Observations:

 * A splay tree moves accessed nodes to the root of the tree, this is very costly
 * there was some success by randomizing splay trees in http://www.informatik.uni-freiburg.de/~salbers/ipl02.ps.gz[]
  * They splay top-down (which is considered more efficent)
  * the splay decision is done probabilistically once for the whole lookup

Ideas:

 . splaying bottom up can be done on a per splay operation base
 . deeper elements shall have a higher chance to splay up, elements near the root can have a small chance
 . the 'zig' case happens only when we are next to the root
 . the 'zig-zig' mirrors the symetrie of a subtree but doesn't contribute to the whole tree balancing
 . the 'zig-zag' case decreases the tree depth, which might be of global benefit


How it got Implemented:

 . optimized bottom up splaying, nodes are still 2 pointers only, recursing
   into the tree keeps a temporary 'trail'
 . probabilistic splay function which adjusts the splaying chance depending on
   the depth of the node
 . ignore the 'zig' case, the node is one level under the root, any
   improvement would be mariginal
 . 'zig-zig' has a normal chance of splaying
 . 'zig-zag' has a higher chance of splaying