if i put trash outside a villagers house will that increase their chance to leave?

There is no way to increase the odds of someone moving out. There's no percentage chance either. Like others said, it's just random.

The only two ways to move out a certain villager you don't want is:

Method 1: Time Travel. The most efficient way to do it

Method 2: Wait until someone get's a thought bubble the first time you exit your house. And if they do, do not talk to them for the rest of that day! Wait until tomorrow to see if anyone else has it that you want gone. Repeat the process until it lands on the one you want gone.

(Method 2 is the best method for both Non TTers and those that do TT)
 
I don't think placing garbage, furniture, etc., will cause a villager to be more or less likely to move out. If it is a mechanic, I've never heard of it.
 
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