Fair dice, and two that aren't
A fair die has the same chance on every face. That is Fair mode here.
This site is a roller. The other two modes are not fair, on purpose. Go roll if that is all you came for.
Look at the probability engine while you roll. The bars are the live chances.
For DMs and designers
Average is how you check the math before the table does. The bars already are the curve. Put a target in and you see whether that DC, trap, or breath weapon kills the party or does nothing.
The probability engine is the number you write down. Advantage on a d20. An 8d6 fireball. 4d6 drop low for ability scores. Same graphs if you are balancing a dice pool for a game you are making.
Fairish is for a short session that should not be all snake eyes. It remembers what already came up and leans the other way.
Fair
This is the boring one. Every face starts even and stays even. A d20 is 5%. A d6 is 16.667%. Last roll does not change the next one. Reset weights does nothing useful here. There is nothing to reset.
Use Fair for normal, multi session games where the chances will eventually come around.
Fairish
This is the default. Duh.
After a face lands, that face loses a chunk of chance. The chunk is a share of the even starting chance, not a share of whatever the face currently has. Drop strength is that share. At 20% on a d20, a 5% face loses 1 percentage point.
That mass does not vanish. It moves to the opposite half of the die. On a d20, 1 through 10 are low and 11 through 20 are high. Roll a 17 and the high faces keep their odds. Each low face gains a slice of the drop. Faces in the same half as the roll are left alone. A face never goes below 0%. Once it is spent, rolling it again does not move anything until you hit Reset weights.
A worked d20 at 20% drop:
- Start. Every face is 5%.
- You roll 20. Face 20 drops to 4%. Faces 1 through 10 each pick up 0.1%. Faces 11 through 19 stay at 5%.
- The next roll is more likely to be low. If a low face lands, probability flows back toward the high half.
Drop strength lives in Settings. 0% means Fairish still tracks faces but the drop is zero, so odds stay even until you raise it. 100% tries to dump the entire base chance off the face in one hit.
Use this for short sessions where few rolls are expected and the averages are very hard to achieve. This dice mode gives you the chance to not suck all the time.
Average
Each reported face is the rounded mean of N independent fair rolls. Curve rolls is N. Default is 2. Two fair d20s that come up 3 and 18 report 11. A 1 only happens when the component rolls are all 1, or close enough that rounding still lands there. Raise curve rolls and the bell tightens around the middle.
The probability bars do not move after you roll. They already are the curve. Find out if your trap or breath weapon is more or less likely to kill the party, or if that DC you eyeballed is a joke.
Aggregation
Aggregation is a fancy word for combining dice. Leave it on None and you get one face per result, like a normal die. Number of rolls is how many of those results you get from one click.
Pick Advantage, Disadvantage, Sum, Drop low, or Drop top and Dice per roll shows up. Number of rolls is how many combinations you get. Dice per roll is how many dice are used in each aggregation. Advantage keeps the highest. Disadvantage keeps the lowest. Sum adds them. Drop low throws away the smallest die and adds the rest. Drop top throws away the biggest.
Three attacks with advantage. Number of rolls 3, Aggregation Advantage, Dice per roll 2. One click, three numbers, each is the higher of two dice.
An 8d6 fireball. Number of rolls 1, Aggregation Sum, Dice per roll 8, die set to d6.
Ability scores the old way. Die set to d6, Aggregation Drop low, Dice per roll 4. Six scores in one click if you set Number of rolls to 6. The number you write down is the three dice you kept, added up, so 3 through 18.
Modifier lives next to Dice per roll. It is a flat bonus or penalty added after keep and drop, the number you write on the sheet. Leave it at 0 and nothing changes. A d20 with Modifier 5 is 1d20+5. Fairish still remembers the face that landed, not the total with the bonus.
Fairish still remembers faces. With Sum, every face that came up loses chance. With Advantage or Disadvantage, only the face you keep loses chance. Drop low and Drop top work the same way on the dice you kept. The die you threw away does not change the memory.
Probability engine
Visualy see how the math maths.
These are the bars. Single die is how likely each face is on the die you picked, right now. In Fair every bar is the same height. In Fairish the heights change after every roll. In Average they make a hill in the middle and stay there.
Turn aggregation on and a second set of bars shows up. That one is the number you write down, not the individual dice. 2d6 Sum goes from 2 to 12, and 7 is the tall bar. Advantage on a d20 is still 1 through 20, but the high faces get fatter. 4d6 drop low is 3 through 18, with 12 and 13 the usual peak. Change the modifier and that second graph slides. 2d6+3 is the same hill, from 5 to 15.
Those bars use the odds as they are this second. After a Fairish roll the odds change, so look again if you want the new picture. The header keeps the last roll next to the config, which is the thing you actually want when you hit Roll from inside this panel. Reset weights is in here too. That wipes Fairish memory on the selected die.
There is a target box in here too. Type a number and it splits the odds into under and over that mark, at or above counting as over. Turn aggregation on and the second graph goes red below the target and green at or above it, same split as the two percentages.
What Default settings does not touch
Default settings restores the tray and the two knobs, drop strength and curve rolls. History stays. Face weights stay. If you want a clean Fairish memory, hit Reset weights in the probability engine.