The chance to start any lynch that isn't mafia. Like saying you jump to any growing wagon for pressure gives you an out if that lynch happens to go through.
But why save it for another night when your chances of dying go up each time? With a 1 shot cop any info is good info. Especially since we have a potential mafia tailor. The chances of you both targeting the same person is lower at the beginning. I guess I'm just not seeing the benefit of waiting here (other than the obvious point that if you are telling the truth, you did possibly get blocked but that was an unforseen circumstance).
how can it both not create any pressure and be an opportunity for lynching someone? if the latter is true the former must also be true. Regardless of whether you disagree with the strength of the play though, it is something i very consistently do as town. I also find it far-fetched that any scum player would legitimately find it somehow helpful to swap their vote around randomly to top wagons in the hopes that it somehow results in town being lynched. I'm not seeing it as a realistic chain of thought for any player.
the math on it is a function of several variables, the two most important of which are the value of the cop shot and the probability of living to the next night. the longer you wait to use it the more valuable the cop shot becomes (if you use it the night before LyLo it can guarantee a win in some cases) and the longer you wait to use it the more likely it is you'll die before getting it off. This makes the optimal time to use it a function of determining the probability of you dying at any given night and the amount the cop shot contributes to your win-chance.
If getting the cop shot off on night 1 increases your teams win chance by 10% and the odds of you living to night 2 are 90% and getting the cop shot off on night 2 increases your win chance by 15% then the EV in terms of win-chance gain is 10% while using it on N1 and 13.5% on N2, meaning using it on night 2 is better.
In reality its basically impossible to mathematically determine the value of a cop-shot and even harder to determine exactly how much the value of the cop shot changes over time, but there is at least a logical argument to hold a shot if you believe that the value of the shot will go up more than proportionally with the risk of it not going off, which is the case here.