If you are reading this then you might be one of the many special people that i come across that seem to think that you should never nl when a bp has just been hit in setups such as but not limited to VDLI

assuming there are six players alive including one bp that's just been hit then the game can be represented like this:

http://gyazo.com/c9e2d7c10da87ff4bdcb83f7d22301c9

Sequence of events when you misplay and lynch:

If the town lynches right now, then there is an m/5 chance of lynching mafia, where m=no. of mafia alive

assuming that the game isn't over, the mafia kills the bp and the game looks like this:

http://gyazo.com/55276ae6bf50911e09d3717af2455577

the town has a 1/4 chance of lynching the last mafia

case where there was one mafia in the original pool of unclears

there is a 1/5 + 1/4 chance of winning = 45% chance of winning

case where there were two mafia in the original pool of unclears

there is a 2/5 * 1/4 chance of winning = 10% chance of winning

Sequence of events where you don't misplay and nolynch

If the town doesn't lynch right now, after the mafia kill the bp the game looks like this:

http://gyazo.com/d5240ae3b5e863d49ed459f54246cd6a

the town has an m/5 chance of lynching the mafia

assuming they lynch and the game is not over

http://gyazo.com/dce0107b10700fd4e37b08df5a139436

the town has a 1/3 chance of lynching the mafia

case where there was one mafia in the original pool of unclears

there is a 1/5 + 1/3 chance of winning = 53% chance of winning

case where there were two mafia in the original pool of unclears

there is a 2/5 * 1/3 chance of winning = 13% chance of winning

it's true that the statistics here assume no one ever gets any reads i.e. in a 3 way 0 unclears the chance of lynching mafia is said to be 1/3, however that doesn't invalidate them

the reason that whether or not the mafia just killed is listed on the images is because it shows which team can nolynch or nokill repeatedly and which can't. In the 3rd image (5 unclears) if the mafia could nokill after one was lynched to keep it a lynch in 4 unclears then they would, but since the town was the last to kill they can't, so they have to play a 3 unclears rather than a 4 unclears game