In the game of baccarat, the banker hand has a slightly higher chance of winning when both hands have initial two-card totals of 0-5. The exact probability of the banker hand winning in this situation is 54.8%, while the player hand has a probability of winning of 45.2%. This is due to the fact that the banker hand is given the opportunity to draw an additional card in certain situations, giving it a slight advantage over the player hand.