user15559: Section 8 of the FIDE Rating Regulations provides the following table

I understand that dp=800 and dp=-800 are arbitary caps at the top and bottom of the table. 
However, in relation to the other scores, what's the formula for the conversion of p into dp, and vice-versa?
As noted in the comments, the regular Elo formula almost works but does not quite work. Does anyone know what the formula is for the adjustment made in the tails?

user15561: As stated in 12.1 the formula above gives a close approximation to tables 8.1a and 8.1b. However it does not explain the precise construction of the table.  Take fore example Rb-Ra = -736. According to the table 8.1b, the resulting expectation equals 100%. But according to the formula, the expectation is 98,57%. 

user7297: It's basically just table 8.1a with the columns switched. E.g. the entry in table 8.1b with rating difference 92-98 and expected score (for the higher rated player) of .63, corresponds with the entry (.63, 95) in table 8.1a.
That table is based on the expected score formula mentioned here:

If Player A has a rating of RA and Player B a rating of RB, the exact formula (using the logistic curve) for the expected score of Player A is 
EA = 1 / (1 + 10 (RB - RA) / 400)

but it's also possible to directly generate table 8.1b from this formula. For example, a rating difference of 92 points (in A's favor) leads to EA = 0.6294.
The inverse formula, calculating the rating difference which corresponds to a certain expected score, is RB - RA = 400 log10(1 / EA - 1).

15559: <p><a href="https://www.fide.com/fide/handbook.html?id=197&amp;view=article" rel="noreferrer">Section 8 of the FIDE Rating Regulations</a> provides the following table</p>

<p><a href="https://i.stack.imgur.com/8zv1Z.png" rel="noreferrer"><img src="https://i.stack.imgur.com/8zv1Z.png" alt="p and dp"></a></p>

<p>I understand that dp=800 and dp=-800 are arbitary caps at the top and bottom of the table. </p>

<p>However, in relation to the other scores, what's the formula for the conversion of p into dp, and vice-versa?</p>

<p>As noted in the comments, the regular Elo formula almost works but does not quite work. Does anyone know what the formula is for the adjustment made in the tails?</p>
 15561: <p>As stated in 12.1 the formula above gives a close approximation to tables 8.1a and 8.1b. However it does not explain the precise construction of the table.  Take fore example Rb-Ra = -736. According to the table 8.1b, the resulting expectation equals 100%. But according to the formula, the expectation is 98,57%. </p>
 7297: <p>It's basically just table 8.1a with the columns switched. E.g. the entry in table 8.1b with rating difference 92-98 and expected score (for the higher rated player) of .63, corresponds with the entry (.63, 95) in table 8.1a.</p>

<p><em>That</em> table is based on the expected score formula mentioned <a href="https://en.wikipedia.org/wiki/Elo_rating_system#Mathematical_details" rel="noreferrer">here</a>:</p>

<blockquote>
  <p>If Player A has a rating of R<sub>A</sub> and Player B a rating of R<sub>B</sub>, the exact formula <a href="https://en.wikipedia.org/wiki/Logistic_curve" rel="noreferrer">(using the logistic curve)</a> for the expected score of Player A is </p>
  
  <p>E<sub>A</sub> = 1 / (1 + 10 <sup>(R<sub>B</sub> - R<sub>A</sub>) / 400</sup>)</p>
</blockquote>

<p>but it's also possible to directly generate table 8.1b from this formula. For example, a rating difference of 92 points (in A's favor) leads to E<sub>A</sub> = 0.6294.</p>

<p>The inverse formula, calculating the rating difference which corresponds to a certain expected score, is R<sub>B</sub> - R<sub>A</sub> = 400 log<sub>10</sub>(1 / E<sub>A</sub> - 1).</p>
