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d1000 In a brief search I found the following: Here's a forum post including images of a Games Workshop publication using the d1000. The d1000 MUTATION TABLE! is simultaneously everything that was ri …

Goodman Games' Dungeon Crawl Classics dice. Long dice that are unstable on their ends. Teetotums are similar. …

According to this MathExchange answer, the 90-degree configuration of a pentagonal trapezohedron has the additional property that the angle between a face and the opposite edge on a vertex is also 90 …

Each of those dice has a 9/20 chance of rolling below a 10. Do a little binomial theorem and we get an 84.7% chance of at most 4 of those dice rolling below a 10. … The most likely case is that exactly 10 out of 17 dice rolled 15+, in which case none of the remaining dice rolled 15+, effectively reducing the d20 to a d14 for those remaining dice. …

Stationary distributions You are probably looking for the stationary distribution of a Markov chain. If a unique stationary distribution exists, it represents what happens if you play the game for an …

following identity: $$ \left\lceil \frac{n}{d} \right\rceil = \left\lfloor \frac{n + d - 1}{d} \right\rfloor $$ In this case the numerator \$n\$ is the sum rolled on the 4d4 and \$d\$ is the number of dice … As for "scalar" they probably mean a result that is a single number (e.g. the sum of some dice), as opposed to a list of individual die rolls. …

Approaches of this type have been proposed on StackExchange, with examples including: Formula for dropping dice (non-brute force) Generating Function for sum of N dice [or other multinomial distribution … Examples include: Roll and Keep in Anydice How to calculate the probabilities for eliminative dice pools (dice cancelling mechanic) in Neon City Overdrive? …

Stacked area plot up to 20 dice This was generated using the algorithm from my CthulhuTech answer. …

NUM_REROLL d DIE } function: N:n pool DIE:d reroll up to MAX_REROLL:n { result: [N d DIE reroll up to MAX_REROLL using DIE] } output [5 pool (d10>=6) reroll up to 1] In fact, this can reroll any dice … that rolled the lowest outcome on any type of dice, not just success-counting dice. …

Mixing different dice also makes things much more difficult. … Fortunately, it turns out that, as long as you can express the dice mechanic in terms of an incremental calculation where you're told how many dice rolled each number in each pool for one number at a time …

Consider just counting 4+s or 5+s on d6s The central limit theorem says that, once you add enough dice together---including these success-counting dice---the total will resemble a normal distribution, … Further reading If you want the full ugly math, you can try my articles on the central limit theorem as it applies to success-counting dice pools, or the fixed-dice equivalent to a success-counting dice …

# action_set: The set of surviving action dice. # leftover_stress: The number of surviving stress dice that rolled # this number or higher. … : 6, 3, 3") but the number of possible such sets grows rapidly with number of action dice (e.g. this example results in 252 rows), so I won't reproduce the table here. …

Compared to an ideal Laplace distribution: Opposed step dice In this type of system, instead of adding a modifier to their roll, the two sides use larger and larger dice as they advance. … Proof Suppose two players roll step dice against each other, with respective sizes \$A\$ and \$B\$, with ties being broken by coin flip. …

The sum of dice also converges to a normal distribution. Therefore, we can try using the margin of success as the number of hits. …

Adding the middle dice together If you just want to add the middle dice together, you can use the @ operator to select individual sorted positions and add them together: output {2..4}@5d12 Or, perhaps … , rather than 3 values for the individual dice. …