Four-Twenty: In the smoke and fog of this annus horribilis emerges the cube position below, born in bygone years, now dubbed Reference Take Point #420. The situation was extracted lovingly from the position archives. White redoubles, and applies massive pressure on Black with the recube, an 8 pointer. Black has a powerful home board, but trails the race by several rolls. Hence Black must hit to win this game. Yet if the guns go quiet and Black misses a shot, or gets no shot at all, then Black may be sadly gammoned.

White already has two checkers off, and likely will bear off pronto into the bathtub. This position is stupendously volatile. Thus the shorter the time horizon of a volatile spot, the more the shot counts matter. Here White attacks, then Black hopes to counter the attack by hitting back. One exchange. Tit-for-Tat. The only time horizon needed. How many rolls clear White’s two blots? Or at least to safety? About one-third of the time. How many rolls leave a pair of white blots? Or just one direct blot?

Then Black must hit. Hitting a direct occurs about one-third of the time. Black will either be hitting from the bar, or in the outfield. Nobody dances in the outfield, so White will likely hit loose when unavoidable. Cut down a few return shots.

Black rewhips the cube whenever White dances, or ineffectively enters. Usually, White should drop this recube.

The volatility inherent in this position is literally off the charts; the swing between White and Black winning exceeds the wagered stake. Rollouts suggest, ballpark, that Black can still win eight-out-of-twenty games, all of them single wins. White wins 9/20 gammons and 3/20 single games.

A staggering fact is that Black can take this cube or pass it, and he loses exactly the same amount either way, four dollars. The cube is a perfectly efficient redouble. As night (and snow) begin to fall, and everyone hunkers down again, a gentle reflection on Take #420 settles softly through this April twentieth evening, like a wisp of smoke.