def calculated_confidence score
  return 0 if score == 0
  n = score.to_f

  upvotes = score
  z = 1.281551565545 # 80% confidence
  p = upvotes.to_f / n

  left = p + (1 / (2.0 * n) * z * z)
  right = z * Math.sqrt((p * ((1.0 - p) / n)) + (z * (z / (4.0 * n * n))))
  under = 1.0 + ((1.0 / n) * z * z)

  (left - right) / under
end

lastb = -1
(0..1000).each do |n|
  c = calculated_confidence(n)
  b = (c*c*256).floor
  if b != lastb then
    printf "%3d %.4f %d\n", n, c, b
    lastb = b
  end
end

__END__
  0 0.0000 0
  1 0.3784 36
  2 0.5491 77
  3 0.6462 106
  4 0.7089 128
  5 0.7527 145
  6 0.7851 157
  7 0.8100 167
  8 0.8297 176
  9 0.8457 183
 10 0.8589 188
 11 0.8701 193
 12 0.8796 198
 13 0.8878 201
 14 0.8950 205
 15 0.9013 207
 16 0.9069 210
 17 0.9119 212
 18 0.9164 214
 19 0.9204 216
 20 0.9241 218
 21 0.9275 220
 22 0.9305 221
 23 0.9334 223
 24 0.9360 224
 25 0.9384 225
 26 0.9406 226
 27 0.9427 227
 28 0.9446 228
 29 0.9464 229
 30 0.9481 230
 32 0.9512 231
 33 0.9526 232
 35 0.9552 233
 36 0.9564 234
 38 0.9586 235
 40 0.9606 236
 42 0.9624 237
 45 0.9648 238
 47 0.9662 239
 51 0.9688 240
 54 0.9705 241
 58 0.9725 242
 63 0.9746 243
 68 0.9764 244
 74 0.9783 245
 82 0.9804 246
 91 0.9823 247
103 0.9843 248
118 0.9863 249
138 0.9882 250
166 0.9902 251
208 0.9922 252
278 0.9941 253
418 0.9961 254
839 0.9980 255