Idiot Savant

Idiot Savant is a perk in Fallout 4.

Effects
This perk will randomly multiply the amount of experience gained from any action that grants experience, including quest completions, making it very useful to grab at a low level so that you can maximize the amount of extra experience gained. The effect is multiplicative with the well rested bonus giving a total multiplier of 3.3 or 5.5 depending on the rank of the skill. The effect is also multiplicative with the additional experience gain resulting from having points a higher intelligence.

When the perk activates, you will see a laughing Vault-Boy above the compass, as well as hearing a laughing sound.

Despite reports from other sources, once you obtain the second rank of the perk, it grants a 5x experience bonus every single time the perk activates. There is no tiered check that determines whether 5x experience is granted, then whether 3x experience is granted.

For Intelligence of 1, this perk has a 10% chance of being triggered. This percentage decreases by 1% per point of Intelligence for a minimum chance of 1% when Intelligence is at 10. At 6 Intelligence, the chance of triggering the perk is 5%.

cliff notes

1-5 INT +any level Idiot is the best bet if you're save scumming (to minimize reloads) or don't want to put too much into INT. Idiot Savant is always worth it on average compared to INT. Even at INT 9, levels 1 and 2 of Idiot Savant are worth ~6% exp each, while INT levels are worth ~3%. 9 INT with no Idiot Savant is, averaged out, equal to 1 INT + Idiot Savant Level 1. However, to be get the same average exp as 1 INT + Idiot Savant Level 2, you need would need a boosted 16 INT. I am entirely ignoring the Level 31 L3 Idiot Savant Perk in all this, but it can obviously be hugely valuable particularly with lower levels of INT. I don't know how often the "Killing Spree" procs. This is difficult to test, and I'm not willing to put the time in. If the proc rate is too low, it might not be worth it past 1-3 INT. If it's decent it might be worth considering getting the perk, and artificially decreasing your INT (with alcohol or otherwise) when fighting large numbers of enemies to optimize gains.

When your intelligence is 0 this perk has no chance of being activated