[math-fun] Tiling questions

I'm impressed by the large fraction of small-size polyominoes and polyhexes that individually tile the plane (using arbitrary congruent copies, which may be flipped over). All polyominoes through the 35 hexominoes tile the plane, plus all but 3 of the 108 distinct heptominoes. And over 94% of the369 octominoes. All polyhexes through the 22 pentahexes tile the plane, plus all but 4 of the 82 distinct hexahexes. And over 91% of the 333 distinct heptahexes. So: Is there some heuristic reason to expect such a high fraction of small-size polyominoes and polyhexes to tile the plane? This phenomenon seems very counterintuitive to me. --Dan