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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.

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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.)

Cover of "Blue Adept" showing the back of a muscular man in a mail skirt an high sandals facing a red-haired woman in a revealing red dress reclining on a red-upholstered divan.  In her hand she holds a red amulet from which a clawed red-skinned vaguely reptilian humanoid is emerging.

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    They don't make book covers like they used to
    – fez
    Commented Mar 31, 2021 at 16:23
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    Side note if I remember correctly: Serfdom is for a fixed duration (20 years perhaps?), and the pay at the end of the term is implied as well worth the time in service. The runner-up prize in the tournament is serfdom for life, and is implied to be an excellent prize. (I also dimly recall that in one round, a contest of Chance/Machine becomes a single pull on a slot machine.) Commented Apr 1, 2021 at 12:58
  • Note that humans and robots did not co-exist. Robots were considered just dumb robots, but had an underground freedom movement of the newly self-aware. The main character worked with a sexy female humanoid robot passing as human (not the one in the picture) connected to the robot underground Commented Apr 1, 2021 at 13:38
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    @CodeswithHammer Yes, 20 years and then you got your gram of Protonite and were kicked off the planet. The tournament was basically for the privilege of staying, and getting richer.
    – DavidW
    Commented Apr 1, 2021 at 13:40
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    Sure, but my point was about the OP's "humans and robots coexisted". That part was remembered incorrectly. The robot character was illegal and pretending to be a human. Not important, but it seemed the female robot stopped being a love interest as soon as he learned what she was. Piers has some odd ideas about sex, but I guess machines isn't one of them. Commented Apr 1, 2021 at 15:44

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