Idiot Savant

Idiot Savant is a perk in Fallout 4.

Effects
For ranks 1 and 2, the perk randomly activates whenever you gain experience from any source, at a rate equal to


 * $$%Chance = \begin{cases} 0, & \mbox{if }Intelligence = 0 \\ \text{min}(1, 11 - Intelligence), & \mbox{if } Intelligence > 0\end{cases}$$

When the perk activates, you will see a laughing Vault-Boy above the compass, as well as hearing a laughing sound. The experience you would have earned will instead by boosted by 3x (for rank 1) or 5x (for rank 2+). This boost is multiplicative with any normally additive experience bonuses from being well-rested or having a high Intelligence.

The probability for the "kill bonus" from rank 3 appears to be independent of the bonus experience from rank 1 and 2 and the probability of it triggering is currently unknown.

Comparison to Intelligence
When comparing a perk point to put into higher Intelligence or Idiot Savant, it is worth comparing the returns you get. Each point in Intelligence returns ~3%. For a non-save-scumming player (i.e. not reloading constantly before a quest turn-in to always trigger the higher experience), a point in Idiot Savant returns on average around 2% in the non-degenerate worst-case, when your player character has 10 Intelligence. At any lower Intelligence, Idiot Savant rank 1 gives superior returns to experience. The same holds for ranks 2 and 3 for Idiot Savant.

In other words, for non-save-scummers, for all but the smartest player characters (e.g. Intelligence 9 or lower), Idiot Savant still provides superior returns on expected experience gain.

For save-scummers and non-save-scummers alike, however, the biggest returns are at low Intelligence. At 1 Intelligence, the first point in Idiot Savant provides a whopping 20% expected return on experience gained. Even at 5 Intelligence, your player character is still expected to get ~8% gain on experience, though the gain is obviously less dramatic.

The upshot is that players at 1-3 Intelligence will benefit the most from Idiot Savant. Non-save-scummers get extremely high expected returns on experience gained. Save-scummers also benefit from low Intelligence since each additional point in Intelligence has increasing returns in how difficult it is to trigger the Idiot Savant event: at 4 Intelligence, you've already almost doubled how hard it is to trigger the Idiot Savant event.

Trivia

 * You can potential exploit any quest for a huge amount of experience. This can be done via saving before finishing a quest and reloading the game until the perk triggers the multiplication.