Krux:Statistics
From Carls wiki
Opening move
There are 39,365 distinct opening moves in Krux. Though this number sounds very exact and definitive, it embeds a few assumptions about what a "distinct opening move" is. For example, two opening moves which lead to the same placement of the pieces, but puts on different hats on piece Ⅰ, are considered distinct. Also, different orders of steps and actions are considered distinct moves, even if they happen to produce identical board positions. This leads to a large proportion (35,267, or 89.59%) of the opening moves being jumper moves. See the pie chart on the left.
However, if we disregard the paths taken, and only look at end results of the opening moves, we find a more manageable 1,177 positions. Several of the opening moves are now represented as one opening position instead. Now we find that over half of the distinct opening positions are made by carrier moves (665, or 56.50%). See the pie chart on the right.
| Image:Initial moves.png A large proportion of the distinct opening moves are jumper moves. (SVG version) | Image:Unique initial moves.png The distribution of opening positions is more uniform. (SVG version) |
Safe and unsafe positions
| Image:Safe and lost moves.png | We define a safe position (green circle) to be one to which a piece can make an initial move such that the opponent doesn't have an immediate winning counter move. In other words, safe positions are those that might occur in perfect play.
In contrast, a lost position (red circle) has a reply which will give Black an immediate win. If you're lucky enough to be running a browser supporting SVG, check out the SVG version. You can hover over each lost position and get a tooltip showing a winning reply. It is possible for the carrier to put both itself and another piece in lost positions. In all such cases, it is possible for Black to use either one or sometimes both of the replies suggested at the corresponding positions. |
