Inclusion Criteria:

          -  Willing and able to provide written informed consent

          -  Histologically or cytologically confirmed adenocarcinoma of the prostate

          -  Presence of metastatic disease documented on imaging studies (bone scan, computed
             tomography [CT] and/or magnetic resonance imaging [MRI] scans)

          -  Patients must have documented evidence of progressive disease as defined by any of the
             following:

               -  Prostate-specific antigen (PSA) progression: minimum of 2 rising values (3
                  measurements) obtained a minimum of 7 days apart with the last result being at
                  least >= 1.0 ng/mL;

               -  New or increasing non-bone disease (Response Evaluation Criteria in Solid Tumors
                  [RECIST] 1.1);

               -  Positive bone scan with 2 or more new lesions (Prostate Cancer Clinical Trials
                  Working Group [PCWG]3)

          -  Surgically or ongoing medically castrated, with baseline testosterone levels of =< 50
             ng/dL (=< 2.0 nM)

          -  Eastern Cooperative Oncology Group (ECOG) performance status of =< 2

          -  Hemoglobin >= 7.5 g/dL in the presence of bone marrow involvement independent of
             transfusion and/or growth factors within 3 months prior to enrollment

          -  Platelet count >= 100,000/uL independent of transfusion and or growth factors within 3
             months prior to enrollment

          -  Serum albumin >= 3.0 g/dL

          -  Medications known to lower the seizure threshold must be discontinued or substituted
             at least 4 weeks prior to study entry

          -  Absolute neutrophil count (ANC) >= 1,500/mm^3

          -  Calculated creatinine clearance (Cockcroft-Gault equation) >= 40 mL/min

          -  Serum potassium >= institutional lower limit of normal (ILLN)

          -  Serum magnesium >= ILLN

          -  Serum bilirubin < 1.5 x institutional upper limit of normal (IULN) (except for
             patients with known Gilbert's disease)

          -  Serum aspartate aminotransferases (AST) or alanine aminotransferases (ALT) < 2.5 x
             IULN for patients without liver metastases; for patients with liver metastases AST or
             ALT < 5 x IULN is allowed

          -  Able to swallow study drugs whole as a tablet/capsule

          -  Male subject with a female partner of childbearing potential or pregnant must agree to
             use two acceptable methods of contraception and not to donate sperm from time of
             screening until 3 months after the last dose of study treatments

          -  Patients must agree to tissue collection for correlative studies (including
             participation in PA13-0291 and PA13-0247 for MD Anderson participants) at the
             specified timepoints

        Exclusion Criteria:

          -  Any prior treatment with: ipilimumab

          -  Treatment within 28 days of cycle1 day1: any other systemic therapy for prostate
             cancer (with the exception of luteinizing hormone-releasing hormone [LHRH] agonists
             and LHRH antagonists for testosterone suppression, and bisphosphonates and RANK-ligand
             inhibitors for bone metastases which are allowed); any other investigational product

          -  Treatment within 12 months of cycle 1 day 1 with any Cyp17-lyase inhibitor, any 2nd
             generation AR antagonist (e.g. enzalutamide), cabazitaxel or carboplatin

          -  Patients treated with any Cyp17-lyase inhibitor, any 2nd generation AR antagonist
             (e.g. enzalutamide), cabazitaxel or carboplatin whose disease progressed while on
             treatment or within 3 months of its discontinuation; patients who have received any of
             these treatments more than 12 months from study entry and whose disease did not
             progress while on treatment or within 3 months of its discontinuation are allowed on
             study

          -  Patients whose disease is refractory (defined as evidence of disease progression while
             on drug or within 3 months of its discontinuation) to more than 2 lines of
             chemotherapy; any number of chemotherapies to which the patient's disease is not
             refractory are allowed, as long as time on treatment did not exceed 6 months (counted
             from day 1 of cycle 1 to day 1 of the last cycle of treatment)

