[MENTION=1861]Loonook[/MENTION] - Fantastic post.
Just the other day my friend apologized after a session he DMed that he used a random die roller on his android phone rather than rolling dice. I guess he thought that it wasn't "real" enough compared to using dice. None of the players had an issue. I then told him that I remember reading in some article or somewhere, years ago, about using a computer to spit out a whole page of each die size and just scratch them off one at a time instead of rolling. And now you just reminded me of the exact same thing.
I definitely think using print outs of random number series is a pretty good way to go for speeding things up. The game I'm thinking of trying this out with uses only 6 sided dice, so that's one big sheet of random numbers.
And of course lightning bounces off of shiney dragon scales.

That's awesome.
Really the reason behind it that I had initially setup was because I lacked extra dice to give to them... Then I sat back, realized that you could in theory generate an entire game with a roll pack, and not have to worry about it.
Dice exist because they were the most useful way to randomize at a time when PCs were in their infancy and too ponderous to take about. On this sweet device I can listen to music, write, chat with my friends from around the world... but I cannot use its ability to perform more calculations and 'rolls' than I can hope to in years of multidice rolls... To my benefit?
If I generate a sheet of rolls, just basic ones, via randomization on a simple excel sheet for 2 characters... I'm approaching almost 1000 d20 rolls/pg. If I played with my nephews using that sheet I may run through one every... 7-8 sessions? Rolling for EVERYONE AND EVERYTHING

. Of course, if each player gets a generated sheet or three at the beginning of the average gaming year they would be good to go.
No muss, no fuss... No cocked dice, no 'it rolled off the table', and no fudging. Now, in theory, your entire character year is 'plotted' for you ahead of time...
But we don't mind that in any other game. I really feel that the ability to take the dice out of the hands of everyone and leave them to a random generator speeds up the game immensely. I need to roll a Reflex Save for 12 individuals? All I need to do is have a line marking the party's Reflex bonuses on a little sheet... match it up... and then compare it to the DC. I can carry a sheaf of sheets around pregenerated that could run a decade of games.. And once the sheet has been used?
I pitch it.
If we eliminated just the d20 through such generation, removing the need to physically roll saves, attacks, skills, etc... Then if damage is generated also... And effects... Heck, how many times do you roll a d4? d12? Percentiles?
Oh what a quick game you can run. And you can provide for completely different types of benefits in combat. Of course it does require a goodly bit of DM trust, but all 'rolls' are visible at the beginning, middle, and end of each session... And it doesn't actually affect the state of play save for the removal of fudging.
FUDGE dice/d6/d10 can also be generated... Of course, since you're probably rolling more you'll need to generate a sheet more quickly.
Again, the DM must be trusted to not screw on rolls, but you can confirm all rolls via the Sheets. And half a ream of paper just eliminated an empire campaign (or more) set of rolls.
Leaving time for, you know, roleplaying

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[MENTION=83293]nnms[/MENTION]: I have to say that seeing the complete lack of focus on a die leading to the declaration that shiny scales reflect back spells and wands was glorious. Definitely made me smile

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Slainte,
-Loonook.