So, you've decided to be a master of emulation.
By utilizing just one singular d6 you can actually roll d2, d3, d4, d6, d8, d10, d12, d20 and d100.
This math requires an understanding of how notation works.
"dX" = usual dice roll, just good old d20 [1-20].
"zX" = zero-based roll, for example z2 results in [0-1] rather than usual d2 [1-2]. It's an equivalent of "dX-1", just a lot more convenient to write down.
"dXR{A,B-C}" - "roll a die and reroll if you get results A, B, or in B-C range".
"AdXLB" - "roll A dices and ignore B lowers results", for example if you roll 4d6L and get 4, 2, 2, 6 - you use only 4, 2 and 6.
Here's also some Excel math:
"Floor(X)" - round down, so 2.9 becomes 2.
"Ceil(X)" - round up, so 2.1 becomes 3.
| Roll... | ...get |
|---|---|
| Floor(d6/3) | z2 (0-1) |
| Ceil(d6/3) | d2 (1-2) |
| Ceil(d6/2) | d3 (1-3) |
| d6R{5,6} | d4 (1-4) |
| d6R{6} | d5 (1-5) |
| d6 | d6 (1-6) |
| z2*4+d4 | d8 (1-8) |
| z2*5+d5 | d10 (1-10) |
| z2*6+d6 | d12 (1-12) |
| z4*5+d5 | d20 (1-20) |
| z10*10+d10 | d100 (1-100) |
It's a mouthful, but actually pretty easy to use after some practice!
Every one of these operations goes from higher radix to lower. If you have no idea what "radix" is - it uses the 1000-100-10-1 way of calculation. This way you can estimate your success/failure without the need to go all the way to the very end. If you need to roll d12 to break a door with DC10 and after "z2..." part you already getting "it's gonna be 6 or lower" - no need to do any math at all.
Some people's brains are wired differently, and it's a lot easier to use some "weird" techniques to calculate the precise roll of a die. Welcome to the neurospicy side of the TTRPG world!
You can exclude any math from the equation by just memorizing that if it's the "lower half" (1, 2 and 3) - it's the lower result, and the "higher" (4, 5 and 6) is the higher.
Or just use odd and even numbers, so 1-3-5 becomes lower, and 2-4-6 becomes higher.
You can roll d4 without rerolls, if you include the orientation itself as a way to transpose 5 and 6 to 1-4 range.
If you roll 5 and it looks like an "X" - it's "1", and if it looks like a "+" - it's "2".
If you roll 6 and it looks like an "=" - it's "3", and if it looks like a "||" - it's "4".
Usually d6 have "5" and "6" sides together, because for fair balance of rolls the "mirror" numbers are placed on the opposite side of a cube. If you never noticed - it's true! 1 is against 6, 2 is against 5, 3 is against 4. We can use this for our advantage, if you roll dice in a way that allows you to see it at least slightly from the side.
If you roll 5 or 6 - just look at a side "below" it, closer to you. For example, on 6 roll you can see 2, 3, 4 or 5 side right "underneath" it. Just use this result instead, swapping 5 for the actual opposite of 6 (which is 1). And if you are not sure which one is closer because of the diagonal placement - just use whichever you consistently prefer. For example, by being lefthanded you can always pick the left one.
You can always be a weirdo techno-wizard and roll in binary. "z2" is just a bit roller after all. You can roll d8 by rolling 3z2, or d6 by using 2z2+z3. Nobody will shame you for that. They might exile you from coming ever again though, but imagine being a Game Master, who scares your player by rolling 2z2+z3 (which looks like 3d6 for the unknowing eye) to roll... a singular d6.