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Spaghetti problem

                               p(single loop) vs n

    1 +#+----+------+------+------+------+-----+------+------+------+----+-+
      +      +      +      +      +      +     +      +      +      +      +
      |                                                        '-'    #    |
  0.9 +-+                                                                +-+
      |                                                                    |
  0.8 +-+                                                                +-+
      |                                                                    |
      |                                                                    |
  0.7 +-+#                                                               +-+
      |                                                                    |
  0.6 +-+                                                                +-+
      |                                                                    |
      |   #                                                                |
  0.5 +-+                                                                +-+
      |     #                                                              |
  0.4 +-+    #                                                           +-+
      |       #                                                            |
      |         ##                                                         |
  0.3 +-+         # #                                                    +-+
      |              # ###                                                 |
  0.2 +-+                  ### ## #                                      +-+
      |                            ## ## ### ###                           |
      +      +      +      +      +      +     + ## ### ### ## ### ### ## ##
  0.1 +-+----+------+------+------+------+-----+------+------+------+----+-+
      0      5      10     15     20     25    30     35     40     45     50


                                E(num loops) vs n

  18 +-+----+------+------+------+------+------+------+------+------+----+-+
     +      +      +      +      +      +      +      +      +      +     ##
     |                                                         '-'   ####  |
  16 +-+                                                           ##    +-+
     |                                                          ##         |
  14 +-+                                                     ##          +-+
     |                                                   ## #              |
     |                                                ##                   |
  12 +-+                                          ## #                   +-+
     |                                         ##                          |
  10 +-+                                    # #                          +-+
     |                                   # #                               |
     |                               # ##                                  |
   8 +-+                          # #                                    +-+
     |                          ##                                         |
   6 +-+                   # ##                                          +-+
     |                   ##                                                |
     |              # ##                                                   |
   4 +-+          ##                                                     +-+
     |         ##                                                          |
   2 +-+   ###                                                           +-+
     |  ##                                                                 |
     +#     +      +      +      +      +      +      +      +      +      +
   0 +-+----+------+------+------+------+------+------+------+------+----+-+
     0      5      10     15     20     25     30     35     40     45     50