Much as I'd like to ... / However hard you try ... (C1 Grammar)
Start with Much as + a full sentence to mean "even though I very much ...". It is a formal, emphatic opener — reach for it instead of a plain although I'd like to when you want to stress how strongly you feel before you turn the idea down. It keeps close company with a small set of verbs for liking, wanting and admiring: like, love, enjoy, admire, respect, want, regret, sympathize. Keep the as: Much as I'd like to ...
Much as + a sentence: even though I'd really like to
Much as I'd like to help, I don't have time.
Much as she admired him, she couldn't agree.
Much as I sympathize, I can't intervene.
Not "Much I'd like to help, I can't." — say "Much as I'd like to help, I can't.". Keep the as: Much as I'd like to ..., not just "Much I'd like to".
Try it: ___ I respect her judgment, I can't support this proposal. (Much as / Much / As much) Answer: Much as — This formal concession starts with Much as + a full sentence: Much as I respect her judgment. "Much" alone drops the as the pattern needs. "As much" reverses the words and is not how this opener is built.
However + a describing word: no matter how ...
Use However + a describing word (an adjective like expensive, or an adverb like carefully) to mean "no matter how ...". It is a compact, formal-leaning alternative to no matter how, common in writing and careful speech. The describing word comes right after However, then the person and action follow: However hard you try ...
However hard you try, it won't work.
However expensive it is, I'll buy it.
However carefully she drove, she was still late.
Not "However you try hard, it won't work." — say "However hard you try, it won't work.". The describing word comes straight after However (However hard), not later in the sentence.
Try it: ___ the task seems, the team always finds a way through. (However difficult / However difficult is the task / However is difficult) Answer: However difficult — The describing word comes straight after However: However difficult the task seems. The second option flips into question order — is the task — but this pattern keeps the normal order, so the person and action follow plainly: the task seems. The third leaves out the describing word altogether, so However has nothing to attach to. However must be followed at once by the word it scopes over: However difficult.
Try as + person + might: no matter how hard they try
Use Try as + a person + might to mean "no matter how hard they try". It fronts the verb try for emphasis and is a formal, literary way to set up a real effort that still fails — reach for it in writing or dramatic speech, not casual chat, where you'd just say "no matter how hard she tried". After the comma, state the result with no joining word: the concession is already built into the pattern.
Try as she might, she couldn't remember his name.
Try as they might, they never caught up.
Try as he might, he could not open the door.
Not "Try as she might, but she couldn't remember his name." — say "Try as she might, she couldn't remember his name.". No but after the comma — the concession already lives inside Try as ... might.
Try it: Try as + a person + might means "no matter how hard they try". Which one fits? (Try as she might, she couldn't remember his name. / Try as she might, but she couldn't remember his name. / Try as she might to, she couldn't remember his name.) Answer: Try as she might, she couldn't remember his name. — The pattern is Try as + the person + might, then the result with no extra joining word: Try as she might, she couldn't remember. The second option adds but, but the concession is already built in, so but is not needed. The third adds a stray to after might, which the pattern does not take.
even if = a supposed case; even though = a real fact
Even though introduces a real fact you concede (it is true). Even if introduces a supposed or hypothetical case (it may or may not be true). Both are everyday concession words — the choice is about meaning, not formality: swapping them changes whether you are stating a fact or imagining a possibility.
Even though it was raining, the match went ahead. (it really was raining)
Even if it rains tomorrow, the match will go ahead. (a supposed case)
Even though she had little time, she finished it. (a real fact)
Not "Even if he was the manager, he still answered the phones. (unclear: it sounds as though you doubt he was)" — say "Even though he was the manager, he still answered the phones.". When the fact is real and you want that understood, even though is the clear choice. Even if is for a supposed case — and because speakers do sometimes use it to concede something known, it leaves the reader unsure which you meant.
Try it: ___ we leave now, we probably will not arrive before the gates close. (Even if / Even though / Even) Answer: Even if — Leaving now is a supposed case, not yet a fact, so use even if: Even if we leave now. "Even though" would claim we have already left, which is not the meaning; "Even" alone cannot open this clause.