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A Breakdown on Fabletop's Dice Probability

alkwyzheir Oct '19  /  edited Oct '19
== Introductions ==
Hello, Alk here! I'm here with this post to share my research regarding the dice mechanics within Fabletop.

To warn the readers, the answers are inevitable to be accurate to the information relayed in the [How to Play] webpage: fabletop.com/help/introduction

The accuracy can be considered obvious due to how the probability uses a programming equation for dice rolling. However, this post is made to reassure the readers regarding the authenticity of the probabilities, as well as providing further proof of this subject.

== Reason ==
So what is all this information for? It really depends on you. As a Game Master, it is important to understand how to balance your game. With this detailed information of data, it will guide you to determine the balance your players and enemies have for their dice stats. Players may also read this information to entertain themselves in any way they can interpret this information.

== Star Probability ==
The [How to Play] webpage has stated that within each dice, there is a 1/3 chance of obtaining a star. We can deduce the rate of odds of obtaining stars for each amount of dice we roll. How exactly are we going to do that?

[Data Calculation]
For counting the probabilities of stars you get from specific dice roll, I have made a whole set of calculations and formulas (made from repetitive trial and error and hypothesis). The results have been shown very satisfactory.

In short, this data was gathered with a method of [Brute Force]. Brute Force is a term you often hear on decoding encrypted passwords by guessing every single possibility (from aaa, aab, aac, aba..., etc). This method was heavily used in order to create a formula to calculate the percentage or odds. I had actually spent 2-4 hours just counting 1903 possible combinations for this, manually.

The formula/spreadsheet is made to show your percentage of odds in getting a minimum of X stars.

You will find the whole spreadsheet here:
justpaste.it/5fdcb
Statistics has officially been fixed!

== Moon & Skull Rolls ==
Itís often surprising to see moon and skull rolls, thinking itís near impossible. Well, itís not. I have taken some data to show how frequent this to happen.

[Data Gathering]
You can find the file containing this post's tracking through this link: justpaste.it/3erek
This does not directly count as table promoting as it's for academic/information purposes. The statistics were tracked through manual counting for over dozens of sessions on a table.

For clarification regarding the spreadsheet, here is some basic explanation of each subject:

Power Used: The amount of PP the player has used throughout the table.
Moon Rolls: The amount of Moon Rolls the character has rolled.
Successful Rolls: The amount of roll that contains at least one star, regardless of the dice amount for the roll.
Failed Rolls: The amount of roll that contains no star, regardless of the dice amount for the roll.
Events/Allies/Enemies: All rolls made by the Game Master
Luck to Luck Ratio: The percentage tendency of rolling successful/moon rolls.
Unique Rolls: The percentage tendency of rolling either moon or skull rolls.

I have taken the track of all the rolls within a table I am playing at. With high sampling, this was the result:

Normal Rolls: 2042
Unique Rolls: 260 - 130 Moon Roll, 130 Skull Roll (shockingly the same)
Total Rolls: 4604

The statistic has shown the number of unique rolls for the whole range of sessions. With this information, we can determine if the unique roll probability is accurate to the data.

[How To Play] states a moon/skull roll will have 1/18 chance of occurring. They will only appear on the first dice in each rolls. Combining them both, you would acquire 1/9 chance of containing a unique roll.

[Website Statement]
Unique Roll Probability = (Moon Roll Probability + Skull Roll Probability) / Total Rolls
1/9 = (1/18 + 1/18) / TR

[Statistics Results]
Unique Roll Probability = (130 + 130) / 2042
URP = 0,1273... = 12,73 % = 1/8,3

To conclude, after a high amount of rolls, the probability of gaining a moon or skull is more or less similar to the main equation of 1/18. The statistics taken have shown that unique rolls have a higher tendency compared to the stated probability.
trotrigar Oct '19
Literal god
frost Oct '19  /  edited Oct '19
Keep in mind that this is just a sample. It doesn't mean that the actual odds are higher than 1 in 18. Only that this was the case in your sample.

Power Point usage or who is rolling (e.g. GM vs player) has no influence on the actual rolls.

See also the dice-related questions here:
fabletop.com/help/about#common-questions

And the dice odds:
anydice.com/program/5d94
alkwyzheir Oct '19
Yeah, I figured.

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