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Replacing 1d20 with 3d6 is nearly pointless
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<blockquote data-quote="FormerlyHemlock" data-source="post: 8792963" data-attributes="member: 6787650"><p>As your table shows, every -2 penalty on 3d6 roughly doubles the difficulty of the task, not just at the extreme ends. If you think of a difficulty modifier, like trying to resist falling down <em>while poisoned</em>, as representing the fraction of universes where an average PC's chance of success turns to failure, then you can pick a modifier (or visualize the severity of an existing modifier) by asking what proportion of successes turn to failures under that modifier. If bad footing is a -2 to dodging, then that means it's quite a severe penalty because in half of all possible universes where you would otherwise dodge, you fail. In half of THOSE universes, being nauseated for -2 makes you fail anyway. The penalties stack nicely and intuitively.</p><p></p><p>Expertise (such as +4 to Dodge) either offsets penalties, or if you have no penalties, starts halving your failure rate instead.</p><p></p><p>There's no way to choose difficulty modifiers on a d20 which nicely represent multiplicative difficulty this way. On a d20, halving the number of possible successes for an average person requires a -5, and then halving it again requires a -2.5, and then -1.25. A difficulty modifier has no fixed meaning, and rules writers often seem to default to low penalties like -1 or -2 which are fairly meaningless unless you are already penalized. In a 3d6 system like Dungeon Fantasy though, taking a -2 for bad footing has a consistent meaning, and you can meaningfully decide whether buying hobnails for your boots is a good tradeoff ($25; avoids the -2 to attack/-1 to defend for bad footing; basically imposes -1 on your stealth attempts, so the entire party has worse odds of being able to surprise monsters).</p><p></p><p>Nobody writes or is proposing to write multiplicative difficulty modifiers for d20 ("-5 if your target number otherwise is under 15, otherwise -2") because it's too much of a hassle.</p></blockquote><p></p>
[QUOTE="FormerlyHemlock, post: 8792963, member: 6787650"] As your table shows, every -2 penalty on 3d6 roughly doubles the difficulty of the task, not just at the extreme ends. If you think of a difficulty modifier, like trying to resist falling down [i]while poisoned[/i], as representing the fraction of universes where an average PC's chance of success turns to failure, then you can pick a modifier (or visualize the severity of an existing modifier) by asking what proportion of successes turn to failures under that modifier. If bad footing is a -2 to dodging, then that means it's quite a severe penalty because in half of all possible universes where you would otherwise dodge, you fail. In half of THOSE universes, being nauseated for -2 makes you fail anyway. The penalties stack nicely and intuitively. Expertise (such as +4 to Dodge) either offsets penalties, or if you have no penalties, starts halving your failure rate instead. There's no way to choose difficulty modifiers on a d20 which nicely represent multiplicative difficulty this way. On a d20, halving the number of possible successes for an average person requires a -5, and then halving it again requires a -2.5, and then -1.25. A difficulty modifier has no fixed meaning, and rules writers often seem to default to low penalties like -1 or -2 which are fairly meaningless unless you are already penalized. In a 3d6 system like Dungeon Fantasy though, taking a -2 for bad footing has a consistent meaning, and you can meaningfully decide whether buying hobnails for your boots is a good tradeoff ($25; avoids the -2 to attack/-1 to defend for bad footing; basically imposes -1 on your stealth attempts, so the entire party has worse odds of being able to surprise monsters). Nobody writes or is proposing to write multiplicative difficulty modifiers for d20 ("-5 if your target number otherwise is under 15, otherwise -2") because it's too much of a hassle. [/QUOTE]
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