There are currently Two dice available right now. The catch dice, and the basic dice.
Uses:
Catch Dice: Catching pokemon.
Basic Dice: Everything that has a 50/50 chance involved.
How to use:
Catch dice: Catch dice are used when a pokeball is thrown at a weakened pokemon. It is a 10 sided dice. Every pokemon has a difficulty rating. This is how likely the pokeball will catch the pokemon. Here are the values.
Easy: 2
Tricky: 4
Hard: 6
Difficult: 7
Very Difficult: 8
Extremely Difficult: 9
Near Impossible: 10
Your dice roll must be higher than the catch rate number. However, there is a way to make things easier. The kind of Pokeball you use will change how high the dice must be. The better the pokeball, the more bonus catch points you get. For example:
Pokeball: +0 (no change)
Great Ball: +2
Ultra Ball: +4
Master Ball: +9 (absolute catch)
Elemental Balls (net balls, dive balls, etc.): +2 for the elements they are associated with, +0 otherwise.
Quick Balls: +3 on posts 1-5, +2 on posts 6-10, +1 on posts 11-15
Timerballs: +0 on posts 1-5, +1 for each additional 5 posts.
Dusk balls: +3 in dark areas (caves, dark forests, etc)
All other Balls: +0
So, if you were catching a pokemon with the "Extremely Difficult" rating using an ultra ball, and the dice roll gave you a 6, you would add 4 to the 6, equaling 10. 4+6=10. Since you need a 9, the catch was a success.
Basic Dice: If there is a situation where there are two possible outcomes, use the basic dice to decide between them. For example: Breeding, Effects, Status.