I'm trying to find out my chances of full custody.

It sounds like your ex wife sure has made some poor choices in involving herself with this new boyfriend. A lot depends on when you were divorced; if within the last two years there is a higher standard required to modify the placement orders; you will need to show that the current  placement arrangement of your child(ren) puts them in some type of imminent physical or emotional harm. If after 2 years, the standard is less stringent, but there is a legal presumption that continuing the current placement arrangement is in the child(rens) best interest. You will still need to show that there is a fairly compelling and significant reason why placement should be changed. If your ex wife is living with this guy, I would think that would have a more significant impact on your chances of gaining placement, rather than a situation where she may he simply dating the guy. You can also consider filing a motion with the family court to request an order that your ex wife be ordered not to have her boyfriend around your chil(ren); that may be significantly less expensive, easier and the chances of success greater, than your pursuing a full blown post divorce custody battle. One can certainly appreciate your concerns as a father for wanting to protect your child(ren) from her boyfriend and being so upset with the choices she has made.