Combining Cat 6 Wires To Get Different Gauge?

Good morning guys, 
 
 
I have a HAI system and have wired Cat6 to a variety of spots in the house.   I am looking to run at HAI Console (4 wire, that looks to be either 16 or 18 gauge) back to the Omnipro2 on a Cat6 cable.   Is there anyway to do that? If I combine wires (e.g. blue and blue/white) what gauge do i get?   Is there a chart out there?  Searched the net unsuccessfully.  
 
 
Cheers, 
 
Happy Holidays 
 
A simple rule-of-thumb that is often usefull is that when you combine two wires of a given gauge X the resulting guage is X-3.
 
Doesn't help if you are combining odd numbers of wires of course.
 
Here I started with the OPII legacy 5.7 serial consoles connected using cat5e and paired up the 8 wires to 4 wires. 
 
That said after I got an HSTouch console/hub; just terminated the ends (well patch panel on one side); its been fine. 
 
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