          -  Flutamide (Eulexin) treatment within 4 weeks of cycle 1, day 1 and bicalutamide
             (Casodex) or nilutamide (Nilandron) within 6 weeks of cycle 1 day 1 (exceptions: if
             progression is documented prior to this time interval, or if patient is deemed by the
             treating physician to be highly unlikely to respond to AR inhibitor withdrawal (e.g.
             if PSA did not decline for 3 months in response to AR inhibitor given as a second line
             or later intervention, or if patient has symptoms attributable to disease progression)
             only a 3 day washout prior to cycle 1, day 1 will be required for any of them

          -  Radiation therapy for treatment of the primary tumor within 6 weeks of cycle 1, day 1;
             patients who have received palliative radiation and recovered are eligible

          -  Any chronic medical condition requiring a higher dose of corticosteroid than 10mg
             prednisone/prednisolone daily; use of inhaled, intranasal, intra-articular and topical
             steroids is acceptable, as is a short course (i.e. =< 1 day) of corticosteroids to
             prevent a reaction to the IV contrast used for CT scans

          -  Active infection (requiring oral or IV antibiotics or antiviral therapy) or other
             medical condition that would make prednisone/prednisolone (corticosteroid) use
             contraindicated; known history of testing positive for human immunodeficiency virus
             (HIV) or known acquired immunodeficiency syndrome (AIDS)

          -  A malignancy (other than the one treated in this study) which required radiotherapy or
             systemic treatment within the past 5 years, or has a >= 30% probability of recurrence
             within 24 months (except for non-melanoma skin cancer or Ta urothelial carcinomas)

          -  Uncontrolled hypertension (systolic blood pressure [BP] >= 140 mmHg or diastolic BP >=
             90 mmHg); patients with a history of hypertension are allowed provided blood pressure
             is controlled by anti-hypertensive treatment

          -  Prolonged corrected QT (QTc) interval on pre-entry electrocardiogram (>= 450 msec)

          -  Known active or symptomatic viral hepatitis or chronic liver disease

          -  Clinically significant heart disease as evidenced by myocardial infarction, or
             arterial thrombotic events in the past 6 months, severe or unstable angina, history of
             clinically significant ventricular arrhythmias (such as ventricular tachycardia,
             ventricular fibrillation, or torsades de pointes), New York Heart Association (NYHA)
             class III-IV heart disease or cardiac ejection fraction measurement of < 40% at
             baseline

          -  Autoimmune disease: patients with a history of inflammatory bowel disease (including
             Crohn's disease and ulcerative colitis) and autoimmune disorders such as rheumatoid
             arthritis, autoimmune thyroiditis, autoimmune hepatitis, systemic progressive
             sclerosis [scleroderma and variants], systemic lupus erythematosus, autoimmune
             vasculitis [e.g., Wegener's granulomatosis] or autoimmune neuropathies (such as
             Guillain-Barre syndrome) are excluded from this study; vitiligo and adequately
             controlled endocrine deficiencies such as hypothyroidism are not exclusionary

          -  Patients who have had a history of illness which put them at current risk for bowel
             perforation such as acute diverticulitis, intra-abdominal abscess, gastrointestinal
             (GI) obstruction and abdominal carcinomatosis

          -  History of seizure or known condition that may pre-dispose to seizure (including but
             not limited to prior stroke or, loss of consciousness within 1 year prior to
             randomization, brain arteriovenous malformation; or intracranial masses such as
             schwannomas and meningiomas that are causing edema or mass effect)

          -  Gastrointestinal disorder affecting absorption

          -  Any underlying medical or psychiatric condition, which in the opinion of the
             investigator, will make the administration of study drug hazardous or obscure the
             interpretation of adverse events

          -  Untreated symptomatic spinal cord compressions

          -  Prisoners or subjects who are involuntarily incarcerated

          -  Subjects who are compulsorily detained for treatment of either a psychiatric or
             physical (eg, infectious disease) illness