Link to previous post:
https://www.reddit.com/r/CompetitiveTFT/comments/1884ab9/tft_math_tome_of_traits/
Hey everyone! Now that I’ve successfully defended my thesis on the generalized Tome of Traits math, I wanted to make an actual guide for Set 10. If you’re interested in the math behind Tomes, or just want to look at some cool 3D surface plots, feel free to take a look at my previous post.
First off, here are the important bits for Tomes:
Never have an odd amount of traits in. I didn’t break this down, but intuitively, a 1/6 chance is higher than a 1/7 chance, etc. Having an odd amount of traits in just reduces your odds with no benefit.
For most TFT sets, including every set that we have had, you never want to pop a tome with 12 traits in. You would rather manipulate your board to have 10 traits in for statistically better odds.
The difference in probability for 8 vs 10 traits in is usually negligible enough (~1%) to warrant popping it even if you don’t have 10 traits in. You still want to manipulate the board to have 8 in.
The difference in probability for 6 vs 8 traits in is usually around ~5%. User discretion is advised in regards to whether it is still worthwhile to pop a tome. Like before, you still want to manipulate the board to have 6 in.
If you’re crazy, you can try and make weird endgame boards of 3 units to guarantee an emblem. Just don’t die to creeps like the streamers do.
Now, on to the specifics.
EDM Units
EDM is the only non-unique trait that doesn’t have an emblem. This means that any EDM unit (Jax, Lux, Zac, Zed) will increase your odds of hitting the traits you want, usually by a decent percentage. Jax and Lux are the only ones, you’re likely to get early. These units also make a good choice to add to your board if you are looking to get to a new breakpoint by adding only one trait in, assuming you already have EDM in of course.
Early 3 trait units:
Early on, these units would be any Superfan (Lillia, Kennen, Neeko, Gnar), Gragas, Ekko, Sett, and Yone. Any unit with 3 traits will help you get to that extra breakpoint, especially in the early game. As you will see later, nearly every level 4 board that I calculated had Gragas and a superfan unit to hit that 10 trait breakpoint. When you are higher level, however, these may actively hurt your odds, since you never want to go over 10 traits. Another thing to note is that most of these units have a defensive trait. If you’re like me and want to see big number, you might want to wait to pop your tome when you’re a higher level and can avoid having defensive traits in. The exception is Yone, which has two offensive and Heartsteel.
Akali:
Akali is a really unique unit because she can provide 3 traits all by herself, one of them being unique. Not only that, but the traits she actually provides are really impactful emblems, being Executioner and either K/DA or True Damage. Now, the only time she actually adds 3 traits is if you don’t have true damage or K/DA on your board. But even adding 2 traits, one of which is unique, is very good for your Tome odds.
Legendaries:
4 legendaries (Illaoi, Sona, Jhin, Kayn) have unique traits, which make them like an EDM unit. Two of them (Kayn, Yorick) have 3 traits, making them like an early unit. Kayn is especially valuable since he has a unique and 3 traits, just like Akali. You’re unlikely to actually be able to use these when popping a tome, though. The legendaries do enable some super wack boards to theoretically guarantee a trait, so godspeed.