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Because this is our mistake, I would like to offer you a 20% discount on the reservation you made with us.

If you replace 'because' with 'since', does it sound less polite, or the same?

Thanks.
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Hi LiJ

I prefer "since" in that sentence simply because the reason being given ("our mistake, not yours") is information that is most likely already known to the listener. I don't think using "because" will actually make it any politer. It seems to me that a "politer" sentence would include some sort of apology rather than a reason.
Comments  
'Since' does sound comfortable to me, too. 
Understand!

Thanks, Amy.