A dealer at a casino holds a game that is played as follows: The player first pays to the dealer, where is some positive integer less than The dealer then intends to flip a coin times. If at any point two consecutive heads are flipped, then the dealer stops flipping the coin, and the player wins and is awarded Otherwise, the player loses (and is awarded nothing). A player pays the dealer The dealer weights the coin before flipping it, changing the probability of flipping heads such that the player's expected net profit is non-positive. The player is not aware of this re-weighing. Find the maximum probability that the dealer should choose.