In the complex world of banking, the compliance consultant's role is akin to the coxswain in a rowing team—guiding, coordinating, and ensuring every movement is aligned with the regulatory expectations. As a business operating in the financial sphere, choosing the right compliance consultant could be the difference between smooth sailing and choppy waters. Therefore, the task of selecting the right consultant requires a methodical approach, a keen understanding of your needs, and the ability to ask the right questions.

Given the intellectual prowess of our readers, we shall draw parallels from the game theory, specifically the 'Prisoner's Dilemma', to explain the dynamics of the banker-consultant relationship. In the classic Prisoner's Dilemma, two individuals act in their self-interest, resulting in an outcome which is less than optimal for both. However, in the case of banking compliance consulting, the ideal scenario is one in which both parties act in mutual interest - the bank in seeking expert advice and the consultant in providing transparent and effective solutions. For the relationship to be symbiotic, it is important that the right consultant is chosen, one who understands the mutual benefits of this partnership.

To start, it is crucial to understand the consultant's experience and knowledge of the regulatory landscape. Just as in chess, where each move is governed by a set of rules, banking is governed by a complex set of regulations that vary across jurisdictions and sectors. Having a consultant with a solid understanding of these rules is paramount. Hence, ask about the consultant's experience with banking regulations, the jurisdictions they have worked in, and their familiarity with the specific type of banking your business engages in.

Next, delve into their problem-solving capabilities. Banking compliance issues can often be intricate puzzles that require analytical skills and innovative thinking. Have the consultants previously managed a compliance crisis? If so, how did they resolve it? Their approach and resolution techniques can provide insight into their problem-solving skills and their ability to handle crises.

Do not shy away from discussing their technology adaptation and integration capabilities. As much as banking is subject to traditional regulatory rules, it is also being subjected to technological upheavals. Blockchain, AI, machine learning - these are not mere buzzwords, but realities the banking sector is facing. A compliance consultant adept in these technologies could be a valuable asset.

Furthermore, ask about their risk management strategies. In Bayesian probability terms, where prior beliefs are updated with new evidence to reach a more accurate conclusion, an effective risk management strategy would consistently update risk assessment models based on new regulatory information, market trends, or internal operations data.

Another important aspect to explore is their communication patterns. Information, as Claude Shannon's Information Theory posits, is subject to noise during transfer. A consultant with clear, concise, and effective communication can ensure minimal information loss during the transfer process.

Lastly, discuss their fees and charges. As any economist would tell you, every decision is a cost-benefit analysis. Understand their fee structure, compare it with the value they can bring to your business and then make an informed decision.

The choice of a compliance consultant is of paramount importance for any banking business. Asking the right questions can be a potent tool in your decision-making arsenal. Remember, this is not just about navigating through the regulations, but also about finding a partner who can guide your business through the complex waters of banking compliance to safer shores.