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Really enjoying the podcast and like your take on rolling a d6 for upping ability scores on leveling up. Looked into the math and got these numbers.
ReplyDeletenumber of 0 occurrences of 6: 353 out of 1,000 - 35.30 %
number of 1 occurrences of 6: 393 out of 1,000 - 39.30 %
number of 2 occurrences of 6: 192 out of 1,000 - 19.20 %
number of 3 occurrences of 6: 55 out of 1,000 - 5.50 %
number of 4 occurrences of 6: 6 out of 1,000 - 0.60 %
number of 5 occurrences of 6: 1 out of 1,000 - 0.10 %
number of 0 occurrences of 6: 3411 out of 10,000 - 34.11 %
number of 1 occurrences of 6: 4004 out of 10,000 - 40.04 %
number of 2 occurrences of 6: 1942 out of 10,000 - 19.42 %
number of 3 occurrences of 6: 541 out of 10,000 - 5.41 %
number of 4 occurrences of 6: 96 out of 10,000 - 0.96 %
number of 5 occurrences of 6: 6 out of 10,000 - 0.06 %
number of 0 occurrences of 6: 33471 out of 100,000 - 33.47 %
number of 1 occurrences of 6: 40243 out of 100,000 - 40.24 %
number of 2 occurrences of 6: 20078 out of 100,000 - 20.08 %
number of 3 occurrences of 6: 5358 out of 100,000 - 5.36 %
number of 4 occurrences of 6: 780 out of 100,000 - 0.78 %
number of 5 occurrences of 6: 68 out of 100,000 - 0.07 %
number of 6 occurrences of 6: 0 out of 100,000 - 0.00 %
number of 0 occurrences of 6: 33440 out of 100,000 - 33.44 %
number of 1 occurrences of 6: 40228 out of 100,000 - 40.23 %
number of 2 occurrences of 6: 20050 out of 100,000 - 20.05 %
number of 3 occurrences of 6: 5420 out of 100,000 - 5.42 %
number of 4 occurrences of 6: 786 out of 100,000 - 0.79 %
number of 5 occurrences of 6: 71 out of 100,000 - 0.07 %
number of 6 occurrences of 6: 5 out of 100,000 - 0.01 %
number of 0 occurrences of 6: 334879 out of 1,000,000 - 33.49 %
number of 1 occurrences of 6: 401654 out of 1,000,000 - 40.17 %
number of 2 occurrences of 6: 201133 out of 1,000,000 - 20.11 %
number of 3 occurrences of 6: 53662 out of 1,000,000 - 5.37 %
number of 4 occurrences of 6: 8007 out of 1,000,000 - 0.80 %
number of 5 occurrences of 6: 645 out of 1,000,000 - 0.06 %
number of 6 occurrences of 6: 20 out of 1,000,000 - 0.00 %
To get 6 sixes in a row the odds are: 1/6 * 1/6 * 1/6 * 1/6 * 1/6 * 1/6
1/46,656
0.00002143347050754458
0.002143347050754458%
~ 1/50,000
Odds of getting no sixes are: 5/6 *5/6 *5/6 *5/6 *5/6 *5/6
0.33489797668038407
33.49%
~ 1/3 of the time
That's amazing! Hey, if you're a numbers person, do you know the probability difference between rolling 1d6 with advantage versus rolling 1d6+1 or 1d6+2 in order to achieve a 6 or more? (This is for my Improved Oracle experiment)
ReplyDeleteSorry, mxbccca, I can't resist answering this :)
DeleteGetting 6 or more on 1d6 with advantage: 11/36 which is about 0.31.
Getting 6 or more on 1d6+1: 1/3 which is about 0.33.
Getting 6 or more on 1d6+2: 1/2 which is exactly 0.5.
This, is great stuff. I'd say that using the plus system gives a better spread when trying to emulate 50-50, Likely and Very Likely (and negative counterparts). Thanks for doing the math: I'm terrible with it :)
DeleteI'll look into it and get back. I'm only on Ep 27, so no spoilers please.
ReplyDeleteThanks!
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ReplyDeleteI tried reformatting the table but it didn't work. :-( If you want to go to the effort, you can align the vertical bars in a text editor with a mono-spaced font.
ReplyDeleteThis is very cool - and somehoe makes me think of the coin flipping scene in Rosencrantz & Guildenstern Are Dead :)
ReplyDeleteThanks for all your efforts!