I'm trying to calculate two or more independent events that have a chance of either succeeding or failing.

The predecessor event has to succeed in order for the next event to be created. If the current event were to fail, the event sequence would go back by 1 event.

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For example:

I'm playing a video game, and in the video game I'm a sorcerer who is able to imbue items with specific enchantments. I'm currently holding a sword that I'm going to enchant.

Each successful attempt will increment the swords damage by 1, and each unsuccessful attempt will decrement it by 1. The sword's damage will not decrease beyond it's default damage.

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I'm able to to calculate these independent events:

Chance of success from Level 0 to 1 = 80%

Chance of success from Level 0 to 2 = 4/5 * 1/2 = 40%

Chance of success from Level 0 to 3 = 4/10 * 2/10 = 8%

Chance of success from Level 0 to 4 = 2/25 * 2/25 = 0.64%

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Since you can fail a level, without going back to level 0. How would I go about adding the fail rates to the calculated succession rates?

The predecessor event has to succeed in order for the next event to be created. If the current event were to fail, the event sequence would go back by 1 event.

--------------

For example:

I'm playing a video game, and in the video game I'm a sorcerer who is able to imbue items with specific enchantments. I'm currently holding a sword that I'm going to enchant.

Each successful attempt will increment the swords damage by 1, and each unsuccessful attempt will decrement it by 1. The sword's damage will not decrease beyond it's default damage.

- I'm able to enchant the sword a maximum of 4 times.
- Level 1-4

- Each enchantment level has a specific pass/fail chance rate.
- Level 1 Enchantment - 80%

- Level 2 Enchantment - 50%

- Level 3 Enchantment - 20%

- Level 4 Enchantment - 8%

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I'm able to to calculate these independent events:

Chance of success from Level 0 to 1 = 80%

Chance of success from Level 0 to 2 = 4/5 * 1/2 = 40%

Chance of success from Level 0 to 3 = 4/10 * 2/10 = 8%

Chance of success from Level 0 to 4 = 2/25 * 2/25 = 0.64%

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Since you can fail a level, without going back to level 0. How would I go about adding the fail rates to the calculated succession rates?

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