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If you want perfect information, yes. But to gain an edge you do not need that. Enumerate all pieces by their starting row from 0 to 7. Have the oracle figure out what a player with a given rating would would move each piece.
"If I tell this player to move the their queen (or queen's pawn, if that looks more plausible for them), does this have a better expected outcome than if I tell them to move their light-squared bishop (or its pawn)?"
Again, this has limitations. The player needs to be a fairly decent chess player. And a decent chess engine would still totally crush them, because the cheating player would be limited to fairly obvious moves. "Sacrifice your queen here for a decisive advantage ten moves down the line" is not a strategy you could communicate in three bits.
But it would probably make the cheater significantly stronger.
I do not have a good example for a channel which can communicate three bits but not five, though.
Sure. On the other hand, humans are also really got at filtering out irrelevant information. Luckily, sound is rather obvious (especially if your baseline is complete silence instead of what you get in a football stadium), and players do not have a lot in their field of view which can be controlled by third parties.
My gut feeling that the optimum for in-person cheating would be to have a computer implanted into your body. Some 28 years after Deep Blue, a chess engine which could defeat mere humans should fit in your guts. A bidirectional connection with a few baud should be well within technical reach, you have all sorts of nerves just waiting to be tapped. Unless you are checking if your cheater is sleeping with a Qi charger on their belly or put them into an imaging scanner, you are unlikely to catch them.
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