The Gaming Den

Have H be the probability of hitting (1/6 to 6/6) and W be the probability of wounding (same). Your base chance (without exploding dice) of causing a wound is H * W. With wounds potentially exploding, on a hit, you have: 1-W of doing 0 wounds, W-1/6 of doing 1 wound, 1/6 of doing one wound and getti...

As an approximation that grows slightly less accurate with the number of rerolls, the expected value for a N sided die rolled X times and taking the highest value gives you N * X / (X+1) + 1/2 No rerolls (so 1 roll): N * 1 / 2 + 1/2 (6.5 for a d12) - exact value One reroll (so 2 rolls): N * 2/3 + 1/...

Shih can make a difficult Stamina role to spend more Chi than they normally have access to from their Virtue rolls, but nobody's really done the math on these. On a d10, you have a 20% change of getting a hit on a difficulty 9 test. You only need one hit, and if you've maxed out your Stamina you've...

How would I calculate the variance/standard deviation/some percent confidence of a die roll? Worse, I'm trying to calculate the variance (or standard deviation, or something that gets me similar information) on exploding dice. I calculated the average of a non-exploding die with x sides as (1+x)/2,...