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Zobrist alternative?
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Vincent Diepeveen



Joined: 09 Mar 2006
Posts: 1738
Location: The Netherlands
PostPost subject: Re: Zobrist alternative?    Posted: Wed Jun 13, 2012 1:01 pm Reply to topic Reply with quote
hgm wrote:
I have bad experience with shifting keys by only 1 bit. I tried it in a simulator, and it drove up the number of key collisions enormously. When rotating keys by bits I could not detect any difference in collision statistics with truly random keys.

I have no explanation for this; it was just an observation.


If you shift it 1 bit, which is a very unlucky amount to shift, there is a multilineair relation between the keys.

If you want to replace the table by a hashfunction, realize the hashfunction will eat several cycles to accomplish the hashing.

Basically we assume you still want to make use of Zobrist and that you can incremental update. As with this self invented form of shogi at 36x36 with 200+ pieces, it'll take a while to play that game for a player.

furthermore 64 bits won't be near enough wth such a huge board size and that many pieces. So you're searching for a bit or 512 to start with anyway.

What you need to design now, which is not so complicated is that given an input piece and a 'to square', you can drop a piece onto that square.

So we have a piece represented in say 8 bits, we have a 'to square' represented in say 11 bits.

From those 2 unique properties you want to generate an unique 512 bits key that doesn't have a multilineair relation. It'll eat a few cycles, but there is many solutions to do so.

Even AES-CBC using 256 bits can generate unique key within 12 cycles a byte overhead, so just to generate a key that's safe enough for Zobrist, assuming 512 bits should be easily possible within a cycle or 10-20.

You can for example precalculate values in some smaller tables.

Say 1 table sized 36*36 entries @ 1024 bits and 1 table of 206+ entries @ 64 bits.

Now using some internal bit rotation from the 1024 bits number to a 512 bits number, using small parts of the 64 bits lookup, you can generate a new number.

Example RNG for this is called RanRot, downloadable from the net obviously.
RanRot works ok for Zobrist.

