Reply to thread

Message

<blockquote data-quote="Halcyon" data-source="post: 2629812" data-attributes="member: 30251">A series of die rolls is just a geometric distribution. In terms of rolling a 1 on a d20, the mean would be 20 rolls, but the variance is very large since all outcomes are equally likely on each trial.&nbsp; The probability of rolling a 1 on the 20th or earlier roll is roughly 64.2%.&nbsp; In other words, if you continuously rolled a d20 until you got a 1, noted how many rolls that took and repeated that process over and over, 64.2% of the time you would roll a 1 by the 20th roll. The table below shows the probablitilty of getting a 1 on the nth roll or less.&nbsp; The left column is the number of rolls and the right column is the cumulative probability.&nbsp; Another way of thinking of the results in this table is to take 1-a given probability, which equals the probability of it taking more than N rolls to get a 1. (E.g. 1-.642=.358, or a 35.8% chance it takes more than 20 rolls to roll a 1).&nbsp; Ive only included the first 50 n's for brevity <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=";)" title="Wink&nbsp; &nbsp; ;)"&nbsp; data-smilie="2"data-shortname=";)" />, but it's easy to extrapolate beyond this (or to other dice (e.g. d12)).1&nbsp; &nbsp; 0.052&nbsp; &nbsp; 0.09753&nbsp; &nbsp; 0.1426254&nbsp; &nbsp; 0.185493755&nbsp; &nbsp; 0.2262190636&nbsp; &nbsp; 0.2649081097&nbsp; &nbsp; 0.3016627048&nbsp; &nbsp; 0.3365795699&nbsp; &nbsp; 0.3697505910&nbsp; &nbsp; 0.40126306111&nbsp; &nbsp; 0.43119990812&nbsp; &nbsp; 0.45963991213&nbsp; &nbsp; 0.48665791714&nbsp; &nbsp; 0.51232502115&nbsp; &nbsp; 0.5367087716&nbsp; &nbsp; 0.55987333117&nbsp; &nbsp; 0.58187966518&nbsp; &nbsp; 0.60278568219&nbsp; &nbsp; 0.62264639720&nbsp; &nbsp; 0.64151407821&nbsp; &nbsp; 0.65943837422&nbsp; &nbsp; 0.67646645523&nbsp; &nbsp; 0.69264313224&nbsp; &nbsp; 0.70801097625&nbsp; &nbsp; 0.72261042726&nbsp; &nbsp; 0.73647990627&nbsp; &nbsp; 0.7496559128&nbsp; &nbsp; 0.76217311529&nbsp; &nbsp; 0.77406445930&nbsp; &nbsp; 0.78536123631&nbsp; &nbsp; 0.79609317432&nbsp; &nbsp; 0.80628851633&nbsp; &nbsp; 0.8159740934&nbsp; &nbsp; 0.82517538535&nbsp; &nbsp; 0.83391661636&nbsp; &nbsp; 0.84222078537&nbsp; &nbsp; 0.85010974638&nbsp; &nbsp; 0.85760425939&nbsp; &nbsp; 0.86472404640&nbsp; &nbsp; 0.87148784341&nbsp; &nbsp; 0.87791345142&nbsp; &nbsp; 0.88401777943&nbsp; &nbsp; 0.8898168944&nbsp; &nbsp; 0.89532604545&nbsp; &nbsp; 0.90055974346&nbsp; &nbsp; 0.90553175647&nbsp; &nbsp; 0.91025516848&nbsp; &nbsp; 0.9147424149&nbsp; &nbsp; 0.91900528950&nbsp; &nbsp; 0.923055025</blockquote>

[QUOTE="Halcyon, post: 2629812, member: 30251"] A series of die rolls is just a geometric distribution. In terms of rolling a 1 on a d20, the mean would be 20 rolls, but the variance is very large since all outcomes are equally likely on each trial. The probability of rolling a 1 on the 20th or earlier roll is roughly 64.2%. In other words, if you continuously rolled a d20 until you got a 1, noted how many rolls that took and repeated that process over and over, 64.2% of the time you would roll a 1 by the 20th roll. The table below shows the probablitilty of getting a 1 on the nth roll or less. The left column is the number of rolls and the right column is the cumulative probability. Another way of thinking of the results in this table is to take 1-a given probability, which equals the probability of it taking more than N rolls to get a 1. (E.g. 1-.642=.358, or a 35.8% chance it takes more than 20 rolls to roll a 1). Ive only included the first 50 n's for brevity ;), but it's easy to extrapolate beyond this (or to other dice (e.g. d12)). 1 0.05 2 0.0975 3 0.142625 4 0.18549375 5 0.226219063 6 0.264908109 7 0.301662704 8 0.336579569 9 0.36975059 10 0.401263061 11 0.431199908 12 0.459639912 13 0.486657917 14 0.512325021 15 0.53670877 16 0.559873331 17 0.581879665 18 0.602785682 19 0.622646397 20 0.641514078 21 0.659438374 22 0.676466455 23 0.692643132 24 0.708010976 25 0.722610427 26 0.736479906 27 0.74965591 28 0.762173115 29 0.774064459 30 0.785361236 31 0.796093174 32 0.806288516 33 0.81597409 34 0.825175385 35 0.833916616 36 0.842220785 37 0.850109746 38 0.857604259 39 0.864724046 40 0.871487843 41 0.877913451 42 0.884017779 43 0.88981689 44 0.895326045 45 0.900559743 46 0.905531756 47 0.910255168 48 0.91474241 49 0.919005289 50 0.923055025 [/QUOTE]

Verification