Assuming there is always a letter with a 50% chance and we choose wrong 11 times in a row. One more and game over. At this point we have 11 Bits of information, which is enough to distuingish between 2048 words.
Actually, we should be correct 50% of the time. Which means 22 Bits of information or 4194304 words.
Additionally, we know the length of the word.
The english dictionaries seem to have between 400k and 1000k words [0] of all word sizes. With 22 Bits we get 4000k words. We do not have to worry about getting hanged using the information-reduction algorithm. ;)