In
Part 1, I looked at probability, notation, number of occurrences
Linear Die/Dice (single) Results
Looking at single die/dice rolls, which are linear in results. Linear means that there is a set incremental probability, which if graphed would form a straight line. Rolling a single die gives linear results. As opposed to rolling multiple dice which would create a curvilinear result, normally more triangular or in a bell curve shape.
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.
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