In Part 1, I looked at probability, notation, number of occurrences

## Linear Die/Dice (single) Results

### Important probability increments

#### Fifty-fifty

The first natural probability divide is half. Fifty-fifty chances, much like the flip of the coin, is a common and popular. All of the dice except d3 can show fifty-fifty percent rolls, since the rest are multiples of two. These are d6, d8, d10, d12, and d20

####

Rule of thirds

Sometimes things aren't just "yes or no" or "black and white". Sometimes you need "maybe" and "gray/grey". Those dice divisible by three can show such results excactly. These are d3, d6, and d12.

#### Quarters

Another popular divisible chance is in quarters. Number of dice divisible by four can show such results exactly. These are d8, d12, and d20.

### Dice Probability d3, d6, d8, d10, d12, and d20

*# number, #% percentage of rolling that number, >% percentage of rolling greater than that number, >=% percentage of rolling greater or equal to that number.*

d3 | |||
---|---|---|---|

# | #% | >% | >=% |

1 | 33% | 67% | 100% |

2 | 33% | 33% | 67% |

3 | 33% | 0% | 33% |

d6 | |||
---|---|---|---|

# | #% | >% | >=% |

1 | 17% | 83% | 100% |

2 | 17% | 67% | 83% |

3 | 17% | 50% | 67% |

4 | 17% | 33% | 50% |

5 | 17% | 17% | 33% |

6 | 17% | 0% | 17% |

d8 | |||
---|---|---|---|

# | #% | >% | >=% |

1 | 13% | 88% | 100% |

2 | 13% | 75% | 88% |

3 | 13% | 63% | 75% |

4 | 13% | 50% | 63% |

5 | 13% | 38% | 50% |

6 | 13% | 25% | 38% |

7 | 13% | 13% | 25% |

8 | 13% | 0% | 13% |

d10 | |||
---|---|---|---|

# | #% | >% | >=% |

1 | 10% | 90% | 100% |

2 | 10% | 80% | 90% |

3 | 10% | 70% | 80% |

4 | 10% | 60% | 70% |

5 | 10% | 50% | 60% |

6 | 10% | 40% | 50% |

7 | 10% | 30% | 40% |

8 | 10% | 20% | 30% |

9 | 10% | 10% | 20% |

10 | 10% | 0% | 10% |

d12 | |||
---|---|---|---|

# | #% | >% | >=% |

1 | 8% | 92% | 100% |

2 | 8% | 83% | 92% |

3 | 8% | 75% | 83% |

4 | 8% | 67% | 75% |

5 | 8% | 58% | 67% |

6 | 8% | 50% | 58% |

7 | 8% | 42% | 50% |

8 | 8% | 33% | 42% |

9 | 8% | 25% | 33% |

10 | 8% | 16% | 25% |

11 | 8% | 8% | 16% |

12 | 8% | 0% | 10% |

d20 | |||
---|---|---|---|

# | #% | >% | >=% |

1 | 5% | 95% | 100% |

2 | 5% | 90% | 95% |

3 | 5% | 85% | 90% |

4 | 5% | 80% | 85% |

5 | 5% | 75% | 80% |

6 | 5% | 70% | 75% |

7 | 5% | 65% | 70% |

8 | 5% | 60% | 65% |

9 | 5% | 55% | 60% |

10 | 5% | 50% | 55% |

11 | 5% | 45% | 50% |

12 | 5% | 40% | 45% |

13 | 5% | 35% | 40% |

14 | 5% | 30% | 35% |

15 | 5% | 25% | 30% |

16 | 5% | 20% | 25% |

17 | 5% | 15% | 20% |

18 | 5% | 10% | 15% |

19 | 5% | 5% | 10% |

20 | 5% | 0% | 5% |

### Deck of Cards

Also, I look at what a person can do with a standard 52 card deck when shuffled. A disadvantage of the card deck is that to retain the probability, one must reshuffle, or the probability changes each additional drawing of cards.I also notice that one can use a 12 sided die/dice and nearly get the same probability, since the difference between 12 and 13 chances is very minimal.

Standard Playing Card 52 card deck (French suit) | ||||
---|---|---|---|---|

Action | #% | >% | >=% | |

Picking one specific card | 1/52 | 2% | ||

Picking one number or face | 1/13 | 8% | ||

1 (ace) | 8% | 92% | 100% | |

2 | 8% | 85% | 92% | |

3 | 8% | 77% | 85% | |

4 | 8% | 69% | 77% | |

5 | 8% | 62% | 69% | |

6 | 8% | 54% | 62% | |

7 | 8% | 46% | 54% | |

8 | 8% | 38% | 46% | |

9 | 8% | 31% | 38% | |

10 | 8% | 23% | 31% | |

jack | 8% | 15% | 23% | |

queen | 8% | 8% | 15% | |

king | 8% | 0% | 8% | |

Picking a face [jack, king, queen] | 12/52 | 23% | ||

Picking one suit [spade, club, heart, diamond] | 1/4 | 25% | ||

Picking a red (or black) | 1/2 | 50% | ||

Picking a non-face | 40/52 | 77% | ||

### Comparing Dice

Here is a linear version, rounded to multiples of 5, comparing all six dice.Dice Comparison Probability | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Die/Dice | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% | 45% | 50% | 55% | 60% | 65% | 70% | 75% | 80% | 85% | 90% | 95% | 100% |

d3 | 33% | 67% | 100% | |||||||||||||||||

d6 | 17% | 33% | 50% | 67% | 83% | 100% | ||||||||||||||

d8 | 13% | 25% | 38% | 50% | 63% | 75% | 88% | 100% | ||||||||||||

d10 | 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% | ||||||||||

d12 | 8% | 16% | 25% | 33% | 42% | 50% | 58% | 67% | 75% | 83% | 92% | 100% | ||||||||

d20 | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% | 45% | 50% | 55% | 60% | 65% | 70% | 75% | 80% | 85% | 90% | 95% | 100% |

### Thoughts on d100

I did consider d100 briefly, but then realized something. Looking over most of the bonuses of the d100 systems, they seem to change by +/-5. If most d100 systems ignore bonuses not multiple of 5, that tells me that going below 5 will not really affect the final result sufficiently. A +1 for a d100 isn't really much of a bonus to affect the outcome. In a sense, they seem like d100/5 systems - basically an exploded d20 systems.### Conclusion

#### I really like d12

Although d20 is the die/dice of the more popular games, I am seeing d12 as a very good one which can also do*the rule of thirds*type results, as well as quarters and halves. Using d12 also somewhat mimics

*a deck of cards*.

I had never considered using a d12 as a main part of a system. However, looking over the probability, I may prefer d12 over d20. Doing so may also help to crush down the run-away bonus/penalties to more like +/-3 ranges much more like

*Fate/Fudge*.

**In the next dice post Curvilinear or Bell Curve Results.**