Nestled within the maze of critical decisions that need to be made regarding alcohol rehabilitation, lies the essential task of selecting the suitable rehab center. This decision, akin to the principle of the Butterfly Effect in Chaos Theory, can set off a chain of events that can either lead to successful sober living or a relapse. As such, having a rational and objective strategy to evaluate prospective rehab centers is critical.

Drawing parallels with the approach of a discerning investigator, one should be armed with an array of probing questions to uncover the necessary details about the rehab center. Let's delve into the key areas of focus.

• The initial question should be about the facility's accreditation and licensing. Similar to how hospitals strive for the Joint Commission's Gold Seal of Approval, alcohol rehab centers should possess accreditations from reputable bodies such as the Commission on Accreditation of Rehabilitation Facilities (CARF). Ensuring that the center is accredited verifies their commitment to meeting established international standards.
• Next, one should investigate the treatment modalities employed by the center. Just as the field of Mathematics has multiple methods to solve a problem, there exist varied approaches to alcohol rehabilitation; these vary from Cognitive Behavioral Therapy to 12-Step Facilitation Therapy. Understanding these treatment modalities and identifying which aligns best with your needs, is paramount.
• Neuroplasticity, the brain's remarkable ability to change and adapt, is a concept that underscores the efficacy of personalized treatment plans. Is the center equipped to provide individualized treatment plans? Rehab centers with a personalized approach, based on an individual’s history, current status, and future needs, tend to yield better results.
• The concept of Pareto Efficiency in economics implies that no one should be made worse off for others to become better off. Correspondingly, does the center's program interfere with your daily life or can they provide outpatient services? Outpatient programs provide the flexibility to continue your everyday activities while pursuing your recovery.
• Another key variable to consider within this equation is post-treatment support. The journey doesn't end with the completion of the rehab program. It’s a continuum that extends into one’s daily life post-rehab. Many centers offer aftercare programs to support this continuum of care, providing a safety net and bolstering the chances of lifelong sobriety.
• Equally important is the question of the program's duration. In the world of drug rehabilitation, time is of the essence. Research suggests that the length of treatment directly correlates with the success of recovery. Hence, explore if the center provides programs of varying lengths and if they can modify the duration based on individual progression.
• The staff's expertise and ratio also play a pivotal role. There is an inherent complexity involved in rehabilitating an individual addicted to alcohol. This complexity is akin to the mathematical concept of a fractal, where each piece of the puzzle bears a resemblance to the larger picture. So, the staff must possess the necessary skills and the center should have an adequate staff-to-patient ratio.
• Cost and insurance coverage are factors that one cannot ignore. Understanding the cost structure and exploring the possibility of insurance coverage can prevent future financial stress, which can be a trigger for relapse.
• Finally, inquire about the center's success rate. However, bear in mind that success in alcohol rehab is not always a binary outcome. In the realm of alcohol rehabilitation, success may be defined in various ways - from complete abstinence to improved social functioning.

In conclusion, the process of choosing an alcohol rehab center cannot be reduced to a simple algorithm. It involves careful consideration of various variables, akin to a complex multivariate analysis in statistics. However, arming yourself with these key questions can significantly aid in choosing the right rehab center and set you on the path to recovery.