The labyrinthine corridors of family law can seem intimidating to the uninitiated, particularly when the stakes involve the custody of your children. It's here where the invaluable guidance of an adept child custody lawyer comes into play. However, the question that invariably arises is, how do you select the most suitable legal advocate for your case? This question is not just rhetorical, but a critical starting point on your journey towards child custody.

Discerning the appropriate lawyer for your case is an exercise that requires diligent focus and thorough interrogation. The interrogation here is not adversarial, but a series of astute questions directed towards the potential lawyer to gauge their capacity and competence in handling your case.

Firstly, delve into the attorney's experience. It's imperative to ascertain their specialization and their years of practice in this field. Your query should seek to uncover whether their active practice involves child custody cases and the proportion of such cases they handle. A statistical approach here can provide concrete data, offering a clear comparative analysis between different lawyers.

A lawyer with a high proportion of child custody cases and a demonstrable winning streak brings to the table a strong grasp of the dynamics involved – a crucial factor in the unpredictable, complex matrix of child custody litigation. Ask for case success rate percentages and use statistical methods to compare multiple lawyers, keeping in mind that while numbers are essential, they are not the only deciding factors.

Secondly, explore their knowledge of local jurisdiction. Laws and court procedures vary across regions, and having a lawyer adept in the local rules can give you a strategic advantage. They'll have a solid understanding of the judicial temperament, local court procedures, and other lawyers within the jurisdiction, which can be pivotal for your case.

Thirdly, discuss your case's specific dynamics and their strategies to tackle them. This is where the application of game theory becomes salient. Invented by mathematician John Nash, game theory explores the possible outcomes of a situation where the results depend on the actions of all those involved. Your discussions with potential lawyers should revolve around the different possible strategies and their respective outcomes, drawing on game theory principles.

Next, talk about the potential costs. Family law proceedings, specifically child custody cases, can be lengthy and expensive. Having a clear picture of potential costs will help you budget accordingly and avoid financial surprises down the line. Here, understanding economic theories such as sunk cost fallacy and opportunity cost can help you make wise decisions regarding the budget for your case.

Another critical question is regarding communication. As the case progresses, prompt and clear communication with your lawyer is pivotal. The frequency, mode, and response time are all factors to consider.

Finally, ask for references. Past clients can provide firsthand insight into the lawyer's practice. However, remember that confidentiality is paramount in legal practice, and a lawyer who readily shares information about previous clients may not respect this principle.

While this process may seem grueling, it is a necessary pathway to ensure that you find a lawyer who is not just competent, but also the right fit for you and your case. The right child custody lawyer will be your advocate, your counselor, and your guide through the complex world of family law, ensuring that your, and most importantly, your child's best interests are kept at the forefront.

In conclusion, selecting a child custody lawyer is a multifaceted decision that should be approached with the same precision, diligence, and rigor as the case itself. It is a decision that should be underscored by thorough analysis, informed by various fields - from mathematics to economics, to provide you with the best chance of a favorable outcome.