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There's always a risk that the player may see any and all options as being traps.
This is not true. For example you are given an opportunity to be promoted, but accepting the offer will also mean that you will be separated with your current partner for the next two years. This is not a trap because the logical effects are observable. The game is not trying to trick you, but to give you an opportunity to evaluate what you think is important to you.
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And being asked to play a game through twice is not a bad thing if the choice makes the game sufficiently different that it increases the replay value. In this case the initial choice should also be of a type that the player will consider more than one option to be valid choices (not an ethical or philosophical choice where the player would feel untrue to themselves to answer in a different way.) If you want the player to replay the game you want the game to be significantly different on the second play-through that the player isn't bored, but having them make a different choice at the beginning of the game is not necessarily the best way to do this, because the player might just make the same choice again.
This is correct. For Webbit's scenario, it seems like a trap because the player will think, "If I kill the kid nothing will happen to me, but that can't be true, because there is a sequel. Something has to happen if I kill the kid. Is the game going to penalize me for being cold blood? Is the game trying to make me regret my decision and come back to make a different choice and have to play the same 20 years again?" Not any kind of reason that will make the player play the game again qualify as 'replayability'. For instance, the player may interpret the endings as delayed 'gameovers' due to an early the choice. He wants to replay the game not because he wants to try something else but that he thinks he had made a wrong decision. But there was no way to tell which decision would be correct, so that player is forced into thinking that the designer wants him to just go trial-and-error.