My favorite die to use is a d10. The reason I like this die is because of its simplicity of math. A d6 has a 16.7% chance of getting each number, a d8 has a 12.5% chance of rolling each number, and so on. These get complex when you start figuring out what you need to roll multiple numbers on the die, and when a second die is added, it becomes exponentially complex. A d10, on the other hand, is very easy to figure out the odds based on percentages. A 1 has a 10% chance of success, a 1-3 has a 30% chance of success, and so on.
I compare it to the way a street is laid out in a city. The d10 is like the city with an organized grid. It’s easy to know exactly where you’re going when someone says 15th Street and 5th Avenue in New York. Other dice are comparable to older cities, like those in Europe, where the roads wind and twist and turn. They have a lot of character and beauty to them, but it’s harder to navigate them, just as it’s hard to quickly determine the odds of other dice.
In my own game, Command Combat: Civil War, I use d10s to very simply measure the odds of units hitting. If there are 3 units firing, they need a 3 or less to hit, a 30% chance. Their exhaustion is handled the same way. For every point of fire placed on them, the fatigue goes up by one. So in the above example, they have a 30% chance of being affected. The mental calculations can be done quickly in the mind so the player can concentrate more on their tactical decisions.
The drawback of the d10 is its expense. You can get d10s relatively cheaply, but they're still more expensive than d6s and it's probably for this reason that so many miniatures games which require a lot of dice, such as Warhammer 40K and Flames of War, have chosen to stick with the d6. One can get a block of them cheaply, and they come in a nicely sized box where they are compactly placed without interfering with the miniatures.
There was an era when the d10 was perhaps the most valued die aside from the d6. In the late 1980s, a number of role playing games began using percentages for their statistics and tests. Games came with two d10s, or sometimes two d20s which were supposed to be used as 10s (11-20 were to be read as 1-10.) This system was easy to calculate the odds for someone as mathematically challenged as myself.
But the system seemed to die out (no pun intended) with the trend of games it was attached to. I think one of the things that happened is that people missed the other forms of dice. I found myself wanting to find excuses to bring other dice into the mix just for some variety.
The d20 revolution, which came along in the early 2000s, learned from this. Even though the d20 was at the center of the system, they made sure to utilize all other kinds of dice to keep it fresh and interesting. The d20 itself, meanwhile, had very similar odds to the d10, but with a little more detail. Rather than each side raising or lowering the odds by 10%, they raise or lower them by 5%.
My only issue with this last point is that I sometimes have to do the math in my head with the d20. Even though it’s simple math, when I hear I need to roll an 11 or lower I have to think in my head for a moment before I remember, oh, that’s a 55% chance of success. But with a d10, when I’m told a 6 or lower, I know immediately it’s a 60% chance without even thinking about it. So when you have to roll dice over and over and over, the simplicity of calculating odds for the d10 puts it ahead of every other dice.