Terminology for a game in which Black and White have the same "probability" to win

Question

Consider a game between two players, Black and White. The game is sequential and ends after finitely many moves. White moves first. The game ends either in the victory of one of the players or in a draw.

Let us call "probability for White to win" the ratio between the number of games that end in a victory of White and the total number of games.

Is there a standard terminology for those games in which Black and White have the same probability to win, i.e. the number of games won by White equals the number of games won by Black, i.e. there is no advantage in playing White?

Moreover, which games (are known to) fall into this category and which not, among chess, draughts, Go and so on?

Answer 1

There is no single word, you could use:

• unbiased
• nonpartisan
• fair
• neutral
• objective
• even handed
• equitable
• impartial

Answer 2

The answer to this related question is excellent.

A fair game is probably closest to what you want. However, under optimal play, the game you describe, which is sequential and finite, must always end in either black winning, white winning, or in a draw. A game that always ends in a win for one of the players is sometimes called unfair. A game that always ends in a draw is sometimes called futile but might also be called fair since it gives neither player an advantage.

That idea that white and black have equal chance of winning implies there must be randomness in your game. Checkes, chess, go have no such randomness and are either unfair or futile. Checkers ends in a draw. Chess and go are unsolved.

Answer 3

It seems that you have two or three different concepts in your question, and I'm not sure which you intended to focus on.

there is no advantage in playing White

If a game has no hidden information and no randomness and has a designated starting player and ends in finitely many moves (like Go or Chess under certain rules barring infinite repetitions), then either white has a winning strategy (even if no one knows what it is), or black does, or both can force a draw. Since Go has no draws, Go can't be fair in this sense: either black or white has the advantage under perfect play. Chess has ties in the form of stalemate, so maybe Chess is "a tie under perfect play".

the number of games won by White equals the number of games won by Black

This is meaningful, but not a very interesting definition. Consider a game in which Black selects "B" or "W" and White selects "1" or "2", and the letter Black chose determines the winner. Certainly Black wins 2 of the 4 possible games, but this game is very unfair since black can win easily. If you seat to include games like this, I doubt there's a name for this.

probability for White to win

You can talk about this, but probability would be in the context of some sort of randomized play. For example, you could take the top 100 Chess players according to FIDE, and speak of the theoretical probability of white winning if two of those players were selected uniformly randomly to play, but that doesn't necessarily tell you what perfect play would be like. I think in Chess it's suspected that White has the advantage, but in the example of Go, different play styles even among the top 10 players makes it unclear which color might have the advantage under perfect play.