The 25 percent take point
When doubled, a player should accept whenever their winning chances are at least 25%, because declining forfeits one point for certain while taking and losing costs two points, and taking and winning gains two. At exactly 25% the expected value of taking equals the certain loss of passing, so the decision reduces to comparing estimated winning probability against this break-even threshold. Gammons and cube ownership shift this line, which means you must price the bet rather than simply ask whether you are the favorite.
