This can be computed and cached according to Pascal's triangle. Instead of determining which dice rolled a particular number, only determine how many dice rolled that number.In a dice pool, you usually care a lot about how many dice rolled a particular number, and you usually don't care about (or even know) in what order the dice were rolled. Instead, iterate "vertically" over one number at a time. Don't iterate "horizontally" over one die at a time.In this case the run length is at most 10 and the score goes up to 10 times the number of dice, which is not too bad. It turns out that, as long as the possible number of states is not large, it's possible to determine the probability distribution of the final score much faster than by enumerating all possible rolls. After all numbers are accounted for, output the score corresponding to the final state.Then, we score the current run (if it's of at least length 3) and the current matching set. In this case we either end the current run, or increment the run length. For each number on the die, see how many dice rolled that number and update the state.In this case the state is the score so far and the current run length, which are both zero before any dice are considered. Many dice pool scoring systems can be formulated as: With the right algorithm, a pool of 10 dice can be computed in under 100 milliseconds, even running in a web browser. (Technically the results go up to 100, but the chances above 60 are so small as to be practically invisible so I omitted them to give more space to the actually-visible part of the graph.) This will hopefully let me see if I want to incorporate a similar dice pool system into a game I am planning. So for instance a roll of 1,2,3,4,5,5,10 the player could pick either 1,2,3,4, 5,5 or 10 to add to their base score for a dice roll, before comparing it to the target number.Īs a future game designer, I'd like to understand what sort of probability curve this creates for a given set of dice pool sizes, say 1-10 dice. The sum of the base and the result is then compared to target numbers or to the results of an opponent's rolls to determine success or failure. The result is then added to a "base" consisting of a related attribute score bought by the player at character creation. An unusual feature is the selection of numbers from the d10 rolls – a player can pick a single highest number, all like numbers, or straights of consecutive numbers, and use these to generate the result. I've recently learnt about CthulhuTech, which has a unique dice pool system:ĬthulhuTech uses a proprietary game system known as "Framewerk" that focuses on a dice pool system.
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