One of my pet peeves in gaming is games that require rolling buckets of dice, meaning routinely rolling more than, say, 5 dice. Typically this is used with D6 in order to get a proper distribution of results. But whatever the reason I find it very slow and clumsy. Rather than rewrite rules such as Flames of War (which I enjoy) I found a way to replace these handfuls of dice with a simple system that uses 2d6.
You play the rules just as written but rather than roll, say, 15 dice, you roll two and read them like percentile dice. So one dice (say, a red one) is the “tens” digit and the other (say, a white die) is the “ones” digit. Thus a red 3 and white 2 is “32.” A red 4 and white 1 is “41.” Much faster and simpler.
Now, you simply look up the result of the two dice on a chart to see how many successes you had. Here is the chart for rolling 15 dice:
Simply identify the score needed, roll your dice, then read to the left to see how many successes you rolled. Needing a 4+ and rolling “43” we read left and see we rolled 8 successes. This works for shooting, saving throws, etc. No more counting dice, no more checking which are hits. Roll 2d6 and read.
The charts map very closely to the probabilities of actually rolling all the dice, though they do eliminate 1 in a million results. For example, needing 6s you can’t get 15 hits on the chart above. But likewise, needing 2s you can’t get 0 hits either.
When dealing with numbers for which there is not a chart  for example, 13  consult two charts and use the same 2d6 roll for both. So you look up on the 10 table and add the result from the 3 table.
If you have a few of the charts handy  give them to your most chart friendly players  you’ll find you no longer need a place to roll 20 dice, nor to spend the time counting dice, rolling, sorting hits, then counting and rolling for saves and sorting those.
Here is a 2 page document that gives you charts up to 25 dice and enough sub charts to roll as many dice as you want  all while using just two normal D6.
Bucket Replacement Charts
