View source for User:Cedges/Median Stats

== Simplification ==

The logarithm function eats multiplications and turns them into additions, which are easier to do in one's head. The median constraint will be met if and only if:

ln(F(x0)/G(x0)) + ln(F(x1)/G(x1)) + ln(F(x2)/G(x2) + ... <= 0

{| class="zebra d20"
|+ Simplifications of Median Rule
|-
! |
! |
! colspan="32" | Result of 4d6, drop lowest
|-
! | Symbol ||
! colspan="2"| 3 
! colspan="2" | 4 
!colspan="2"| 5 
!colspan="2"| 6 
!colspan="2"| 7 
!colspan="2"| 8 
!colspan="2"| 9 
!colspan="2"| 10 
!colspan="2"| 11 
!colspan="2"| 12 
!colspan="2"| 13 
!colspan="2"| 14 
!colspan="2"| 15 
!colspan="2"| 16 
!colspan="2"| 17 
!colspan="2"| 18
|-
| F(X)/G(X) ||
|colspan="2"| 1/1296
|colspan="2"| 1/259
|colspan="2"| 15/1291 
|colspan="2"| 12/427 
|colspan="2"| 37/630 
|colspan="2"| 68/611 
|colspan="2"| 227/1160 
|colspan="2"| 349/1069 
|colspan="2"| 497/947 
|colspan="2"| 664/799 
|colspan="2"| 209/158 
|colspan="2"| 249/115 
|colspan="2"| 1127/300 
|colspan="2"| 1221/169 
|colspan="2"| 17 
|colspan="2"| 432/7
|-
| ll(X)
| ln(F(X)/G(X))
|colspan="2"| -7.1670
|colspan="2"| -5.5568
|colspan="2"| -4.4551
|colspan="2"| -3.5718 
|colspan="2"| -2.8348 
|colspan="2"| -2.1955 
|colspan="2"| -1.6312 
|colspan="2"| -1.1194 
|colspan="2"| -0.6447 
|colspan="2"| -0.1850 
|colspan="2"| 0.2797 
|colspan="2"| 0.7725 
|colspan="2"| 1.3235 
|colspan="2"| 1.9775 
|colspan="2"| 2.8332 
|colspan="2"| 4.1225
|-
|colspan="34" | Approximation 1
|-
| points || 
|colspan="2"| -26
|colspan="2"| -20
|colspan="2"| -16
|colspan="2"| -13
|colspan="2"| -10
|colspan="2"| -8
|colspan="2"| -6
|colspan="2"| -4
|colspan="2"| -2
|colspan="2"| 0
|colspan="2"| 1
|colspan="2"| 3
|colspan="2"| 5 
|colspan="2"| 7 
|colspan="2"| 10 
|colspan="2"| 15
|-
| difference || ||
|colspan="2"| 6
|colspan="2"| 4
|colspan="2"| 3
|colspan="2"| 3
|colspan="2"| 2
|colspan="2"| 2
|colspan="2"| 2
|colspan="2"| 2
|colspan="2"| 2
|colspan="2"| 1
|colspan="2"| 2
|colspan="2"| 2
|colspan="2"| 2
|colspan="2"| 3
|colspan="2"| 5 ||
|-
|colspan="34" | Approximation 2
|-
| points || 
|colspan="2"| -33 
|colspan="2"| -25 
|colspan="2"| -20 
|colspan="2"| -16 
|colspan="2"| -13 
|colspan="2"| -10 
|colspan="2"| -7 
|colspan="2"| -5 
|colspan="2"| -3 
|colspan="2"| -1 
|colspan="2"| 1 
|colspan="2"| 4 
|colspan="2"| 6 
|colspan="2"| 9 
|colspan="2"| 13 
|colspan="2"| 19
|-
| difference || ||
|colspan="2"| 8
|colspan="2"| 5
|colspan="2"| 4
|colspan="2"| 3
|colspan="2"| 3
|colspan="2"| 3
|colspan="2"| 2
|colspan="2"| 2
|colspan="2"| 2
|colspan="2"| 2
|colspan="2"| 3
|colspan="2"| 2
|colspan="2"| 3
|colspan="2"| 4
|colspan="2"| 6 ||
|-
|colspan="34" | Approximation 3
|-
| points || 
|colspan="2"| -43 
|colspan="2"| -33 
|colspan="2"| -27 
|colspan="2"| -21 
|colspan="2"| -17 
|colspan="2"| -13 
|colspan="2"| -10 
|colspan="2"| -7 
|colspan="2"| -4 
|colspan="2"| -1 
|colspan="2"| 2 
|colspan="2"| 5 
|colspan="2"| 8 
|colspan="2"| 12 
|colspan="2"| 17 
|colspan="2"| 25
|-
| difference || ||
|colspan="2"| 10
|colspan="2"| 6
|colspan="2"| 6
|colspan="2"| 4
|colspan="2"| 4
|colspan="2"| 3
|colspan="2"| 3
|colspan="2"| 3
|colspan="2"| 3
|colspan="2"| 3
|colspan="2"| 3
|colspan="2"| 3
|colspan="2"| 3
|colspan="2"| 5
|colspan="2"| 8 ||
|-
|colspan="34" | Approximation 5
|-
| points || 
|colspan="2"| -76 
|colspan="2"| -59 
|colspan="2"| -47 
|colspan="2"| -38 
|colspan="2"| -30 
|colspan="2"| -23 
|colspan="2"| -17 
|colspan="2"| -12 
|colspan="2"| -7 
|colspan="2"| -2 
|colspan="2"| 3 
|colspan="2"| 8 
|colspan="2"| 14 
|colspan="2"| 21 
|colspan="2"| 30 
|colspan="2"| 44
|-
| difference || ||
|colspan="2"| 17
|colspan="2"| 12
|colspan="2"| 9
|colspan="2"| 8
|colspan="2"| 7
|colspan="2"| 6
|colspan="2"| 5
|colspan="2"| 5
|colspan="2"| 5
|colspan="2"| 5
|colspan="2"| 5
|colspan="2"| 6
|colspan="2"| 7
|colspan="2"| 9
|colspan="2"| 14 ||

|}