[
  {
    "comment": "uniform over {1,2,3}, VaR_0.5 = 2 (P[X<2]=1/3 ≤ 0.5, P[X<3]=2/3 > 0.5)",
    "probs": ["1/3", "1/3", "1/3"],
    "vals":  ["1",   "2",   "3"],
    "alpha": "1/2",
    "expected": "2"
  },
  {
    "comment": "two-point: losses 10 and 20 with equal prob, VaR_0.4 = 10",
    "probs": ["1/2", "1/2"],
    "vals":  ["10",  "20"],
    "alpha": "0.4",
    "expected": "10"
  },
  {
    "comment": "two-point: same distribution, VaR_0.5 = 20 (P[X<20]=0.5 ≤ 0.5, equality holds)",
    "probs": ["1/2", "1/2"],
    "vals":  ["10",  "20"],
    "alpha": "0.5",
    "expected": "20"
  },
  {
    "comment": "two-point: same distribution, VaR_0.6 = 20 (P[X<20]=0.5 ≤ 0.6)",
    "probs": ["1/2", "1/2"],
    "vals":  ["10",  "20"],
    "alpha": "0.6",
    "expected": "20"
  },
  {
    "comment": "degenerate: single outcome, VaR is always that value",
    "probs": ["1"],
    "vals":  ["5"],
    "alpha": "0",
    "expected": "5"
  }
]