For Hideous Laughter, the target makes a Wisdom Saving Throw (rolls a d20, plus their wisdom save bonus - their wisdom modifier, or their wisdom modifier plus their proficiency bonus, if they are proficient with wisdom saves), against your Spell Save DC, which is a fixed number (your save DC is 8 + your casting ability modifier (whatever ability you cast with; for Wizards that's intelligence, for Sorcerers it's Charisma) + your proficiency bonus).
In most cases, this means you're save DC in BG3 will be 13-14. Most creatures will not be proficient in Wisdom saves, and will have a +1 or +2 So, they'll be slightly below 50% chance to pass the save and avoid your spell, or to put it the other way, you'd have a roughly 50% chance to stick the spell successfully.
BG3 Does not do a sufficient (or even any) job of explaining this right now.
The trouble with Hideous Laughter right now, as well, is that, as with all other saving throw spells, is that the target is given their save at the wrong time, thus meaning that you functionally ALWAYS have disadvantage with the spell, because they have to fail the save TWICE before you get any effect out of it... and Tasha's in particular is currently giving targets advantage on the save when it shouldn't, making it even harder to land.
