Dice Tray

As an option, have a "character" dice tray that the can use to shoot quick dice during the game. The DM would be able to add that dice tray "character" to its campaign.

The dice tray could have, clearly visible, numerous dice options.

1d3, 1d4, 1d6, 1d8, 1d10, 1d12, 1d20  (so far similar to the actual dice column)

then

2d4, 2d6, 2d8, 2d10, 2d12, 2d20

3d4, 3d6, 3d8, 3d10, 3d12, 3d20

4d4, 4d6... etc. 

With quick modifiers that you can check before rolling the dice ( [  ] +1 [  ] +2  [   ] +3 , etc.), and the usual option for advantage.