There's another way to think about it which I actually use. Look in the empty bin and say "zero", then move an apple and say "one".

When playing games with the kids, we start at 0 being the position you are currently in, then count from there.

e.g. in snakes and ladders, if you are on spot 30 and roll a 5, tap spot 30 and say "zero", then spot 31 is "one" etc.. till you are at spot 35 saying "five".

Teaches the kids about zero and avoids miss counts from the younger ones counting their current position as "one"