I see a lot of folk getting real angry with king from about turn 2 if he hasn’t got a solid lead yet …
In a typical game the chances of the King getting an unseen turn 1 is between 1 in 14 and 1 in 7 depending on if there is a t1 conversion
turn 2 , assuming perhaps 1 kill again you are looking between 1 in 12 and 1 in 6 .
turn 3 , assuming perhaps 2 furtehr kills you are now looking at 1 in 10 and 1 in 4/5 .
turn 4 , with a total of 5 players dead and the mastermind now discoverable you are looking at about 3 in 8 maybe
turn 5 , under the normal rule of use all your abilities as fast as possible you are now out of investigates and can just guard yourself . Although at this stage if you have saved a peek , you will probably be looking at a solid 50/50 chance of getting an unseen and within that you can get the important chance of discovering the mm .
The trouble is if you are a good king at about this time you will be getting hanged because you haven’t given any info yet .Although in my mind it seems that at this later stages your investigates are far more worthwhile .