Badugi Dilemma

[karpov]

Before the last draw and HU you are first to act and you have A23Q Badugi, you know villain is drawing 1 because he acted out of turn when he called your bet. What is better, stay pat leaving him with a max of 8 outs or draw one and he will have 10 outs to beat you but you also have the chance to improve to a better Badugi and bet the river. By the way a 123 value bet won't work because he has such a rough hand the will only call you or raise you with a better hand. I believe there is a lot of math involve to solve this dilemma.