In this case the chosen copy in the green room should update on the anthropic evidence of being chosen to make the choice. That copy had a 1⁄18 probability of being chosen if the coin flip came up heads, and a 1⁄2 probability of being chosen if the coin flip came up tails, so the odds of heads:tails should be updated from 9:1 to 1:1. This exactly canceled the anthropic evidence of being in a green room.
In this case the chosen copy in the green room should update on the anthropic evidence of being chosen to make the choice. That copy had a 1⁄18 probability of being chosen if the coin flip came up heads, and a 1⁄2 probability of being chosen if the coin flip came up tails, so the odds of heads:tails should be updated from 9:1 to 1:1. This exactly canceled the anthropic evidence of being in a green room.