When is nothing the right answer?

I've been talking and thinking a lot about BJJ gameplans recently as try and design a plan which I can reliably train and then execute.  As I trial new ideas, refine techniques and learn from my mistakes and mis-steps I have come across a point which has puzzled me.


Is there ever a situation where the right move to do nothing?  This was prompted by a roll with Ben on Friday where he caught me in a knee-ride setup for an armbar, which as soon as I started to defend I realised was also a choke setup.  If I defended one, I'd be giving up the other.  And so I've been thinking hard about these "no-win" scenarios.  In training, it is obviously the best time to try something, make mistakes and learn from them, but what about in a competition?  Do you stall and defend and hope that you've mentally been tabulating points right?  Or do you just go for it and hope that the other person makes a mistake?  Obviously there are many different scenarios to be had, and if you were clearly in the lead then stalling would be the preferred (in terms of winning) choice.  


Assume for a moment that you find yourself in a similar "no-win" setup in competition.  You know that roughly a minute is left and you are behind on points.  Is it better to go for broke and risk it now, or wait and hope that your opponent gives you that bit of space or opportunity?


During some other rolls with people I've been able to win the positional battles, but their submission awareness and defense has been great and I've not been able to even go for, let alone apply a sub.  Stalling in a controlling position is never the morally right option, but it is a great way to win a fight.  But when your opponent has such good defense that chasing a submission is putting your position and lead at risk, is it better to choose to just stall?


I don't know what the right answer here is.  But I think I know what I'll be trying.