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Re: Splicing 3-strand line to double braid
I'm confused, the reason you use the 1 1/4 3 strand is strength and bounce. A splice is a weak point, and the smaller double braid you can cleat is a weak point.
Go with 12 strand, 1 inch - strength is same, fits and has bounce. It's also better looking and coils without hockles (it's what I use for a mooring, albeit 3/4 inch).
Otherwise your best bet is a modification of the single strand eye splice here (page 6) http://www.neropes.com/Resources/84906_NEROPE.pdf
I had the same reaction. The weakest 'link' is whatever fits through your chocks, and there is no point wrangling a thicker line outside it. It will not make a difference in strength of the whole line (which will break at the weakest link) and just contribute aggravation.
The exception would be if you would go to the extreme of using a steel cable or some of the modern high-tech lines through the chocks but this is not what you were asking about.