80's sci fi book, players picked random game elements to compete

Question

I'm looking for the title of a book I read that always stuck with me. Some kind of sci fi society in which people competed in games. Each competitor picked random elements like "Cold", "Water", "Low Gravity", "Strategy", "Dexterity" and the game computer would come up with a game on a world that fit all those elements. I just remember it being so ingenious!

Answer 1

This definitely reminds me of "The Game" in the Apprentice Adept series by Piers Anthony.

Quoting the series Wikipedia page about The Game:

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.

The first book of the series, where The Game was introduced, was Split Infinity (1980) which definitely fits your timeframe.

A description of the selection mechanism, and the deeper menu tree:

They went to a booth and played the Grid. Stile had the numeric facet; good. He regarded that as more fundamental. He would not choose MENTAL, of course; this was not a fun challenge where he wanted a good Game, but a serious challenge where he needed to win with least risk. He did not care for the 50-50 chance that CHANCE offered. Tome was pretty fair on machine arts, such as the theremin, so that was not a good risk. So it had to be Stile's strong column, PHYSICAL.

Tome chose MACHINE, of course. Immediately the subgrid showed:

1.MOTION 2. ACTION 3. OBSERVATION

Nine types of machine-assisted competitive sports, ranging from cycle racing in 1A to stellar location in 3C. Stile had the letter facet of this grid, unfortunately; he could not select the machine-racing column, and knew that Tome would not. Tome would go for observation-unless he figured Stile for water. That would put them in 3B, which amounted to sonar location of sunken ships. Tome was not really sharp at that. But he was a fair hand at water-hydrant dueling, so might go for ACTION. Therefore Stile went for AIR instead.

He won. It came up 1C: dueling by guns, lasers, and similar powered distance weapons. Tome was good at this, but Stile was better, and both knew it.

Answer 2

I suspect you're thinking of Split Infinity, first book of the Apprentice Adept series by Piers Anthony.

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