In state-of-the-art adaptive streaming solutions, to cope with varying network conditions, the client side can switch between several video copies encoded at different bit-rates during streaming. Each video copy is divided into chunks of equal duration. To achieve continuous video playback, each chunk needs to arrive at the client before its playback deadline. The perceptual quality of a chunk increases with the chunk size in bits, whereas bigger chunks require more transmission time and, as a result, have a higher risk of missing transmission deadline. Therefore, there is a trade-off between the overall video quality and continuous playback, which can be optimized by proper selection of the next chunk from the encoded versions. This paper proposes a method to compute a set of optimal client strategies for this purpose.