" Conversely, finding out things about the player does not reduce my uncertainty about what value the dice will reveal very much. For instance, if I find out that the player really wants the sum of the values revealed by the dice to be seven, I will think that they are about as likely to roll a seven as they would be to roll a one if I had learned that the player really wanted to avoid rolling a seven. "

You mean "...about as likely to roll a seven as they would be if I had learned that they really wanted to avoid rolling a seven."

In general this one needs a lot of proof-reading

Not sure you need all those examples--maybe you could delete the toilet example, for instance?

Again, nice job! I look forward to reading the comments.