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It is vital that players be allowed to double whenever the rules permit it. If a means is provided to forgo the opportunity, that's fine, but the system must not prevent doubling.
It is not all that uncommon that a player may wish to double while stuck on the bar -- maybe he has borne off all but one checker and his opponent has a closed board. In a situation like this you would require him to double at the first opportunity or not at all? But what if he decides not to double at first, or rolls without thinking about doubling, and then later decides he wants to double?
It is not the server's job to assess when someone's position has "improved", or whether doubling would be a good move. It is the server's job to enforce the rules of backgammon.
Furthermore, it is not necessary for one's position to improve in order for doubling to become correct. In the situation I described above, the player may choose not to double because he has gammon chances. After he dances a few times, those gammon chances will be reduced, and he will want to double. He must be allowed to do so.
KotDB: My earlier suggestion in this situation "Autopass until I can make a move" should therefore become "Autopass until I can move again, and I don't want to double from this position"