Say, it’s you who is the Sleeping Beauty, awaken and told by the dungeon master:
Here is a fair coin. I will toss it and if it lands head up, your memories will be erased and you will be put to sleep again and then you’ll wake up after some time in this exactly the same scenario.
If the coin lands tails up, however, you’ll get this fair coin to play with as long as you wish. After then, you will be asked for a number. If that number is equal to the number of times you have been awakened like this, you will be freed.
If your number isn’t right, your memories will be erased and you will be put to sleep again and then you’ll wake up after some time in this exactly the same scenario.
What is your strategy to be freed? If not this time, but eventually?
You know that this dungeon master is telling you the truth. So this may be your first time or the second or the Nth time.
What is your best strategy to escape?
Talk about it here:
http://lesswrong.com/r/discussion/lw/pd5/open_thread_august_28_september_3_2017/dwkw
protokol2020 
>If that number is equal to the number of times you have been awakened like this, you will be freed.
Does “number of times you have been awakened like this” mean all of them, or just the number in this iteration?
Just the number of this iteration. Since you have been captured to see if you are clever enough to devise a strategy to escape. It may be your first awakening. It may be, that the fair coin has landed 3 times head up already. You don’t know.
But if there was no coin tossing by the dungeon master, you could be sure it’s your first time, after which you’ll be freed, saying it’s 1.