user11144: Assume a 32-piece tablebase would exist. It would be a Chess God. Surely there have been estimations of its ELO?
According to the very related question, two problems arise:
a) At any point the practical MaxELO<=400+second best rated player.
b) ELO drift over time.
Thus, a) I'd like to know the theoretical maximum (not the practical as given in the linked answer), b) at some arbitrary but fixed time (maybe the one at where it was answered somewhere in the internet).
c) Wiki data for chess computers for convenience. No S-curve to see yet (maybe due to b)...)

user15223: Source

So the question arises: what happens if you let the system ponder for eight hours, or for eighty, or run on a far larger number of processors? My prediction: it will not cross Elo 4000 — nothing ever will. The draw in chess will prevent that from happening: a 3900 program will always be able to hold the game, however strong the opponent.

By the way current computers aren't close to perfect play in general. They might be really hard to beat from the starting position, but give them a more dubious position and they can still lose (and fail to win the reverse).

user17330: I'm arguing below that it is logically problematic to even define such a thing.
The ELO of the strongest computers is really defined only relative to a ladder of weaker computers, starting from the ELO of best human players. A program A winning a certain percent of points against a 2775 ELO grandmaster will be assigned ELO 2875. A program B winning the same percentage of points against A will be assigned ELO 2975. And so on, up to maybe 3700 ELO of AlphaZero. The differences between ladders are better to be reasonable, as, e.g., pitching AlphaZero against a human would lead to 100% of wins in practice, and no numeric value of ELO can be assigned on that basis.
Now, how do we assign ELO to God? Inevitably, by measuring it against a weaker program, say W, that plays imperfectly. But since God is omniscient, not only it knows the best move in each position, it also can exploit ideally any imperfection in W's play. So, either W itself plays perfectly, in which case every game will be a draw, or God will win 100% of games. In the latter case, it is impossible to define the ELO of God relative to W.
So the only way to define the ELO of God is to say that it is equal to the ELO of any program W that itself plays perfectly, but is not necessarily omniscient. This ELO, again, can only be assigned relative to some weaker program V. But that ELO difference is defined not so much by the fact that W plays a perfect (i.e., evaluation-preserving) move at every position, but by how well it exploits the fact that V plays imperfectly - i.e., two programs W,W' that both play perfectly can have a different relative ELO against V. But on the other hand, they must have the same ELO, as they draw all games against each other (and God).
All these problems are really exacerbated by the fact that we cannot even meaningfully assign an ELO difference to two deterministic programs by pitching them repeatedly against each other, as all the outcomes will be the same... So we need something like randomizing over starting positions (in which case the ELO difference will be severely dependent on the ensemble of these positions), or use non-deperministic programs... That may solve the problem of the highest rung of the ladder, but still it is clear that the "number of rungs" in a ladder reaching perfect play from human level is not well defined - it depends on the programs in the ladder and how adapted they are against each other's weaknesses.

11144: <p>Assume a 32-piece tablebase would exist. It would be a Chess God. Surely there have been estimations of its ELO?</p>
<p>According to the very related <a href="https://chess.stackexchange.com/questions/8630/is-this-really-limitation-of-absolute-elo/8637#8637">question</a>, two problems arise:</p>
<p>a) At any point the practical MaxELO&lt;=400+second best rated player.</p>
<p>b) ELO drift over time.</p>
<p>Thus, a) I'd like to know the <em>theoretical</em> maximum (not the practical as given in the linked answer), b) at some arbitrary but fixed time (maybe the one at where it was answered somewhere in the internet).</p>
<p>c) <a href="https://en.wikipedia.org/wiki/Swedish_Chess_Computer_Association" rel="nofollow noreferrer">Wiki data</a> for chess computers for convenience. No S-curve to see yet (maybe due to b)...)</p>
 15223: <p><a href="https://en.chessbase.com/post/how-god-plays-chess" rel="nofollow noreferrer">Source</a></p>
<blockquote>
<p>So the question arises: what happens if you let the system ponder for eight hours, or for eighty, or run on a far larger number of processors? My prediction: it will not cross Elo 4000 — nothing ever will. The draw in chess will prevent that from happening: a 3900 program will always be able to hold the game, however strong the opponent.</p>
</blockquote>
<p>By the way current computers aren't close to perfect play in general. They might be really hard to beat from the starting position, but give them a more dubious position and they can still lose (and fail to win the reverse).</p>
 17330: <p>I'm arguing below that it is logically problematic to even define such a thing.</p>
<p>The ELO of the strongest computers is really defined only relative to a ladder of weaker computers, starting from the ELO of best human players. A program A winning a certain percent of points against a 2775 ELO grandmaster will be assigned ELO 2875. A program B winning the same percentage of points against A will be assigned ELO 2975. And so on, up to maybe 3700 ELO of AlphaZero. The differences between ladders are better to be reasonable, as, e.g., pitching AlphaZero against a human would lead to 100% of wins in practice, and no numeric value of ELO can be assigned on that basis.</p>
<p>Now, how do we assign ELO to God? Inevitably, by measuring it against a weaker program, say W, that plays imperfectly. But since God is omniscient, not only it knows the best move in each position, it also can exploit ideally any imperfection in W's play. So, either W itself plays perfectly, in which case every game will be a draw, or God will win 100% of games. In the latter case, it is impossible to define the ELO of God relative to W.</p>
<p>So the only way to define the ELO of God is to say that it is equal to the ELO of any program W that itself plays perfectly, but is not necessarily omniscient. This ELO, again, can only be assigned relative to some weaker program V. But that ELO difference is defined not so much by the fact that W plays a perfect (i.e., evaluation-preserving) move at every position, but by how well it exploits the fact that V plays imperfectly - i.e., two programs W,W' that both play perfectly can have a different relative ELO against V. But on the other hand, they must have the same ELO, as they draw all games against each other (and God).</p>
<p>All these problems are really exacerbated by the fact that we cannot even meaningfully assign an ELO difference to two <em>deterministic</em> programs by pitching them repeatedly against each other, as all the outcomes will be the same... So we need something like randomizing over starting positions (in which case the ELO difference will be severely dependent on the ensemble of these positions), or use non-deperministic programs... That may solve the problem of the highest rung of the ladder, but still it is clear that the &quot;number of rungs&quot; in a ladder reaching perfect play from human level is not well defined - it depends on the programs in the ladder and how adapted they are against each other's weaknesses.</p>
