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Roll a number of extra dice along with the base roll

I will start with an example for 0.75 and then explain how this can be more generalized. First, you have your base STAT roll with no modifiers which can be whatever you want. For this example, let's assume it has a 60% chance of success (such as a d20 that needs to roll at most a 12, it doesn't really matter here).

Now if you want to roll STAT-1, you still do the base STAT roll, but you also roll an extra 1d4. In order for STAT-1 to succeed, the base STAT roll must succeed and the 1d4 can't have a result of 1. This gives STAT-1 a chance of success equal to 0.6*0.75.

For STAT-x, you simply roll and extra xd4 and if any of these d4 rolls a 1 it is a failure, giving you the progression you want.

For STAT+1, you roll an extra 1d4 but this time, it is a success if the base STAT roll succeeds, or if the 1d4 rolls a 1 (or if things both things happen). This causes the chance of failure to go from 0.4 to 0.4*0.75. Similarly for STAT+x, you roll x additional 1d4 and you get a success if any of them is a 1.

Using an extra d4 like this gives you a progression of 0.75 because that's the probability of not rolling a 1 on a d4. You can adjust this to other numbers by using different dice and different ranges of numbers. For example using a 1d3 would allow a 2/3 (0.66...) progression.

Roll a number of extra dice along with the base roll

I will start with an example for 0.75 and then explain how this can be more generalized. First, you have your base STAT roll with no modifiers which can be whatever you want. For this example, let's assume it has a 60% chance of success (such as a d20 that needs to roll at most a 12, it doesn't really matter here).

Now if you want to roll STAT-1, you still do the base STAT roll, but you also roll an extra 1d4. In order for STAT-1 to succeed, the base STAT roll must succeed and the 1d4 can't have a result of 1. This gives STAT-1 a chance of success equal to 0.6*0.75.

For STAT-x, you simply roll and extra xd4 and if any of these d4 rolls a 1 it is a failure, giving you the progression you want.

For STAT+1, you roll an extra 1d4 but this time, it is a success if the base STAT roll succeeds, or if the 1d4 rolls a 1 (or if things both happen). This causes the chance of failure to go from 0.4 to 0.4*0.75. Similarly for STAT+x, you roll x additional 1d4 and you get a success if any of them is a 1.

Using an extra d4 like this gives you a progression of 0.75 because that's the probability of not rolling a 1 on a d4. You can adjust this to other numbers by using different dice and different ranges of numbers. For example using a 1d3 would allow a 2/3 (0.66...) progression.

Roll a number of extra dice along with the base roll

I will start with an example for 0.75 and then explain how this can be more generalized. First, you have your base STAT roll with no modifiers which can be whatever you want. For this example, let's assume it has a 60% chance of success (such as a d20 that needs to roll at most a 12, it doesn't really matter here).

Now if you want to roll STAT-1, you still do the base STAT roll, but you also roll an extra 1d4. In order for STAT-1 to succeed, the base STAT roll must succeed and the 1d4 can't have a result of 1. This gives STAT-1 a chance of success equal to 0.6*0.75.

For STAT-x, you simply roll and extra xd4 and if any of these d4 rolls a 1 it is a failure, giving you the progression you want.

For STAT+1, you roll an extra 1d4 but this time, it is a success if the base STAT roll succeeds, or if the 1d4 rolls a 1 (or if both things happen). This causes the chance of failure to go from 0.4 to 0.4*0.75. Similarly for STAT+x, you roll x additional 1d4 and you get a success if any of them is a 1.

Using an extra d4 like this gives you a progression of 0.75 because that's the probability of not rolling a 1 on a d4. You can adjust this to other numbers by using different dice and different ranges of numbers. For example using a 1d3 would allow a 2/3 (0.66...) progression.

Source Link
Sdjz
Sdjz
  • 36.6k
  • 15
  • 170
  • 238

Roll a number of extra dice along with the base roll

I will start with an example for 0.75 and then explain how this can be more generalized. First, you have your base STAT roll with no modifiers which can be whatever you want. For this example, let's assume it has a 60% chance of success (such as a d20 that needs to roll at most a 12, it doesn't really matter here).

Now if you want to roll STAT-1, you still do the base STAT roll, but you also roll an extra 1d4. In order for STAT-1 to succeed, the base STAT roll must succeed and the 1d4 can't have a result of 1. This gives STAT-1 a chance of success equal to 0.6*0.75.

For STAT-x, you simply roll and extra xd4 and if any of these d4 rolls a 1 it is a failure, giving you the progression you want.

For STAT+1, you roll an extra 1d4 but this time, it is a success if the base STAT roll succeeds, or if the 1d4 rolls a 1 (or if things both happen). This causes the chance of failure to go from 0.4 to 0.4*0.75. Similarly for STAT+x, you roll x additional 1d4 and you get a success if any of them is a 1.

Using an extra d4 like this gives you a progression of 0.75 because that's the probability of not rolling a 1 on a d4. You can adjust this to other numbers by using different dice and different ranges of numbers. For example using a 1d3 would allow a 2/3 (0.66...) progression.