos Bronze yield rate
3 Normals 3N 63 Bronze cards 25.4%
5 Normals 5N 111 Bronze cards 44.4%
Obviously, this means you'll get a Bronze from 5N almost twice as frequently, so 5N is the clear winner, right? Not quite. In terms of absolute number of cards used, the rates are actually pretty close. Remember: it takes more cards to do 5N combos, so you can do fewer combos with the same number of cards.

Here's a high-quality, super-detailed, visually-stunning graph of my simulation of based on the yield rates, using the same number of cards as input: Number of Bronzes Acquired

Blue is 3N, Orange is 5N. You can see that 5N ended up yielding more Bronzes, but for the first part of the sim it was neck-and-neck, with 3N yielding more for a bit. When run many times, the lines tend to blur. Most of the time they're close to equal. When they're not, 5N is likely to be higher (though not by much).

My suspicion is that the yield rates are tuned to be equal. 44.4% is a weird rate, but it stayed steady as I did combos (i.e. it wasn't 40% one day and then 49% the next, averaging to 44%. It stayed right around 44% each time).

So if the yield rates are supposed to be equal, why did I suggest to do 5N combos at the top of the article?

The biggest difference is number of taps.

It takes four taps to do a 3N combo (select 3 cards, hit combo) vs six for 5N. But, because you spend cards faster in 5N, that combo type actually ends up needing fewer taps. A simple example: to spend fifteen cards in 3N you need twenty taps compared to just eighteen in 5N. Doesn't seem like much, until you think about just how many Basic packs RNGesus throws your way during League farming. More tangibly: to spend 3000 cards via 3N combos, it'll take you 1332 taps vs just 1200 for 5N.

You can see the separation in the graph below: Taps Per Combo


Based on this data, my recommendation would be to do only 5N combos. You use less of your time and effort (fewer taps) while perceiving more success (more happy feeling) for roughly the same number of cards. The only time I'd recommend doing 3N combos is if you're really hunting for upgrade material. But because Normal/Bronze cards have such a low likelihood of successful upgrades, I'm not sure the tradeoff is worth it over time.

Thanks for reading!

This is the first data-dive that I've published, but I have a few more in the works! Most notable is a very similar experiment with Bronze combos, along with a quick dive into the patterns I've seen in my FA Tracker. So stay tuned for those in the (hopefully) near future!