user15223: 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?

user18143: I didn't do the experiment but I  think it should be something like 
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) 

user15223: 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.
Partial answer #2: Komodo developer Larry Kaufmann writes here that -

Komodo is rated 3423 CCRL Rapid on four cores, but will be playing on a 32 core Threadripper which should boost its Rapid rating to around 3600.

If each core contributes roughly the same to speed, then 32 cores is 8x the speed of the original, and that translates to about 180 elo. (Of course this makes it seem like Komodo scales better than Stockfish, but Stockfish is going from 43 to 192 cores which is much more firmly in the logarithmic part of the curve.)
Partial answer #3: the performance of Komodo 14 drops from +80 elo (2 threads vs 1 thread) to +4 elo (128 threads vs 64 threads). The performance of Stockfish 11 drops from +90 elo (2 threads vs 1 thread) to +14 elo (128 threads vs 64 threads). Source. In this range, the scaling looks pretty linear.

user825: 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.


15223: <p>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?</p>

<p>Is there a general relation for this? Also, does this scaling depend on which engine is used, and if so, why?</p>
 18143: <p>I didn't do the experiment but I  think it should be something like <a href="https://i.stack.imgur.com/LOzvS.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/LOzvS.png" alt="enter image description here"></a></p>

<p>As @SmallChess said in his <a href="https://chess.stackexchange.com/a/24340/18143">answer</a>: required computational power grows exponentially and at a certain depth it would be just way too big.</p>

<p>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) </p>
 15223: <p>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.</p>
<p>Partial answer #2: Komodo developer Larry Kaufmann <a href="http://talkchess.com/forum3/viewtopic.php?f=2&amp;t=73759#p841287" rel="nofollow noreferrer">writes here</a> that -</p>
<blockquote>
<p>Komodo is rated 3423 CCRL Rapid on four cores, but will be playing on a 32 core Threadripper which should boost its Rapid rating to around 3600.</p>
</blockquote>
<p>If each core contributes roughly the same to speed, then 32 cores is 8x the speed of the original, and that translates to about 180 elo. (Of course this makes it seem like Komodo scales better than Stockfish, but Stockfish is going from 43 to 192 cores which is much more firmly in the logarithmic part of the curve.)</p>
<p>Partial answer #3: the performance of Komodo 14 drops from +80 elo (2 threads vs 1 thread) to +4 elo (128 threads vs 64 threads). The performance of Stockfish 11 drops from +90 elo (2 threads vs 1 thread) to +14 elo (128 threads vs 64 threads). <a href="http://talkchess.com/forum3/viewtopic.php?f=2&amp;t=74188" rel="nofollow noreferrer">Source</a>. In this range, the scaling looks pretty linear.</p>
 825: <p>Multicore is important for chess engines, but it doesn't scale forever.</p>

<ul>
<li>Up to certain depth, no matter how much hardware you have, you just don't have enough computational power</li>
<li>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.</li>
<li>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.</li>
</ul>
