first case....... chessplaying ghosts
Yes. Correspondence with the dead proven by Prof. Eisenbeiss.
Who from the non-god position will correlate the simplest explanation with the observations? Two guys played a chess game? That is all the article outlines. One of the guys claims it was not him playing chess, but a dead person. There is nothing beyond that to examine. Not only is that not proof it is not evidence either. It is a claim.
You have a point there. Even if there were a real other party (the dead person) playing, maybe it was an alien or demon using mind control.

Perhaps, but there is no evidence for that. The point is this:
Those explanations are needlessly complicated. The simplest explanation is that the personality of the deceased person has persisted and is able to communicate the information that was receievd.
I disagree. It is not the simplest explanation as it invokes additional, unnecessary assumptions. Specifically, in addition to the assumption that the 'psychic' is telling the truth, it introduces the assumption that we should ignore all of the hundreds of times that people have claimed to perform such "supernatural" abilities but have failed or have conclusively been found to be liars. Since we do have evidence that others who have made similar claims have either failed to prove their claims or have been proven outright liars, we only need to introduce one assumption to reach a conclusion, i.e. that the supposed "psychic" is a liar.
Hey the joint, this is my reply to you

A working explanation must be powerful enough to explain all of the observations (Salient Points) as they are collateral assumptions. It is not enough that an explanation is simple, it must also account for the facts.
I'm not sure what you're getting at here. All of that reinforces exactly what I said. The simplest explanation that explains all of the facts without introducing additional unverifiable assumptions is that he is a liar. Claiming otherwise introduces additional 'facts' that can't be accounted for, i.e. assumptions.
The assumption that he is a liar is placed in doubt when you consider the Salient Points.
For example, if you assume he is a liar then you are not only proposing a highly elaborate fraud lasting almost 8 years, but you are also proposing that the fraudster would be satisfied receiving no compensation for his work and meticulous research (Salient Point #1). Also, you would be proposing that Salient Point #2 is explained by another party assisting the fraudster, so now you are proposing a conspiracy. To explain Salient Point #4 you would be proposing that the information from the dead chess-player's children was acquired by the aforementioned fraud-ring.
So to summarize, I will quote from the AECES summary of the case:
The combination of the skill of the game plus the correct esoteric data vastly diminishes the potential for explaining the information by fraud as this is likely to have required major collaboration from numerous highly respected people.
So in fact the assumption that Rollans is a liar will produce many collateral assumptions, thus it is far from a simple explanation.