<p>We study a multi-server strategic queueing model in which customers choose among servers that differ in service rates and service valuations. Customers can either commit to a specific server or adopt a flexible strategy by joining multiple queues simultaneously. Service is received from the server that completes the request first, after which redundant requests are canceled. This flexibility option presents a clear trade-off: customers benefit from potentially shorter waiting times, but risk receiving lower-quality service from less desirable servers. Rational customers take into account that their welfare depends not only on their own decisions but also on the decisions of other customers, thereby engaging in a noncooperative game. We characterize the Nash equilibrium outcomes of this strategic queueing game, highlighting how customers balance waiting time reduction against the uncertainty in service quality. Our analysis demonstrates that introducing the flexibility option leads to higher overall social welfare, even when customers act to maximize their own welfare. We further examine the socially optimal allocation and the revenue maximizing pricing strategy when flexibility is offered at a price.</p>