Head and shoulders (Osler and Chang's rules on 15-minute closes, zigzag cut-off k x volatility, k = 3 and 6) on XAUUSD (spec hs_spec.md). Run 2026-10-16T19:36:30.354Z; 500 control runs per variant. Results in R = the pattern's height (head to neckline); a trade that reaches its target makes +1 R before costs.
data: 7067434 one-minute bars, 2004-06-11 00:19 .. 2026-10-07 16:57 New York (minute close stamps)
15-minute bars: 512811; volatility and zigzag from bar 2001 (2004-07-16 01:15)
patterns, k = 3: 21797 zigzag pivots; 451 valid patterns (221 tops, 230 inverse), 282 broke the neckline in time (62.5%); median 74 bars (15 minutes each) from the left to the right shoulder; mean height $14.44 an ounce
  by year (tops/inverse/broken): 2004 5/1/3 | 2005 9/11/11 | 2006 8/9/10 | 2007 7/10/13 | 2008 11/11/12 | 2009 10/7/10 | 2010 11/7/13 | 2011 16/8/11 | 2012 6/10/9 | 2013 8/12/9 | 2014 9/8/13 | 2015 4/7/6 | 2016 11/13/18 | 2017 8/12/18 | 2018 15/16/18 | 2019 7/15/11 | 2020 15/11/18 | 2021 10/10/14 | 2022 5/13/15 | 2023 12/10/10 | 2024 12/11/12 | 2025 13/7/12 | 2026 9/11/16
patterns, k = 6: 7435 zigzag pivots; 211 valid patterns (118 tops, 93 inverse), 138 broke the neckline in time (65.4%); median 216 bars (15 minutes each) from the left to the right shoulder; mean height $26.47 an ounce
  by year (tops/inverse/broken): 2005 9/2/9 | 2006 5/2/6 | 2007 4/1/4 | 2008 3/7/8 | 2009 7/4/6 | 2010 2/1/1 | 2011 3/1/4 | 2012 6/4/5 | 2013 5/6/6 | 2014 2/3/5 | 2015 7/6/7 | 2016 2/2/3 | 2017 7/4/6 | 2018 6/9/7 | 2019 7/2/7 | 2020 4/4/6 | 2021 11/4/10 | 2022 3/7/6 | 2023 4/6/8 | 2024 9/4/7 | 2025 7/8/8 | 2026 5/6/9

=== HS-LS-3: tops (sell) and inverse patterns (buy), zigzag cut-off 3 x volatility ===
  DEV      n=   90 net 9.74 R  avg 0.108 R  PF 1.33 t 1.26
  VAL      n=   93 net 21.78 R  avg 0.234 R  PF 1.87 t 2.94
  HOLDOUT  n=   96 net 14.49 R  avg 0.151 R  PF 1.49 t 1.86
  ALL      n=279 net 46.01 R avg 0.165 R (gross 0.203 R, cost 0.038 R a trade); $ per ounce 392.42; PF 1.55 t 3.48
  win rate 166/279 = 59.5% (95% Wilson 53.6-65.1%); ended by {"target":170,"stop":109}: target 60.9%, stop 39.1%; came back to the neckline before the exit: 81.0%
  mean height $14.47 an ounce; mean distance to the stop 0.851 R; hours held median 7.92 max 152.10; the 10 best trades 10.12 R; worst open loss -1.76 R
  longs (inverse patterns) n=140 net 24.70 R gross 29.85 R | shorts (tops) n=139 net 21.31 R gross 26.83 R
  drawdown on closed trades -7.10 R; including open losses -7.29 R; financing: scenario A (3% a year) net 43.78 R, scenario B (today's swap) net 45.17 R
  by year (n, net R): 2004 3 1.08 | 2005 11 0.07 | 2006 10 4.43 | 2007 12 -1.81 | 2008 12 -0.27 | 2009 10 5.86 | 2010 13 -0.53 | 2011 11 -2.37 | 2012 8 3.28 | 2013 9 3.76 | 2014 13 -2.01 | 2015 6 -1.83 | 2016 18 7.31 | 2017 18 6.74 | 2018 18 5.06 | 2019 11 2.74 | 2020 18 2.37 | 2021 13 0.99 | 2022 15 1.24 | 2023 10 3.97 | 2024 12 7.27 | 2025 12 -0.39 | 2026 16 -0.96
  control (entries moved to other days, stop and target scaled by volatility, 500 runs, 1 s): mean trades 223.63, median avg -0.034 R, 5-95% -0.121 .. 0.055 R; real avg 0.165 R at percentile 100.00
  [PASS] 1 PF >= 1.2 in validation: VAL PF 1.87
  [PASS] 2 >= 50 trades in each period: 90 / 93 / 96
  [FAIL] 3 t >= 2.0 on development: DEV t 1.26
  [PASS] 4 above 95th pct of the control: percentile 100.00
  [PASS] 5 positive without top-10 trades: 35.89 R
  [PASS] 6 holdout net positive (flagged used): HOLDOUT net 14.49 R PF 1.49
  VERDICT Buried (5/6 gates)
  rule 3: 32 trades are open across a suspect or unclear gap; without them avg 0.185 R, gates passed 5/6 -> Buried (verdict unchanged)

