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Let's take a first conditional sentence, expressing a real possibility:

If I do my homework, I can go out.

How to express the same real possibility in the past? If I simply change it to the past tense, it becomes a second conditional sentence:

If I did my homework, I could go out.

As far as I understand, it expresses an unreal or improbable possibility in the present. I want to express a real and probable possibility in the past (as in, "At the time when I was a teenager, if I ..."). How to do it?

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    "Could" has more than one meaning depending on context. In your second sentence it is the past tense form of "can", and means "was able to". So that second sentence does have your intended meaning. If you don't like the way "could" sounds there you could say "If I did my homework, I was allowed to go out." – nnnnnn May 21 '16 at 11:56
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If I did my homework, I could go out.

This can either be a (present) unreal conditional, or a past real conditional. It depends on context (whether you are talking about the present or the past) to determine which meaning it has. Also if it refers to the past, it indicates something that regularly occurred. This is seen in the similar sentence using would:

If I did my homework, I would go out.

when would is equivalent to used to.

Additionally, you can also use the simple past in the apodosis (the main clause) in a past real conditional:

(Back when I was a teenager,) if I did my homework, I went out...if I didn't do it, I stayed in.

This also talks about repeated or habitual activity. Compare

(Back when I was a teenager,) I went out with my friends every day.

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