What is a healthy large-kibble food to use for training as well as regular feeding? Smaller kibble of most dog food falls through my fingers too easily.

Well, not knowing anything about your dog, I'll still say that regular kibble may not be the best choice for marker training. This is just MHO. I use a higher-value food reward.

Agree 100% with Connie. The dog needs to look at whatever treat you uses as a reward worth performing for and not just meal time.

I reward my dogs with little pieces of raw meat (different types), sometimes a bit of white cheese, which they adore. If they have performed an exercise especially well, they sometimes get a meaty bone, they are so keen on, but not too often, because gnawing on it slowns down they training. I weigh the portion for the whole day adjusted to individual weight and use half of it twice a day. Maybe that they get something extra for a very short surprise-session in between.
So they don't need any other meals. At least for my dogs this works well and I can cut the pieces to the sizes which is most practical for them.

Sounds good!

In re larger kibble or high value incentive bits in training.

In the first instance, I use the palm of my hand to provide the treat or reward, because I value my fingers. Once burned twice warned. And the size of the bit is less an issue.

I am kind of a contrarian in that I use the kibble I feed the dogs as a reward. And I sometimes use a bigger reward at the conclusion of a session.

Apparently I love the pronoun I. What does that imply?

Anyway, as a dog health priority, I keep kind of a running tally of the calories consumed by my dogs throughout the day. And the total should approximate the optimum level of calories for the size and efforts of the dog for the day inclusive of meals and rewards, in my opinion.

In point of fact, I have tried all kinds of high value rewards over the years, and some the dogs devour and some they aren't thrilled about. But they all accepted the kibble with enthusiasm. I wonder if I am starving them. Nah.

In truth, I use food rewards sparingly in favor of tactile and voice praise. I have worked with dogs whose owners were obsessed with treat rewards to the point where the dog trained them. If the dog sensed no reward was likely, it would all but ignore the exhortations of the owner. Funny and not so much at the same time.

The original question had to do with larger kibble bits for rewards. Little kibble bits taken from a pouch and in the palm of the trainer's hand will work fine. Bigger is not necessarily better, I think.

What do i know. Just two cents.

Since my dogs are raw fed, they actually think that a high quality kibble is a treat.

I agree with Mike, though on size. Small is fine as long as you deliver it correctly. If you get into larger rewards, the dog may take more time to eat it so you don’t get as many reps in. Larger size also means more calories and may limit your training time in that way, since you will be limited in how much you can give them as a reward treat.

If you are feeding kibble as well, maybe find an exotic flavor and use that for training only to keep it somewhat novel for the dog.