Yes. However we usually contract "had". So for "you had" becomes "you'd", and "I had" becomes "I'd". So I think it is possible that you just aren't hearing the 'd', but it's possible that people aren't saying it because they don't realise they are making a mistake. As Lydie says it is more American to drop the 'd' completely, and you often hear it in songs such as in the song" You better watch out "

Americans will often completely drop the 'd in speech, and doing so doesn't sound at all unnatural or incorrect. Wow, it's getting late. I better go. "I'd better go" would sound fine, but not preferable. "I had better go" sounds unnatural.

Americans almost always shorten the "had" in "had better" to just a "d" sound, using contractions like "you'd better," "I'd better," "we'd better." The "had" is still there, but it's harder to hear. In natural speech, Americans pretty much never say "had better" (it's the same as using "didn't," "isn't," and "can't" instead of "did not," "is not," "cannot"). A lot of Americans do also shorten the phrase to simply the word "better." You're right about the meaning. But the correct form is "had better," and in many cases, the "had" is just shortened in speech, so you might not hear it.

Hello! As a native speaker of British English, we generally use "had better" more often that just "better". Americans usually say "better". But even Americans, I think, say "had better" for some forceful instruction, so: "You had better be asleep before your father gets home" — this would be a strict instruction from a tired mother, whereas: "You better be asleep before your father gets home" — this would more likely be an instruction from a sibling, or a casual remark from a parent.

Another thing to consider is the pronunciation. Maybe you haven't heard native speakers say it much because we normally use the contraction 'you'd better' and the 'd' is often not heard so it tends to sound more like 'you better' instead of 'you had better'. I hope that helps!