Revision f164bd83-2b83-4069-8c5e-cdf8e7af2f16 - Code Golf Stack Exchange

# Python 3, <s>197</s>196 bytes

<!-- language-all: python -->

 from random import*;c=choice;r=range(1,7);u=c(r);l=c(list(set(r)-{u,u^7}));print(r''' ________
 /\ \
 / \ %d \
 { %d }-------}
 \ / %d /
 \/_______/'''%(u,l,3*u*l*(u*u-l*l)%7))

Test it on **[ideone][1]**

Right-handed (switch to a lefty by swapping `u*u` with `l*l` on the last line)

Bound to be beat - but let's get the dice rolling *sigh* - especially since all my attempts to golf the ASCII except going raw and using old-school formatting all failed to save bytes; 
- any further golfing tips for a n00b gladly appreciated.

 [1]: http://ideone.com/uulCzl