In turn, the covariance matrix for a pool of dice is just the sum of the covariance matrices of the individual dice; like the variance of the univariate case, the covariance matrix of a dice pool "stacks" additively.
The center of each ellipse is simply the mean result of the dice pool.
Note that the [68–95–99.7 rule](https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule) only applies to univariate distributions. With bivariate distributions, the rule is closer to 39-86-99, following the [chi distribution](https://en.wikipedia.org/wiki/Chi_distribution). So about 39% of the results will fall within the ellipse, and 86% will fall within twice as far. However, if you only consider a single dimension at a time, then the original 68–95–99.7 rule applies.
