Say I run Komodo on my 4-core machine. How much stronger would Komodo be if I used an 8-core machine? A 40-core machine? A 4000-core machine?

Is there a general relation for this? Also, does this scaling depend on which engine is used, and if so, why?

  • +1; also of interest: how the strength scales with the increasing RAM availability. – GloriaVictis Apr 29 '19 at 8:29
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    Nowadays answers to this are heavily dependent on the ability of software to use multiple cores efficiently. It's always a question of diminishing returns, but whether the cutoff is at 2, 4, 8... cores depends on the software. Browse through some Superuser questions: superuser.com/search?tab=Relevance&q=is%3aq more cores) – user4378 Apr 29 '19 at 13:57
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    See Amdahl's law. Any computer program can benefit of only so many cores, adding more will not help speed the computation up. Any chess program is a computer program and thus limited by the law. They may differ in the level of sophistication and optimization, but it is safe to say that you won't get much more performance from 4000 cores compared to 40 cores from a program you run on 4 cores. – Pavel Apr 29 '19 at 14:46
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Multicore is important for chess engines, but it doesn't scale forever.

  • Up to certain depth, no matter how much hardware you have, you just don't have enough computational power
  • Yes. Scaling is heavily implementation dependent. For example, a simple mutex would make multithread programming much easier (any decent programmer will agree here), but that'd also make the engine run much slower than another engine runs without mutex locking.
  • 40 cores machine will play stronger than an 8-core machine, although it's hard to state how much. A 4000 core machine should also play stronger than a 40 core, but it's harder to justify the costs for smaller Elo improvement.
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    Is there any possible estimate for "how much"? Say, "doubling the computational power is approximately ~50 elo"? – Allure May 6 '19 at 4:20

Partial answer: TCEC Stockfish plays with 43 cores and threads, while the so-called Redfish kitbitzing engine (which is basically Stockfish on stronger hardware) plays with 192 cores and 256 threads. Running at 4x the speed (as measured by nodes per second), Redfish is +50 elo stronger than TCEC Stockfish.

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I didn't do the experiment but I think it should be something like enter image description here

As @SmallChess said in his answer: required computational power grows exponentially and at a certain depth it would be just way too big.

for simpler position however it's not the case because the engine would've explored all the possibilities before reaching its full capacity (ie: maximum depth)

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  • The graph seems about right (assuming it is strenght increase vs resource increase). For simple positions it does not help to have more compute, but for complex positions it can carry you across the tipping point, so I would leave specific positions out of the discussion. – Dennis Jaheruddin Apr 29 '19 at 14:03

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