=== HS-L-3: inverse patterns only (buy), zigzag cut-off 3 x volatility ===
  DEV      n=   41 net 9.22 R  avg 0.225 R  PF 1.90 t 1.95
  VAL      n=   49 net 8.07 R  avg 0.165 R  PF 1.57 t 1.50
  HOLDOUT  n=   52 net 6.37 R  avg 0.122 R  PF 1.36 t 1.06
  ALL      n=142 net 23.66 R avg 0.167 R (gross 0.203 R, cost 0.037 R a trade); $ per ounce 75.33; PF 1.56 t 2.54
  win rate 84/142 = 59.2% (95% Wilson 50.9-66.9%); ended by {"stop":56,"target":86}: target 60.6%, stop 39.4%; came back to the neckline before the exit: 81.7%
  mean height $13.50 an ounce; mean distance to the stop 0.820 R; hours held median 8.33 max 141.47; the 10 best trades 9.79 R; worst open loss -1.76 R
  longs (inverse patterns) n=142 net 23.66 R gross 28.86 R | shorts (tops) n=0 net 0.00 R gross 0.00 R
  drawdown on closed trades -4.55 R; including open losses -4.74 R; financing: scenario A (3% a year) net 22.49 R, scenario B (today's swap) net 17.57 R
  by year (n, net R): 2004 1 -0.69 | 2005 4 1.49 | 2006 7 2.02 | 2007 7 -0.34 | 2008 5 0.55 | 2009 4 1.06 | 2010 5 2.76 | 2011 2 -0.29 | 2012 6 2.67 | 2013 5 2.27 | 2014 7 -2.14 | 2015 3 -0.57 | 2016 10 0.50 | 2017 10 4.34 | 2018 7 2.84 | 2019 7 0.84 | 2020 8 -0.31 | 2021 8 1.96 | 2022 11 -0.08 | 2023 6 3.72 | 2024 7 4.95 | 2025 3 -0.78 | 2026 9 -3.09
  control (entries moved to other days, stop and target scaled by volatility, 500 runs, 0 s): mean trades 113.22, median avg -0.020 R, 5-95% -0.151 .. 0.110 R; real avg 0.167 R at percentile 99.60
  [PASS] 1 PF >= 1.2 in validation: VAL PF 1.57
  [FAIL] 2 >= 50 trades in each period: 41 / 49 / 52
  [FAIL] 3 t >= 2.0 on development: DEV t 1.95
  [PASS] 4 above 95th pct of the control: percentile 99.60
  [PASS] 5 positive without top-10 trades: 13.87 R
  [PASS] 6 holdout net positive (flagged used): HOLDOUT net 6.37 R PF 1.36
  VERDICT Buried (4/6 gates)
  rule 3: 11 trades are open across a suspect or unclear gap; without them avg 0.181 R, gates passed 4/6 -> Buried (verdict unchanged)

