棋类先手总能获胜吗？

abababa

如题。对于常见的几种棋类，比如象棋、围棋、黑白棋、五子棋，在给定的规则下，如果没有平局（某些），先手总能获胜吗？
一些小游戏也是先手总能获胜，对棋类是不是有相同的结论？

hbghlyj

What is the relation between the checkers game and math?
There is a branch of math called game theory that studies strategic interaction by rational decision makers. Game theory can be used to study many things, including checkers.

Checkers is a two player game of perfect information. By Zermelo’s theorem, there are three possible states of reality:

• The player that moves first can always win.
• The player that moves second can always win.
• One of the players can force a draw.

This is a truly remarkable result that is true of all two player games of perfect information.

Chess? Yep.

Tic-Tac-Toe? Yep.

Connect Four? Yep.

And, in fact, we know more specifically about checkers. Per an article published in 2007 which I will link below, Checkers has actually been solved. Perfect play by both players will always result in a draw.

Game Theory is a truly remarkable field unique in the depth of its mathematical beauty and the breadth of its applications. I encourage you to learn more about it.

hbghlyj

跳棋: Chinook (World Man-Machine Checkers Champion)
Perfect Play: Draw! (一场完美的比赛将以平局告终)

象棋: MacQuarrie, John (January 2005). "Mathematics and Chess, Fundamentals"
First-move advantage in chess - Wikipedia

In chess, there is a general consensus among players and theorists that the player who makes the first move (White) has an inherent advantage. Since 1851, compiled statistics support this view; White consistently wins slightly more often than Black, usually scoring between 52 and 56 percent.

(...)

Chess players and theoreticians have long debated whether, given perfect play by both sides, the game should end in a win for White or a draw. Since approximately 1889, when World Champion Wilhelm Steinitz addressed this issue, the consensus has been that a perfectly played game would end in a draw (futile game).

统计数据:
chessgames.com/chessstats.html

Number of games in database: 1,286,723
Years covered: 0 to 2022

All time controls (1,286,723 games)
White wins 482,590 games (37.51%)
Black wins 359,734 games (27.96%)
444,365 games are drawn (34.53%)

Only classical time controls (1,157,004 games)
White wins 429,600 games (37.13%)
Black wins 318,617 games (27.54%)
408,766 games are drawn (35.33%)

Only non-classical time controls (129,719 games)
White wins 52,990 games (40.85%)
Black wins 41,117 games (31.70%)
35,599 games are drawn (27.44%)