Recube/Answer by O'Hagan

We teach the beauty of using Woolsey's Law whenever you are trying to decide whether to cube or not.  So the first you you do is ask yourself if the taker should take or drop, and how strongly you feel about it. 

Blue needs to ask himself if he's sure Red has a take.  My over the board estimates are that Red's basic 8-cube takepoint at this score (if he just takes and never redoubles) is around 25%, the 8-cube gammon values are about 12.5% for each side, and Blue's  16-cube takepoint is right around 10%.  Extreme gammon's actual figures (using the Kazaross-Rockwell MET) are 24.62%, 13.4%, and 10.56%.  So Red's takepoint is 25% plus 13.4% of Blue's net gammons less recube vig.  Rounding Red's net gammons to 40% raises the takepoint to a little over 30% and recube vig will probably lower this to around 28%.  Are Red's cubeless chances over 28% in this position?  Obviously they are, so it's an easy take.

Once you decide it's an easy take, it's generally wrong to double, but it still could be a double if there are sufficient market losers.  Generally, the only time you should send over an inefficient redouble at a normal match score like this is when you have an extremely volatile position.  In all other cases you're better off waiting.  This is not an extremely volatile position so Blue is better off taking a roll and then reassessing his position after Red rolls as well. 

Another reason not to give up the cube here is that it greatly reduces your gammon value.  The 4-cube gammon value is right around the normal 50% (.5) at this score but it goes down to 13.4% (.134) if you redouble.  This reduced gammon value will allow Red to take more chances than normal to go for the win while worrying little about getting gammoned, so after receiving an 8-cube, Red's winning chances will actually go up.
What if this position occurred in a money game?  The somewhat surprising answer (per the Extreme Gammon rollout) is that it's still not quite good enough to redouble.  If redoubling's a mistake in a money game, then you know it's an even bigger mistake at this score.

Below is the extremeGammon you can see, it would be a 28% blunder to redouble and about twice as big an error for Red to drop.