The Redowaczka is basically a Galopade and a music change to 2/4 time. When the polka became the vogue, the Redowa and polka merged to become the Redowa-Polka or Half and Half. The Spanish had their "Half and Half's as well. The Menuet Afandangado is partly composed of the Minuet and Fandango. The Menuet Allmandado is intermixed with steps from the Minuet and Allemanda. Other dances as well would merge and later these mixings would be called the Half and Half.
The Modern term "Half and Half" dance was named in 1912 by Vernon Castle. It is basically a comedy routine whereas the dancers costume is half male and half female and the dancer would dance by themselves, miming the effect of dancing with oneself. The Cinquante-Cinquante which was invented by Mae Murray and Jack Mason in 1914 was a variation of the Castle's Half and Half.
The costume were generally half a tuxedo (and top hat) sewn together with the other half being a ball or cocktail gown or other costume