Reply to thread

Message

<blockquote data-quote="DanMcS" data-source="post: 1577730" data-attributes="member: 6530">Yeah, they're messing with the server clock, I was actually driving around in my car yesterday at the time I supposedly posted the answer.&nbsp; Heh.Formula as follows:You can roll 1-20.&nbsp; So can your opponent.&nbsp; You will win from 0-20 out of 20 of his rolls.&nbsp; For instance, if you are more skilled by 10, and roll an 11, your result is a 21, you win 20/20 times since he can't roll a 21.Example:&nbsp; I am more skilled than my opponent by +4 (I have a +7 and he a +3, but only the difference matters).You roll: you win(out of 20 of his rolls)20:2019:2018:2017:2016:1915:1814:1713:16...3:62:51:4For instance, if I roll a 17-20, my result is above 21+, he cannot win.&nbsp; If I roll a 1, my result is 5, I win only when he rolls a 1-4.The formula is as follows:&nbsp; There are 400 results possible.The number of times I win is 20* (D-1): this accounts for my roll of 20,19,or 18.Then the formula for the sum from when I roll 17 to 1 is the sum from 20 to 4.&nbsp; Turns out, this is the sum from 20 to D, which is(20+D) * (21-D)/2.That is, (17-4)/2 * 24, which is actually a really complicated way to do it, now that I think about it.&nbsp; A simpler formula would be the sum from 1 to 20 minus the sum from 1 to (D-1), which is210 - (D^2-D)/2.&nbsp; Hmph.Anyway, the whole thing sums up to the number of times I win out of all 400 tries, which is20 * (D-1) + 210 - (D^2 -D)/2.Simplified out, that's [190 + (41*D -D^2)/2], all over 400, which becomes0.475 + [(41*D-D^2)/800].</blockquote>

[QUOTE="DanMcS, post: 1577730, member: 6530"] Yeah, they're messing with the server clock, I was actually driving around in my car yesterday at the time I supposedly posted the answer. Heh. Formula as follows: You can roll 1-20. So can your opponent. You will win from 0-20 out of 20 of his rolls. For instance, if you are more skilled by 10, and roll an 11, your result is a 21, you win 20/20 times since he can't roll a 21. Example: I am more skilled than my opponent by +4 (I have a +7 and he a +3, but only the difference matters). You roll: you win(out of 20 of his rolls) 20:20 19:20 18:20 17:20 16:19 15:18 14:17 13:16 ... 3:6 2:5 1:4 For instance, if I roll a 17-20, my result is above 21+, he cannot win. If I roll a 1, my result is 5, I win only when he rolls a 1-4. The formula is as follows: There are 400 results possible. The number of times I win is 20* (D-1): this accounts for my roll of 20,19,or 18. Then the formula for the sum from when I roll 17 to 1 is the sum from 20 to 4. Turns out, this is the sum from 20 to D, which is (20+D) * (21-D)/2. That is, (17-4)/2 * 24, which is actually a really complicated way to do it, now that I think about it. A simpler formula would be the sum from 1 to 20 minus the sum from 1 to (D-1), which is 210 - (D^2-D)/2. Hmph. Anyway, the whole thing sums up to the number of times I win out of all 400 tries, which is 20 * (D-1) + 210 - (D^2 -D)/2. Simplified out, that's [190 + (41*D -D^2)/2], all over 400, which becomes 0.475 + [(41*D-D^2)/800]. [/QUOTE]

Verification