Seems straightforward to me. McGonagall knows that she does not recall being handed 100 Galleons an hour ago, so the three states of the world with high probability are: 1) She is not in a universe where she will hand Harry 1 Galleon, 2) She is in a universe where she hands Harry 1 Galleon and Harry breaks the agreement, or 3) She is in a universe where she hands Harry 1 Galleon and Harry keeps the agreement in a way that leaves her unable to recall this happening. By not handing Harry a Galleon, she will ensure that she is in universe 1. By handing Harry a Galleon, she will find herself in universe 2 or 3. She should therefore give Harry a Galleon if she judges it less than 99 times more likely that Harry will break the agreement than fulfil it in a way consistent with her experience.
As Harry has access to a time machine, he doesn’t need to decide to give her 100 Galleons before he gets the 1 Galleon, so the situation is quite different to one based on predicting her actions, as Omega does in the Counterfactual Mugging. Rather it has most of the properties of the forward-time version of the gambit: “If you give me 1 Galleon now, I’ll hand you 100 Galleons in one hour”, except that McGonagall has a big piece of evidence that the promise will be broken, namely that she doesn’t remember it being kept.
Seems straightforward to me. McGonagall knows that she does not recall being handed 100 Galleons an hour ago, so the three states of the world with high probability are: 1) She is not in a universe where she will hand Harry 1 Galleon, 2) She is in a universe where she hands Harry 1 Galleon and Harry breaks the agreement, or 3) She is in a universe where she hands Harry 1 Galleon and Harry keeps the agreement in a way that leaves her unable to recall this happening. By not handing Harry a Galleon, she will ensure that she is in universe 1. By handing Harry a Galleon, she will find herself in universe 2 or 3. She should therefore give Harry a Galleon if she judges it less than 99 times more likely that Harry will break the agreement than fulfil it in a way consistent with her experience.
As Harry has access to a time machine, he doesn’t need to decide to give her 100 Galleons before he gets the 1 Galleon, so the situation is quite different to one based on predicting her actions, as Omega does in the Counterfactual Mugging. Rather it has most of the properties of the forward-time version of the gambit: “If you give me 1 Galleon now, I’ll hand you 100 Galleons in one hour”, except that McGonagall has a big piece of evidence that the promise will be broken, namely that she doesn’t remember it being kept.