[ChrisLomont]

>it's that you can't apply statistics to prove this at all

If there are not statistical differences, then there are no performance differences. Cheating by definition should imply performance differences.

If he is cheating, then at some point in the future, if that method becomes detectable and he has to stop, then his play will suddenly suffer, which would be more evidence.

Claiming that statistics cannot answer this question with statistics is not true. It may be hard, or the current sample too small, but claiming stats is not usable is a misunderstanding of statistics.

>This is like the statistical analyses that show election rigging by highlighting a statistically improbable distribution of results

This only works on the public, and is not what professional statisticians that analyze elections do.

And even here, if the event is rare enough, say 1 part in quadrillions, and the analysis is correct, then yes, we would certainly conclude there was rigging.

All human knowledge is statistical. Things we claim to be true are only statistically true to large odds, so even for election rigging, if the stats reach some level of certainty, then it is completely valid proof that would hold in court.

The pop idiocy of election rigging claims has never risen to that level.

>it is completely avoidable if you cheat competently

No, it is not. It may only lower the signal to noise ratio, but there is still detectable differences. If you continually improve the statistics and are forced to lower the signal, eventually the signal would be so low as to not affect the system, which in this case is chess games.

Physics, for example, can tease events out of on the order of 1 part in trillions and demonstrate signal. Plenty of other things do the same.

[SilverBirch]

What is the difference between a 2500 ELO player and a cheater with a computer calibrated to 2500 ELO? Statistically, nothing. That's what I'm saying. What's the difference between a 2300 player taking that odd tip to boost their ELO to 2500. Statistically, again, probably nothing.

[SideQuark]

>Statistically, again, probably nothing.

Yes, there still is. Any program tuned to play some level does so by making suboptimal moves enough to get that lower rating, while making really profound moves more often than a player at say 2500 would make. A 2500 human has a certain level of understanding and all of their moves show this.

Ever play a top engine set to play weaker? They make amazing moves far too often for a weak player, and try to compensate by making poor moves once in a while. No weak human plays this way.

Play chess? I've played for decades, and you can see the difference (and certainly top GMs see it too). You hear in commentaries on analysis of top engines making moves that are not human. Any engine does that - tuning it down only makes it do them less, but still enough that someone that plays a lot at a high level will notice.

A human playing 2500 and a computer playing 2500 are not making the same moves, and it shows even there.

If you know any GMs, ask them the same question and see what answer you get. You will get the one I just gave.