Another player and I have been talking about our relative luck stats in a game we are in. He mentioned that while his luck stats are better than mine, it would be nice to have some control over when you got the good rolls versus the bad rolls. Obviously some matter more than others. :)

That made me think of Yahtzee where you roll your dice and get to choose where best to apply them. Is there some good way of hybridizing that with Risk (not on this site, but just in general)?

Maybe you roll a big set of dice to start and then select which ones you want to use for each attack and defense? And then how would you replenish them once they're gone? Would that make for an interesting game or would each player always just start with their 6s and move on to their 5s once they're done?

Better maybe to start with a small stack of like +1's or +2's or something, and be able to apply them when to your dice when you need. 

"Oops, rolled a 3 there, needed a 4: Using a +1."

Maybe you could earn them, from a territory on the board, or by accomplishing something specific - maybe they just get handed out at the beginning of the game. 

One of the house rules we used to play with was the ability to change one die (must of been once per turn) if you had the card of the country you were attacking from.

The +1s would be a lot more practical.

For the Yahtzee version, I was thinking that when making an attack you could roll as many dice as you wanted to (up to the number of units you could attack with anywhere on the board) and then select the dice 3 at a time to use. The catch would be that you had to then attack with all of them... even the bad ones. No pun intended.

Not sure what the defenders would do in that case. I guess just roll normally. But it might be fun if both players had a pool of dice to draw from and both had to decide when to use the high dice and when to use the low dice.

That would be an awesome way to simulate the "fortunes" of a real battle. Some guys are going to be effective, some, not so much. 

*Alright, heroes come line over here, and canonfodder come line up over here.*

When it comes to play on WG, one of the fundamental problems with letting players choose dice is that the defender isn't present to participate in reciprocal fashion.  But that wasn't the question posed.  So here's my idea..

Players roll and are allowed to redistribute the pips on their dice.  The primary directive is that they can't ever convert rolls such that the sum of the pips becomes greater.

Variants:

Players are allowed to create numbers larger than the number of sides on the dice.

There could be a cap on the total number of pips that can be moved.

Players are allowed to use less pips than they roll, saving pips in reserve for future battles. (send your fodder out on the battlefield first.) If for instance, this were implemented on WG, and in order to reduce the offensive players advantage, the offensive player would have to 'announce' before each roll how many pips to add or subtract from the total. The offensive dice would be rolled, pips moved, then defensive dice rolled. (Unused pips are lost on the next turn).

Obviously this works even better if the defensive player is present to alter their pips as well, but it's interesting to note that the game would play better virtually because players only reveal their dice after moving pips.