I have recently been playing Axis And Allies with some friends of mine on the weekends. While I totally enjoy the strategy aspect of the game I am driven to near insanity by my horrible rolling streaks.  The game is centered around 6 sided dice to decide if you hit or miss and I always roll high and miss even when the probabilities are totally on my side.  I have been brain storming and can't come to a conclusion on this solution to my problem I've come up with. My idea is to use 12 sided dice instead of 6 sided and double the attack-defend values that were in place with the 6 sided dice. Infantry which had an attack of 1 with a d6, would have an attack of 2 with a d12. So instead of having to roll a 1 with a d6 to get a 'kill', you would have to roll a 1 or 2 to get a kill with a d12.  I understand the probabilities wouldn't be changed, but I am curious if I would more consistantly roll closer to the probabilities with a d12. I am hoping this would make the game more strategic based instead of just luck.
Any comments on my d6 to d12 idea changing anything as far as consistancy would be very appreciated.

Your results of how often you roll a 1-2 on a d12 will be exactly the same as your results of how often you roll a 1 on a d6 ;)

Here's an interesting exercise for next time you play A&A, if you are up for the paperwork:  keep a record of how many times you roll against a given target number versus how many times you make it.  (e.g. let's say you attack with 3 infantry and 2 tanks, you'd record 3 at 1 and 2 at 3, and then if you hit with one infantry and both tanks, you'd record 1 hit for 1s and 2 hits for 3s.

At the end of the game, total up all your hits in each category and see how close to probability you are.  You may be surprised ;)

There's no practical difference.

If you had a system where you can have a certain number of adjustment points and can modify the roll after it was made by spending these points AND (excuse my sentence length) you get one of these points back on a six, that would lend some strategy.

In multi dice roll games (A&A or D&D), I wonder at the point actually. As rafial indicates, it'll hit an average eventually. So you just make a plan based on averages. Then you roll..simply to see if the plan falls apart. Not to see if some opponent busts out some clever move, but just to see if the plan crumbles in the face of something you can't control. Not that gambling isn't fun, but the handling time of making an overall plan in order to just gamble it all away...better to play snakes and ladders for gambling fun.

Think of it this way ..

it would be weirder and more statistically improbable if you NEVER had "streaks". These magically-mundane dice would be special indeed.