The “directly relevant information” is the information you know, and not any information you don’t know.
If you want to construct a bet, do it among all possibly existing people that, as far as they know, could be each other. So any information that one person knows at the time of the bet, everyone else also knows.
If you don’t know the time, then the bet is among all similarly situated people who also don’t know the time, which may be people in the future.
The “directly relevant information” is the information you know, and not any information you don’t know.
If you want to construct a bet, do it among all possibly existing people that, as far as they know, could be each other. So any information that one person knows at the time of the bet, everyone else also knows.
If you don’t know the time, then the bet is among all similarly situated people who also don’t know the time, which may be people in the future.