This is made worse by the current Labs, in which a "random card in your hand" is given the dead unit's stats. Since there is randomness involved, the whole combat math are simply not available whatsoever, so you have to actually do it by hand! The madness! Seriously though, the Eye is just too good at the moment, that's why we are so dependent on it.
Some suggestions:
Whenever randomness are involved, just make an overlay over the whatever area the random effect is going to happen and write RANDOM in big red letters there. For Teemo's effect for example, the RANDOM overlay is on your library, while for the current lab, the RANDOM overlay is on each of your on-hand units.
If the damage is actually variable depending on RNG like Make It Rain for example, make a ? mark at the unit/Nexus health. You can possibly do the slight math needed to check the actual range, so I don't need the range itself need to be put there.
If the unit/champion summoned is random, eg. Thresh's level-up effect, just put a facedown card on the battlefield to let players know that there will be a random card being summoned there, similar to the additional card draw.
Of course the Riot devs are basically much better in this UX stuff than me, so I believe they'll figure out a way. But I would highly appreciate if the UX stuff doesn't get in the way of actual gameplay.
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