As part of a software testing process, output verification poses a challenge when the output is not numeric or textual, such as graphical. The industry practice of using human oracles (testers) to observe and verify the correctness of the actual results is both expensive and error-prone. In particular, this practice is usually unsustainable when developing web applications - the most popular software of our era. This is because web applications change frequently due to the fast-evolving requirements amid popular demand. To improve the cost effectiveness of browser output verification, in this study we design failure-based testing techniques and evaluate the effectiveness and efficiency thereof in the context of web testing. With a novel application of the concept of adaptive random sequence (ARS), our approach leverages peculiar characteristics of failure patterns found in browser layout rendering. An empirical study shows that the use of failure patterns and inclination to guide the testing flow leads to more cost-effective results than other classic methods. This study extends the application of ARSs from the input space of programs to their output space, and also shows that adaptive random testing (ART) can outperform random testing (RT) in both failure detection effectiveness (in terms of F-measure) and failure detection efficiency (in terms of execution time).