Probability Sticky

Naeddyr

two
Validated User
This is a bit clunky, but it should work:

http://anydice.com/program/f65d

This is an anydice function that takes a sequence and then outputs the biggest set as raw numbers, which is really not what you're supposed to do with anydice, but it works. So when rolling 2d6, a 1 and a 2 becomes a '2', while a 1 and a 1 becomes '11'. In your system, these numbers have the same "greater than" properties as what you want: bigger numbers are more matching dice, so a 555 beats a 66.

The raw curves (in the above link) don't do you any good, so you want to compare instead:

http://anydice.com/program/f65e

by using

Code:
output [biggest set of 2d6] > 55
you can put your 'target number' in the second number there (55) in the example, and it will give you the percentage value of winning against that number. In this case, beating 55 requires 66 (which is the same as rolling 12 on 2d6, put there for comparison).

http://anydice.com/program/f660

This is an example of hitting 5-5-5-5 with various numbers of dice. You need 9d6 just to break the 10% line.

When doing long lists like here, use "transpose view" to fwip the axises.
 
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Dabuel

Registered User
Validated User
Hi,
A new resolution system that I do not know how to calculate the probabilities.

Players roll 2 white D10 and 1 black D10. You will only look at the result of one of the white dice and add your skill to get your final number.
- If a white dice rolls the highest then this is the dice you add your skill to.
- Should the black dice be equal to or higher than the best white die, then remove the black dice along the highest white dice. The remaining white dice is the dice you add to your skill.

This sounds convoluted but the idea is that a player should be able to get extra white (advantage) and black dice (disadvantage) depending on the circumstances.
Just looking at the unmodified roll above (2 white and 1 black) what would the distribution be? I’m hoping that the average roll will be around 5 :)

Any help would be immensely appreciated!
Thanks
Dabuel
 

phatonin

Chaos is a bladder
Validated User
Hi,
A new resolution system that I do not know how to calculate the probabilities.

Players roll 2 white D10 and 1 black D10. You will only look at the result of one of the white dice and add your skill to get your final number.
- If a white dice rolls the highest then this is the dice you add your skill to.
- Should the black dice be equal to or higher than the best white die, then remove the black dice along the highest white dice. The remaining white dice is the dice you add to your skill.

This sounds convoluted but the idea is that a player should be able to get extra white (advantage) and black dice (disadvantage) depending on the circumstances.
Just looking at the unmodified roll above (2 white and 1 black) what would the distribution be? I’m hoping that the average roll will be around 5 :)

Any help would be immensely appreciated!
Thanks
Dabuel
Let me do some shameless self promotion for the Yadrol dice roller.

It seems that your mechanic results in an average just above 6, and a median between 7 and 8.
 

Dabuel

Registered User
Validated User
Let me do some shameless self promotion for the Yadrol dice roller.

It seems that your mechanic results in an average just above 6, and a median between 7 and 8.
Excellent! Thanks phatonin! Is there any way of getting the probabilities for individual results e.g. the chance in percent to roll a 4 etc.
 

phatonin

Chaos is a bladder
Validated User
Excellent! Thanks phatonin! Is there any way of getting the probabilities for individual results e.g. the chance in percent to roll a 4 etc.
There's a button "Exact", that does exactly this. Keep in mind this is a simulation, not an analytical computation.
 

Dabuel

Registered User
Validated User
There's a button "Exact", that does exactly this. Keep in mind this is a simulation, not an analytical computation.
Ok, thanks. I think I successfully managed to modify your script into a generally applicable one where you can change the number of white (W) and black (B) dice ie the number of advantages and disadvantages.

sample ( B=1; W=2; black = Bd10; white = Wd10; hiwhite = highest of white; if highest of black >= hiwhite then (white - highest of white -lowest (W-2) of white) else hiwhite) as "bnw"

It is great to see that you can crank up the dice numbers without it having to stop working. I think that some of the alternative statistics programs suffer from this.

As a feedback I would love to see a table which broke down the numbers so that you do not need to check the graph to make an estimation.

Anyway, great to see such a good tool! Big thanks again!
 

phatonin

Chaos is a bladder
Validated User
Ok, thanks. I think I successfully managed to modify your script into a generally applicable one where you can change the number of white (W) and black (B) dice ie the number of advantages and disadvantages.

sample ( B=1; W=2; black = Bd10; white = Wd10; hiwhite = highest of white; if highest of black >= hiwhite then (white - highest of white -lowest (W-2) of white) else hiwhite) as "bnw"

It is great to see that you can crank up the dice numbers without it having to stop working. I think that some of the alternative statistics programs suffer from this.

As a feedback I would love to see a table which broke down the numbers so that you do not need to check the graph to make an estimation.

Anyway, great to see such a good tool! Big thanks again!
I didn't put on the number of black and white dice for to reasons. The first is to keep it simple. The second is that I don't know how it works. I would assume something like that:

1. if highest die is white -> take that number
2. if highest die is black, remove the highest white and the highest black, back to step 1.

Is that it?
 

Dabuel

Registered User
Validated User
I didn't put on the number of black and white dice for to reasons. The first is to keep it simple. The second is that I don't know how it works. I would assume something like that:

1. if highest die is white -> take that number
2. if highest die is black, remove the highest white and the highest black, back to step 1.

Is that it?
Yes you are right! Which makes me realize that my modified script above only works if B=1. It does not compare the 2nd highest black dice etc...
Normally you will have at least one more white than black dice. I’m thinking that pushing your luck to the extreme may require a roll with more black than white which could result in all white dice being removed = catastrophic failure.
Thanks again! The fact that I was at all able to modify your script shows that your program is easy and intuitive .
Thanks again!
 
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