With some experimentation you can get the number of bits down and limit the amount of rotations you need. It will get down the total number of cycles you 'waste' onto it. It'll work fine.
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Subject Author Date/Time
Zobrist alternative? H.G.Muller Tue Jun 12, 2012 7:35 pm
      Re: Zobrist alternative? Kevin Hearn Tue Jun 12, 2012 7:44 pm
      Re: Zobrist alternative? Daniel Shawul Tue Jun 12, 2012 8:19 pm
            Re: Zobrist alternative? H.G.Muller Tue Jun 12, 2012 8:54 pm
                  Re: Zobrist alternative? Daniel Shawul Tue Jun 12, 2012 9:46 pm
                        Re: Zobrist alternative? Daniel Shawul Wed Jun 13, 2012 3:24 am
                        Re: Zobrist alternative? Daniel Shawul Wed Jun 13, 2012 4:14 am
                              ignored idea here Daniel Shawul Wed Jun 13, 2012 4:00 pm
                                    Re: ignored idea here Daniel Shawul Thu Jun 14, 2012 1:30 am
                                          Re: ignored idea here H.G.Muller Thu Jun 14, 2012 5:50 am
                                                Re: ignored idea here Daniel Shawul Thu Jun 14, 2012 12:52 pm
                                          Re: ignored idea here Edmund Moshammer Thu Jun 14, 2012 8:21 am
                                                Re: ignored idea here Edmund Moshammer Thu Jun 14, 2012 9:27 am
      Re: Zobrist alternative? Wylie Garvin Tue Jun 12, 2012 8:27 pm
            Re: Zobrist alternative? H.G.Muller Tue Jun 12, 2012 8:36 pm
                  Re: Zobrist alternative? Vincent Diepeveen Wed Jun 13, 2012 1:01 pm
                  Re: Zobrist alternative? Wylie Garvin Wed Jun 13, 2012 10:57 pm
                        Re: Zobrist alternative? H.G.Muller Thu Jun 14, 2012 5:42 am
                              Re: Zobrist alternative? Robert Hyatt Thu Jun 14, 2012 1:17 pm
                                    Re: Zobrist alternative? H.G.Muller Thu Jun 14, 2012 2:17 pm
                                          Re: Zobrist alternative? Wylie Garvin Thu Jun 14, 2012 6:11 pm
                        Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 10:05 am
      Re: Zobrist alternative? Reinhard Scharnagl Wed Jun 13, 2012 9:52 am
            Re: Zobrist alternative? Edmund Moshammer Wed Jun 13, 2012 9:58 am
                  Re: Zobrist alternative? Reinhard Scharnagl Wed Jun 13, 2012 12:49 pm
                        Re: Zobrist alternative? Edmund Moshammer Wed Jun 13, 2012 1:15 pm
                              Re: Zobrist alternative? Reinhard Scharnagl Wed Jun 13, 2012 1:41 pm
                                    Re: Zobrist alternative? Edmund Moshammer Wed Jun 13, 2012 3:55 pm
                                          Re: Zobrist alternative? Reinhard Scharnagl Wed Jun 13, 2012 4:03 pm
      Re: Zobrist alternative? H.G.Muller Wed Jun 13, 2012 2:19 pm
            Re: Zobrist alternative? Vincent Diepeveen Wed Jun 13, 2012 2:44 pm
            Re: Zobrist alternative? Vincent Diepeveen Wed Jun 13, 2012 2:48 pm
                  Re: Zobrist alternative? Vincent Diepeveen Wed Jun 13, 2012 3:28 pm
                  Re: Zobrist alternative? H.G.Muller Wed Jun 13, 2012 4:01 pm
                        Re: Zobrist alternative? Vincent Diepeveen Wed Jun 13, 2012 5:42 pm
                              Re: Zobrist alternative? H.G.Muller Wed Jun 13, 2012 5:51 pm
                        Re: Zobrist alternative? Vincent Diepeveen Wed Jun 13, 2012 6:27 pm
            Re: Zobrist alternative? Daniel Shawul Wed Jun 13, 2012 5:29 pm
            Re: Zobrist alternative? Karlo Bala Jr. Thu Jun 14, 2012 9:50 am
      Re: Zobrist alternative? Reinhard Scharnagl Thu Jun 14, 2012 8:49 am
            Re: Zobrist alternative? H.G.Muller Thu Jun 14, 2012 9:09 am
            Re: Zobrist alternative? Daniel Shawul Thu Jun 14, 2012 1:11 pm
                  Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 10:12 am
      Re: Zobrist alternative? Don Dailey Thu Jun 14, 2012 4:46 pm
            Re: Zobrist alternative? Don Dailey Thu Jun 14, 2012 6:38 pm
                  Re: Zobrist alternative? Daniel Shawul Thu Jun 14, 2012 6:57 pm
                        Re: Zobrist alternative? Don Dailey Fri Jun 15, 2012 2:39 pm
                              Re: Zobrist alternative? H.G.Muller Fri Jun 15, 2012 3:46 pm
                                    Re: Zobrist alternative? Daniel Shawul Fri Jun 15, 2012 5:22 pm
                                          Re: Zobrist alternative? H.G.Muller Fri Jun 15, 2012 5:38 pm
                                                Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 10:17 am
                              Re: Zobrist alternative? Daniel Shawul Fri Jun 15, 2012 5:04 pm
                                    Re: Zobrist alternative? Don Dailey Fri Jun 15, 2012 6:00 pm
                                          Re: Zobrist alternative? Daniel Shawul Fri Jun 15, 2012 7:27 pm
                                                Re: Zobrist alternative? Don Dailey Fri Jun 15, 2012 8:16 pm
                                                      Re: Zobrist alternative? Daniel Shawul Fri Jun 15, 2012 8:42 pm
                                                      Re: Zobrist alternative? Daniel Shawul Fri Jun 15, 2012 9:14 pm
                                                            Re: Zobrist alternative? Don Dailey Fri Jun 15, 2012 10:59 pm
                                                                  Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 12:17 am
                                                                        Re: Zobrist alternative? Don Dailey Sat Jun 16, 2012 4:28 am
                                                                              Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 6:30 am
                                                                                    Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 10:09 am
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 10:22 am
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 10:42 am
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 10:54 am
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 11:03 am
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 11:08 am
                                                                                          Re: Zobrist alternative? Don Dailey Sat Jun 16, 2012 12:03 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 12:55 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 2:21 pm
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 2:25 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 2:44 pm
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 12:35 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 1:11 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 1:15 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 1:56 pm
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 2:05 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 2:10 pm
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 2:22 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 2:29 pm
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 2:35 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 2:39 pm
                                                                                          Re: Zobrist alternative? Don Dailey Sat Jun 16, 2012 3:49 pm
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 4:35 pm
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 2:11 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 2:13 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 2:19 pm
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 2:29 pm
                                                                                          Re: Zobrist alternative? Vincent Diepeveen Sat Jun 16, 2012 2:32 pm
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 4:19 pm
                                                                                          Re: Zobrist alternative? Don Dailey Sat Jun 16, 2012 4:50 pm
                                                                                          Re: Zobrist alternative? Daniel Shawul Sat Jun 16, 2012 4:25 pm
                                                Re: Zobrist alternative? Don Dailey Fri Jun 15, 2012 8:21 pm
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