"To paint the town red" is an expression that means "To have a wild time", "To enjoy oneself immensely" or "To go on a spree".
There are two likely sources for this phrase, one of which dates back to the 1850's and one of which dates back nearly two millennia.
The 'youngest' of the two origins was first recorded in the 1850s (or there about) so it was most likely in common usage for a fair amount of time prior to then.
It comes from when American Indians would burn down towns whilst on the warpath, thus giving the town a nice red outline when seen from afar. This would then have been extended to apply to cowboys who, in their search for revelry and fun, would ride in to town whooping and firing their guns in a manner that was similar to the aforementioned Indians. Thus "painting a town red" came to signify wildness and revelry.
The second source that I had comes from the Roman times.
It seems that, after winning battles, Roman soldiers used to enjoy painting the walls of the city with the blood of their vanquished foes. It can only be imagined that this would have been done with great merriment and revelry, after all they had just won a battle. So from this "painting a town red" became a term for a good, fun, night out.
There is also an opinion that suggests that the phrase just comes naturally due to red being a color that represents danger and violence in many cultures. It thus becomes natural to use this phrase to signify "to do violence".
That's it! Now go have fun :)
Charles Earle Funk - "A Hog on Ice"
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