Newer Thoughts on Probability

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Well, it’s been quite some time since the original thread on dice probability for d10 Core, and the website move earlier this year caused my pretty graphs to go away. So, I had to make them again. While making them again, I decided to make different ones that more closely illustrate what I’m going for with the system.

Sit back, relax, and enjoy your soda and popcorn. Let’s get started!

First, considering a dice system like d10 Core is complicated. Rather than summing all the sides and getting a number, each side of the die is important because that number is compared to the enemy’s dice. Whoever has the highest roll on each set, comparing highest to highest down the line, wins in each pair. Whoever has the most hits wins the task check, and the winner subtract’s the loser’s hits to get the number of hits he had over the enemy.

So, if I have 3 dice and roll 10, 9, 8, and my friend Bob rolls 3 dice and gets 9, 9, 7, I beat him twice and tie once. Since he didn’t win any, I got two “hits” on the task, which adds to damage or makes it more spectacular than just a regular success.

Let’s take a look at the first chart:

Chance of rolling n number on d10

Result Probabilities on a d10

This chart shows the probability of rolling a 1 through 10 on a d10 at least one time on any of the dice you roll. On 1 die, it’s obviously harder because you only have one die to roll, and the probability curves downward as you add more die with an expectation of a higher roll on the die. The noticeable down-trend for all dice begins at 6, so the next chart talks a little bit about the “high rolls”, 7-10.

higher rolls

Expectation of a higher result on given dice

As we can see, moving the requirement of a higher roll (more likely to win in any given task) takes things down a notch. One of the most important features of this chart is that it demonstrates visually the disparity between one die and five dice of returning a high number on any one. With a 30% chance difference between 1 die and 5 dice, this indicates that someone rolling 1 die against even 5 dice still has a chance; it guarantees the system does not have “impossible” situations, and it also guarantees that no task can be reduced so far that it becomes boring, trivial, and silly. People with more dice still have a clear advantage than those with less, but no side is an automatic winner – a feature that I disliked in most games I’ve played as characters get more powerful.

Which brings us to the final chart. The following starts at a minimum of three dice – a decent amount of dice for a brand-new character just starting out for any given roll. The chart shows disparity between 3, 4, and 5 dice rolls were at least 3 faces must show up as the result or higher.

At Least 3 High

At least 3 dice roll high numbers

Right on target. A person rolling 3 dice has a 6% chance to roll at least 7 or higher on each face in a single roll, while a person with 5 dice has a 31.74% chance to roll at least 7 on at least 3 of their dice. The disparity is 25%, well within the realm of possibility of making it so higher-dice players don’t automatically decimate everything they see. The gaps close much faster at each increment of the expected result on at least 3 dice, becoming within 1% of each other at a result of 10.

That’s it for today! Time to head out for now.

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