=== HS-LS-6: tops (sell) and inverse patterns (buy), zigzag cut-off 6 x volatility ===
  DEV      n=   43 net -3.54 R  avg -0.082 R  PF 0.82 t -0.60
  VAL      n=   39 net 1.81 R  avg 0.046 R  PF 1.13 t 0.35
  HOLDOUT  n=   53 net -4.00 R  avg -0.075 R  PF 0.83 t -0.67
  ALL      n=135 net -5.73 R avg -0.042 R (gross -0.022 R, cost 0.020 R a trade); $ per ounce -167.94; PF 0.90 t -0.59
  win rate 60/135 = 44.4% (95% Wilson 36.3-52.9%); ended by {"target":62,"stop":73}: target 45.9%, stop 54.1%; came back to the neckline before the exit: 87.4%
  mean height $26.41 an ounce; mean distance to the stop 0.801 R; hours held median 21.37 max 478.30; the 10 best trades 10.20 R; worst open loss -2.20 R
  longs (inverse patterns) n=63 net 2.12 R gross 3.22 R | shorts (tops) n=72 net -7.86 R gross -6.20 R
  drawdown on closed trades -8.25 R; including open losses -9.09 R; financing: scenario A (3% a year) net -7.33 R, scenario B (today's swap) net -5.23 R
  by year (n, net R): 2005 9 -2.06 | 2006 6 0.88 | 2007 4 -3.26 | 2008 8 1.65 | 2009 6 -0.45 | 2010 1 -0.93 | 2011 4 2.24 | 2012 5 -1.62 | 2013 5 -1.22 | 2014 5 1.90 | 2015 6 -0.86 | 2016 3 1.64 | 2017 6 1.94 | 2018 7 -0.71 | 2019 7 -0.89 | 2020 6 -0.84 | 2021 10 0.90 | 2022 6 -2.61 | 2023 7 -1.95 | 2024 7 1.27 | 2025 8 2.41 | 2026 9 -3.19
  control (entries moved to other days, stop and target scaled by volatility, 500 runs, 1 s): mean trades 109.73, median avg -0.021 R, 5-95% -0.151 .. 0.103 R; real avg -0.042 R at percentile 37.20
  [FAIL] 1 PF >= 1.2 in validation: VAL PF 1.13
  [FAIL] 2 >= 50 trades in each period: 43 / 39 / 53
  [FAIL] 3 t >= 2.0 on development: DEV t -0.60
  [FAIL] 4 above 95th pct of the control: percentile 37.20
  [FAIL] 5 positive without top-10 trades: -15.94 R
  [FAIL] 6 holdout net positive (flagged used): HOLDOUT net -4.00 R PF 0.83
  VERDICT Buried (0/6 gates)
  rule 3: 23 trades are open across a suspect or unclear gap; without them avg -0.023 R, gates passed 0/6 -> Buried (verdict unchanged)

=== HS-L-6: inverse patterns only (buy), zigzag cut-off 6 x volatility ===
  DEV      n=   16 net 3.02 R  avg 0.189 R  PF 1.70 t 0.96
  VAL      n=   20 net 1.11 R  avg 0.056 R  PF 1.17 t 0.30
  HOLDOUT  n=   28 net -2.39 R  avg -0.085 R  PF 0.79 t -0.58
  ALL      n=64 net 1.74 R avg 0.027 R (gross 0.044 R, cost 0.017 R a trade); $ per ounce 68.73; PF 1.08 t 0.28
  win rate 29/64 = 45.3% (95% Wilson 33.7-57.4%); ended by {"stop":33,"target":31}: target 48.4%, stop 51.6%; came back to the neckline before the exit: 84.4%
  mean height $31.95 an ounce; mean distance to the stop 0.798 R; hours held median 18.70 max 478.30; the 10 best trades 10.03 R; worst open loss -1.40 R
  longs (inverse patterns) n=64 net 1.74 R gross 2.85 R | shorts (tops) n=0 net 0.00 R gross 0.00 R
  drawdown on closed trades -4.58 R; including open losses -5.57 R; financing: scenario A (3% a year) net 1.05 R, scenario B (today's swap) net -1.61 R
  by year (n, net R): 2005 1 -0.36 | 2006 2 1.05 | 2007 1 -0.87 | 2008 6 1.64 | 2009 3 0.34 | 2011 1 0.93 | 2012 2 0.30 | 2013 4 -2.07 | 2014 3 1.84 | 2015 2 -0.56 | 2016 2 0.76 | 2017 2 1.82 | 2018 5 -0.87 | 2019 2 0.19 | 2020 4 -0.78 | 2021 3 -0.05 | 2022 5 -2.07 | 2023 4 -0.68 | 2024 2 1.84 | 2025 4 1.87 | 2026 6 -2.52
  control (entries moved to other days, stop and target scaled by volatility, 500 runs, 0 s): mean trades 52.19, median avg 0.024 R, 5-95% -0.153 .. 0.201 R; real avg 0.027 R at percentile 51.20
  [FAIL] 1 PF >= 1.2 in validation: VAL PF 1.17
  [FAIL] 2 >= 50 trades in each period: 16 / 20 / 28
  [FAIL] 3 t >= 2.0 on development: DEV t 0.96
  [FAIL] 4 above 95th pct of the control: percentile 51.20
  [FAIL] 5 positive without top-10 trades: -8.28 R
  [FAIL] 6 holdout net positive (flagged used): HOLDOUT net -2.39 R PF 0.79
  VERDICT Buried (0/6 gates)
  rule 3: 9 trades are open across a suspect or unclear gap; without them avg 0.036 R, gates passed 0/6 -> Buried (verdict unchanged)

buy and hold over the same data, for reference: 384 -> 4109.91