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[ToA] Hex-crawling and Long Rests
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<blockquote data-quote="CapnZapp" data-source="post: 7238191" data-attributes="member: 12731"><p>Okay, so the encounter frequency has been characterized as "0-3" so far.</p><p></p><p>But the reality is that you make three d20 rolls a day, where 16-20 indicates an encounter.</p><p></p><p>So the probabilities are:</p><p></p><p>Zero encounters: <strong>42%</strong></p><p>One or more encounters: <strong>58%</strong></p><p></p><p>Exactly one encounter: <strong>42%</strong></p><p>Exactly two encounters: <strong>14%</strong></p><p>Exactly three encounters: <strong>1.5%</strong></p><p></p><p>Average number of encounters is 0.75. That is, over ten hexes you will have seven and a half encounter on average.</p><p></p><p>This is significantly less than what a simple range (such as "0-3" would led you to believe). The number of times you will have, say, seven encounters (or more) in, say, five hexes' time (to account for a modicum of being-lost-ness) is unlikely to say the least, only 6%. </p><p></p><p>My conversation above was pretty much predicated on that number being significantly higher. Say 40% of all five-hex treks result in 7+ encounters. What number do we need to change on our d20 rolls to achieve this?</p><p></p><p>It turns out 40% is the answer! In other words, if we change the encounter roll from 16-20 (25%) to 13-20 (40%) we get the following probabilities:</p><p></p><p>Zero encounters: <strong>22%</strong></p><p>One or more encounters: <strong>78%</strong></p><p></p><p>Exactly one encounter: <strong>43%</strong> (almost exactly the same)</p><p>Exactly two encounters: <strong>29%</strong></p><p>Exactly three encounters: <strong>6%</strong></p><p></p><p>Average number of encounters is now 1.2 </p><p></p><p>Over five hexes you will have 7+ encounters with a... 39% probability. <img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite1" alt=":)" title="Smile :)" loading="lazy" data-shortname=":)" /></p><p></p><p>Zapp</p><p></p><p></p><p>PS. Thanks to AnyDice for numbers!</p></blockquote><p></p>
[QUOTE="CapnZapp, post: 7238191, member: 12731"] Okay, so the encounter frequency has been characterized as "0-3" so far. But the reality is that you make three d20 rolls a day, where 16-20 indicates an encounter. So the probabilities are: Zero encounters: [B]42%[/B] One or more encounters: [B]58%[/B] Exactly one encounter: [B]42%[/B] Exactly two encounters: [B]14%[/B] Exactly three encounters: [B]1.5%[/B] Average number of encounters is 0.75. That is, over ten hexes you will have seven and a half encounter on average. This is significantly less than what a simple range (such as "0-3" would led you to believe). The number of times you will have, say, seven encounters (or more) in, say, five hexes' time (to account for a modicum of being-lost-ness) is unlikely to say the least, only 6%. My conversation above was pretty much predicated on that number being significantly higher. Say 40% of all five-hex treks result in 7+ encounters. What number do we need to change on our d20 rolls to achieve this? It turns out 40% is the answer! In other words, if we change the encounter roll from 16-20 (25%) to 13-20 (40%) we get the following probabilities: Zero encounters: [B]22%[/B] One or more encounters: [B]78%[/B] Exactly one encounter: [B]43%[/B] (almost exactly the same) Exactly two encounters: [B]29%[/B] Exactly three encounters: [B]6%[/B] Average number of encounters is now 1.2 Over five hexes you will have 7+ encounters with a... 39% probability. :) Zapp PS. Thanks to AnyDice for numbers! [/QUOTE]
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