I mean, the exact number isn't going to be possible to judge unless you know the generation of the great-great grandparents on the mother's side. It's not common to keep tracking after the first few generations because it stops telling you very much. For example, an F2 bernadoodle is a cross between two F1 bernadoodles - so each parent is 50/50. However, because each 50/50 parent passes on a random number of poodle and a random number of bernese genes, it's really unlikely an F2 dog has 50/50 genes from each breed.
Think of two jars of 100 marbles. One has only red marbles, one has only blue. You take 50 from each and put it into a new jar, and you know you have exactly a 50/50 mix. Now take two jars with a 50/50 mix of red and blue marbles, and randomly grab 50 from each of those jars and put it in a new one. Chances are, you have more of one color than another, right? This is a super simplified explanation of how genes are going to get passed through multiple generations without back-breeding. You don't really know how many poodle genes vs. how many bernese genes are getting passed on to each puppy after that first cross. So after a few generations of breeding, the generational number gets really meaningless because it tells you absolutely nothing about the genetics or physical/behavioral traits of the dog. This is why most places won't use beyond F3 or just say "multi-generational". You can't actually know the percentages of each breed's genetics in an individual puppy beyond that F1 cross - at least not without individual DNA tests.
The exception to this is cases like the Bengal cat, which started as F1 hybrids to Asian Leopard Cats, because some places ban higher generation Bengals because they have too much wild animal DNA, so you may need to know your cat's generation to know whether they're legal to keep. Still only useful on a legal level, not as a way to judge how your cat will look and behave.
Think of two jars of 100 marbles. One has only red marbles, one has only blue. You take 50 from each and put it into a new jar, and you know you have exactly a 50/50 mix. Now take two jars with a 50/50 mix of red and blue marbles, and randomly grab 50 from each of those jars and put it in a new one. Chances are, you have more of one color than another, right? This is a super simplified explanation of how genes are going to get passed through multiple generations without back-breeding. You don't really know how many poodle genes vs. how many bernese genes are getting passed on to each puppy after that first cross. So after a few generations of breeding, the generational number gets really meaningless because it tells you absolutely nothing about the genetics or physical/behavioral traits of the dog. This is why most places won't use beyond F3 or just say "multi-generational". You can't actually know the percentages of each breed's genetics in an individual puppy beyond that F1 cross - at least not without individual DNA tests.
The exception to this is cases like the Bengal cat, which started as F1 hybrids to Asian Leopard Cats, because some places ban higher generation Bengals because they have too much wild animal DNA, so you may need to know your cat's generation to know whether they're legal to keep. Still only useful on a legal level, not as a way to judge how your cat will look and behave.
