How does randomness give O(log n) worst case?
Randomness gives O(log n) in *expectation*, not worst case—that's an honest trade. With probability 1/2, a node is promoted one level; with probability 1/4, two levels; with probability 1/8, three levels. This produces roughly equal numbers of nodes per level (50% at level 1, 25% at level 2, etc.), so the total height is O(log n) with very high probability. Worst case is O(n), but practically impossible.
Answered in
Skip Lists: The Shortcut Nobody RotatesBalanced trees rebalance with rotations. Skip lists layer express lanes with random promotion—same O(log n) search, simpler locking.
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