Yes, your boolean logic is correct. And a very simple thought experiment will provide a solution. If you have a 2 and a 3, will you ever call? No. Never. Unless you plan to bluff. But there are so many middling hands to bluff from that might have a chance of actually winning anyway. So there is NO REASON to call with such a crappy hand, unless you really want your opponents to think you are psychotic. Can that be used to an advantage?!?
My very limited experience with "Dogs playing poker" tells me that cards 10 and higher are helpful and cards under 8 or 9 are downright toxic. But it depends on how many players are in the end game. Fewer players allow a bit more risk, more players mean I have to bail at the least provocation.