Differences

This shows you the differences between two versions of the page.

--- chess:programming:magic_bitboards:calculate_magic_numbers [2021/10/27 23:17] – [Using the Magics during a game] peter
+++ chess:programming:magic_bitboards:calculate_magic_numbers [2021/10/28 00:00] (current) – [Determine Magic Numbers] peter
@@ Line 98: / Line 98: @@
   * **magic** is the random 64-bit number.
     * At this time this is done by trial-and-error, as no known formula to provide a perfect solution.
+      * It is just luck/probability that a number is found that happens to calculate unique indices for unique MoveBoards.
+    * Ideally no gaps should be between each index, i.e. a perfect hash.
   * This should result in 64 magic rook numbers and 64 magic bishop numbers.
+    * The index returned by the magic formula is always an integer less than the total number of BlockerBoards.
+  * These indexes will be used to determine where to store each BlockerBoards corresponding MoveBoard within an array.
+    * The MoveBoard are just stored at the index calculated by these pre-programmed good magics.
+  * While this example of the Rook at e4 has 1024 BlockerBoards, each of which has a corresponding MoveBoard, you may end up storing less than 1024 MoveBoards.
+    * For two different BlockerBoards that have the same MoveBoard, the magic could calculate two different indices or it could calculate the same index for both.
+    * As long as the MoveBoards are the same, it is okay for the index to collide.
 </WRAP>
@@ Line 116: / Line 126: @@
 All of the Blocker Masks, Blocker Boards, and Move Boards should be initialized.
+<WRAP info>
+**NOTE:**  The index returned by the magic formula is always an integer less than the total number of BlockerBoards (BB).
+  * Each BB has a corresponding MoveBoard (MB).
+  * When searching for magics, each MB is being calculated  with a slow algorithm and storing the MB at the index calculated by the candidate magic number.
+  * At engine startup, the MBs are recalculated with the slow algorithm and then they are just stored at the index calculated by your pre-programmed good magics.
+</WRAP>
 ----