Hello!
I'm making a video game and was hoping for some help with a probability problem.
The player can level up, and upon doing so, they are given the choice of 3 upgrade options, randomly chosen from a pool of 20 options. Each option can be upgraded 5 times, once each time the player levels up.
I want to calculate the average number of skills the player has at each level, as well as the average tier of their skills.
For example:
Upon reaching level 2, we know that all players will have 1 skill, and that skill will be at tier 1. We know this because the player starts at level 1, and levelling up to level 2 is when their first skill unlocked.
Upon reaching level 3, there is a chance that the player will be able to upgrade that same skill again, while also being guaranteed to have 2 new skills to choose from.
If the player is given the chance to upgrade that same skill and does so, they will have 1 skill, now at tier 2. If they choose one of the other skills, they will have 2 skills, with an average skill tier of 1.
Any help would be great!
I'm making a video game and was hoping for some help with a probability problem.
The player can level up, and upon doing so, they are given the choice of 3 upgrade options, randomly chosen from a pool of 20 options. Each option can be upgraded 5 times, once each time the player levels up.
I want to calculate the average number of skills the player has at each level, as well as the average tier of their skills.
For example:
Upon reaching level 2, we know that all players will have 1 skill, and that skill will be at tier 1. We know this because the player starts at level 1, and levelling up to level 2 is when their first skill unlocked.
Upon reaching level 3, there is a chance that the player will be able to upgrade that same skill again, while also being guaranteed to have 2 new skills to choose from.
If the player is given the chance to upgrade that same skill and does so, they will have 1 skill, now at tier 2. If they choose one of the other skills, they will have 2 skills, with an average skill tier of 1.
Any help would be great!