In case

JT: Might I enquire, Mr M, who it is you agree with?

AHD:

those beginning with if, can be tricky. In certain clauses, you use should for all three persons: if I (or you or he) should decide to go, if it should begin to snow.

Would is not acceptable in these situations, but it does appear in other kinds of conditional clauses: He might surprise you if you would give him a chance.

JT: I submit that is not acceptable because means 100% so that meaning simply has never arisen in English. It's excluded because of meaning, not any grammatical considerations. When we use , we have a conditional, a volitional meaning "would be willing to".

AHD: The best advice is to follow what sounds most natural. If you’re really not sure, try a verb form in the indicative: if it begins to snow. You can also try the subjunctive: if you were to give him a chance.

BBC English says
if you should… / if you happen to…
Note that we use should in the if-clause in the first conditional if we want to suggest that something is very unlikely.

JT: I disagree, at least that it always means, "something is very unlikely".

1) Oh, are you going to the bar? If you should run into Bob, tell him to call me.

My expectation is that Bob is often there, at the bar, and given that the bar is hardly stadium sized, "you" are going to see him. Here it must mean, "very likely or at the least likely".

It's a slightly weakend version of,

"If you run into Bob, ... ."

The AHD allows for a "if it begins to snow" to replace, "if it should begin to snow". They [and I] seem to agree that the difference is not great, certainly not as great as that suggested by the BBC English remark. More pondering is needed!

Now, I'm not saying that it can't mean "something is very unlikely". I just ran into another example that has caused me, not a little consternation but its locale eludes me at the moment.

FYI:

http://www.usingenglish.com/poll/320.html

BBC English says
if you should… / if you happen to…
Note that we use should in the if-clause in the first conditional if we want to suggest that something is very unlikely. We can use happen to in a similar way or even combine them:
If you should / happen to change your mind about coming to the beach tomorrow, give me a ring.
I don't expect him to, but if he should happen to show up, whatever you do, don't let him in!

>>>>>>>>>>>>>>

JT: I, like Mr P, am puzzled by the BBC's contention, especially given their example sentence. There are differences between BrE and AmE but I find it very difficult to believe that BrE and AmE could be so far apart on such a substantive part [modal ] of English.

I don't expect him to, but if he should happen to show up, whatever you do, don't let him in!

The first part, "I don't expect him to", and the second part, " but if he should happen to show up" are not equal measures of each other. To my mind, they are, at the least, strong contrasts, if not virtual opposites. This is illustrated by the 'but'.

Paraphrased: I think it unlikely he will show up BUT in the event that he does show up, then ...

Here I agree with Mr P that "should happen" or even a "should show up" do not express any measure of certainty. Possibly, it's a slightly softened, maybe a concessive but it basically says nothing more than "if he shows up, ...".

Mr P's example is, to my mind, more of a concessive should, like a concessive may or might, in

Be that as it may/might, we still have to consider that ...

A: Don't worry, he'll be there. I guarantee it.

B: [But] If he should decide to cancel his appointment, break both his legs.'

I will also suggest that the "unlikely should" could reflect a negative should. A negative implication of could be viewed as a positive which would be a reflection of small chance, ie. "something that is unlikely to occur, might occur; something that is unlikely to be so, might be so. It only depends on the speaker's frame of reference.

I still find it difficult to accept a positive ever being viewed as "unlikely". That's the problem I have with "man ga ichi ni".

Is it a bad translation? I mean, "bad" in the sense of inaccurate or is there some idiom being used in Japanese that I'm missing that renders the translation accurate?