Since this thread got linked, I might as well resurrect it…
The 6502 was indeed used in a number of dedicated chess computers, perhaps most notably including the Mephisto Rebel series programmed by Ed Schröder. There's a document (attached) titled "Inside Rebel" which described, at a high level, many of the techniques it relied upon - I've confirmed some of these details by examining a disassembly of the Mephisto Academy ROMs. Notable by its absence is a transposition table; most of the address space of the 6502 was occupied by the program ROM. But by sophisticated search and evaluation techniques, a 5MHz 65C02 could search parts of the game tree to about 16 ply (if given sufficient time), and thereby solve endgames up to 8-move depth. These machines were still doing well in computer chess tournaments around 1990, which seems very late.
A successor to these machines was the Mephisto RISC, which used an ARM2 (VL86C010, so no cache). The greatly improved execution efficiency and higher clock speed made a big difference, but Schröder still didn't implement a transposition table AFAIK, just ported over an expanded version of Rebel. However, that machine arrived just when the company was getting out of the dedicated chess computer business; the greater capabilities of desktop computers had made it too specialised a market to sustain.
Some chess computers used other CPUs. There was one competing in serious tournaments that used a 68030, for example, and earlier ones that used a 68000. Curiously, Mephisto had the 68000-based Berlin which was only similar in strength to the 6502-based Mephisto Polgar, despite having much more clock speed, ROM and RAM to work with. It took the Berlin Professional, using a 68020, to make a significant improvement - but again, using more resources and a higher clock speed to merely equal the Mephisto RISC of several years earlier.
Low-end consumer machines for novice players often used some random microcontroller, such as a Hitachi SH4 or a 68HC05, with a very limited chess engine squeezed in. My family once had a Tandy 1450 portable of this type, which apparently had just 5KB ROM and 256 nybbles of RAM, scarcely enough to write an engine that knows all the rules and can search a few ply. Clearly the focus here was on cost and battery life, not playing strength. Consumer chess computers of this unambitious sort are still on the market; they are what you find if you look on Amazon.
But there is now a professional-grade chessboard with integrated engine, based around a Raspberry Pi. This allows it to run several different engines with various playing styles and strength. This, of course, brings everything back to the ARM CPU.
Perhaps notably, I have not been able to find any dedicated chess computer that used a Z80 family CPU. Of course there were chess games released for Z80 based micros. Some 1980s machines used a 6800 family CPU, such as the Hitachi 6301. A very early Mephisto model used an RCA 1801. But most of the serious 1980s machines did use a 6502.
As 65xx enthusiasts, I'm sure one of us could find the time to rig up a 65816 to some sort of sensor-board arrangement…
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