I thought a little about Advantage in DnD5e and here’s a very short post about it. Advantage is quite simple. If a roll is made with advantage, the player rolls two d20s and takes the higher number as the result. Disadvantage reverses the situation and the player rolls two d20s and takes the lower number.
Content warning: Sloppy statistics and a chance of horrible mistakes.
One interesting question regarding various mechanics is ‘How long does it take to figure out who is better?’ Characters in the world don’t observe each other’s bonuses but rather the results of the checks and checks have a random component in them. So it is very much possible that a more skilled character loses multiple times to a less skilled one. Luckily, we can use (or abuse) a few methods from statistics to take a stab at this problem.
It’s been a while since the last time (part I and part II). Besides dice pools and linear RNGs, a common way to get a random number is to roll a few dice and sum their results. This results in a curved distribution where some results are more probable than others. For example, rolling 3d6, you can only get result 3 by getting three ones but there are multiple ways of adding to e.g. 7 using numbers between 1 and 6. Continue reading “Dice Math III – Summing dice”
In part 1, I covered some properties of a linear dice mechanic using d20 system as an example. Another very common mechanic is the dice pool. The basic idea is that the player rolls multiple similar dice and counts the number of dice that have result equal to or greater than a target number. The number of ‘hits’ is then the result of the roll. Games that use it are numerous: Shadowrun, World of Darkness, Burning wheel, Warhammer (the miniature game!). For example, in Shadowrun, the dice are d6s and the target number is five. So rolling 7 dice and getting numbers 2,3,3,5,6,1,4 would result in two hits. Sometimes there are additional complications, like exploding dice, re-rolls or botches. I’ll cover these on a separate post. The next part is going to be a little math heavy.