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I am not a electrician, but my father was. He taught me alot, enough to do the wiring for my entire home (and tub).Be safe not sorry. Replace the existing wire with #6/4wire. Make sure the box breaker is 50 amp. and that you have the proper disconnect located 5 - 10 feet from the tub. Also you must have a GFCI breaker either at the main box or at the tub disconnect. I put my GFCI at the tub end, got the box with 50amp GFCI breaker at home depot for about $80, and put a std. 50amp breaker in the main box. Found that to be the least expensive route.Again be safe not sorry, you don't want to risk electrocution or a fire.
According to the national electric code for 3 wires in a cable or raceway, 90 deg ambient, #8 THHN is good for 55 amps. Being safe is one thing, being wasteful is another.
Definitely do not use the wire that's in place. If you follow this advice, go ahead and run #6 THHN copper...this will be greater than needed for a 50 amp circuit but, should you ever get another tub that utilizes a 60 amp circuit, the #6 would not have to be upgraded.