In the book humans and robots co-existed. The main story was about opponents playing games. Each opponent input choices into a computer which then selected the game to be played. Strength, stamina, strategy, agility were the types of characteristics a player could input. The game could be wrestling, chess, a sport, or some obscure game. A slave even had the ability to win freedom by winning the ultimate championship.
This sounds like the Apprentice Adept series by Piers Anthony, specifically Blue Adept where the protagonist, Stile, competes in the tournament to gain citizenship. The games take place on Proton; the description on Wikipedia is:
The main pastime of Proton inhabitants is The Game. When two persons want to play a round, they proceed to a Game console. There, one player chooses one of four categories: 1. PHYSICAL, 2. MENTAL, 3. CHANCE, or 4. ARTS. The other player chooses among A. NAKED, B. TOOL, C. MACHINE, or D. ANIMAL. (In this context, naked does not necessarily mean unclothed but rather unassisted by external tools.) Once the grid is completed, players continue on subgrids until they select a particular game to play. For instance, in the books, Stile plays a Naked/Arts round in interpretive dance, while later on the same category produces extemporaneous poetry. Chance/Tool covers board and card games, among others. Most sports are under Physical, but so is Tiddlywinks. Due to the wide variety of contests available, any given round could take any one of thousands of forms.
The non-citizens are serf, not slaves, however. While they don't have the rights or privileges of citizens they are not owned and are able to leave (without pay if they don't serve their full 20-year stint). If serfs serve their full 20-year term, they are paid a gram of the magic energy mineral "Protonite" that is the world's major/only export, and required to leave. The pay is enough to set them up for the rest of their life anywhere else, so it's worthwhile for a lot of people, and the life of a serf is not that bad.
The major robot character is Stile's Proton love interest Sheen, who other than being of lower legal status than a serf, is shown to be a fully-conscious being, albeit with some constraints imposed by her programming. (Sheen is distinct from Stile's Phaze love interest Neysa, who is a unicorn.)