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<blockquote data-quote="Esker" data-source="post: 7892815" data-attributes="member: 6966824">There is no statistics going on here; just probability. That's because there is no data; just calculations. Statistics is trying to find a good model to describe a set of observations from the world (the data). Probability is examining the properties of models in and of themselves. This is the latter. There is no comparison between assumptions and reality to be made here (except I guess for the basic assumptions of fair and independent dice that everybody takes as given) because there are only the probability models, no observations for them to fit.We have two mechanical systems for stochastically producing successes and failures. All that matters as far as the game is concerned is whether the probabilities of success translate reasonably, which they do. The actual numbers that show up on the die are a means to adjudicating success or failure; they have no other purpose or meaning in themselves. I'm honestly not sure what you think I'm claiming that has you so riled up, except that you really seem to want the actual numbers on the dice to be the same.Presumably you meant to say 11 there (12 happens if 3d6 = 11). The probability of rolling an 11 only matters insofar as it is normally the difference between the difficulty of a DC 11 check and a DC 12 check. That's it. And we don't necessarily even care that much about that, as long as the success rate for DC 11 and the success rate for DC 12 are individually about right (or, if we're comparing two systems that use different DC calculations, then that the corresponding probabilities match up). It still doesn't seem like you're getting that, since you keep hammering on the gaps in the dice distribution itself.</blockquote>

[QUOTE="Esker, post: 7892815, member: 6966824"] There is no statistics going on here; just probability. That's because there is no data; just calculations. Statistics is trying to find a good model to describe a set of observations from the world (the data). Probability is examining the properties of models in and of themselves. This is the latter. There is no comparison between assumptions and reality to be made here (except I guess for the basic assumptions of fair and independent dice that everybody takes as given) because there are only the probability models, no observations for them to fit. We have two mechanical systems for stochastically producing successes and failures. All that matters as far as the game is concerned is whether the probabilities of success translate reasonably, which they do. The actual numbers that show up on the die are a means to adjudicating success or failure; they have no other purpose or meaning in themselves. I'm honestly not sure what you think I'm claiming that has you so riled up, except that you really seem to want the actual numbers on the dice to be the same. Presumably you meant to say 11 there (12 happens if 3d6 = 11). The probability of rolling an 11 only matters insofar as it is normally the difference between the difficulty of a DC 11 check and a DC 12 check. That's it. And we don't necessarily even care that much about that, as long as the success rate for DC 11 and the success rate for DC 12 are individually about right (or, if we're comparing two systems that use different DC calculations, then that the corresponding probabilities match up). It still doesn't seem like you're getting that, since you keep hammering on the gaps in the dice distribution itself. [/QUOTE]

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