A running game is when you are ahead in the race and rush your checkers home, while a holding game is when you hold an anchor point and wait for a chance to hit the opponent. You choose a running game when your pip count is lower, so you avoid contact and simply race off. You choose a holding game when you are behind: you keep a made point in the opponent's territory as an anchor, staying safe there until a shot appears to hit a passing blot. Reading the pip count tells you which plan fits, and switching plans as the position changes is part of good play.
Backgammon
Running vs holding game in backgammon: what is the difference?
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