Best spot in line on a glass-tile bridge

Ten contestants line up to cross a bridge made of $10$ rows of tiles, each row having a left and a right tile. In every row exactly one tile is safe and the other breaks, and nobody can tell which. The person at the front of the line chooses a tile in each row in turn; a wrong choice eliminates them, after which the next person in line takes over (now knowing which tile in that row is safe) and continues forward. The first contestant to reach the far side wins. Which position in the line ($1$ = front) maximises a contestant's chance of winning?

Position $6$. Each row's first guess is a fresh 50/50, so the total number of eliminations is $\text{Binomial}(10,\tfrac12)$. The winner is the person at position (eliminations $+1$), and the binomial mode is $5$, so position $6$ is best.