From b0c03c1917c0dd16772daecc07936401a7ac2b4d Mon Sep 17 00:00:00 2001 From: "@permadeath.com" Date: Sat, 29 Aug 2026 01:15:44 -0400 Subject: [PATCH] docs(harness): lead the self-discordance section with the curve, not the figure `2p(1-p)` peaks at p=0.5, so the answer differs per scenario and the suite-wide one is an average over that curve. That is what makes 8x12 coverage the right follow-up rather than a bigger version of the same probe. Change-Id: Ief5a04ef0fb58270a26b7806ee45ffc10f65bbb7 --- plan/harness.md | 32 +++++++++++++++++++++++++------- 1 file changed, 25 insertions(+), 7 deletions(-) diff --git a/plan/harness.md b/plan/harness.md index 8d594ac..5f0d59f 100644 --- a/plan/harness.md +++ b/plan/harness.md @@ -405,6 +405,24 @@ project has run is measuring dice. The between-bot rate is `paired_games_needed`'s own default, **0.426** - 46 of 108, measured r6 against r7. The self-discordance had never been measured. +**The argument first, because the argument is what generalises.** Self- +discordance is `2p(1-p)`, which is *maximised at p = 0.5*. A scenario both sides +win about equally sits at the top of that curve; a scenario one side always +takes sits near the bottom, because the dice cannot change who wins. So the +question "does a discordant pair carry information" has a different answer for +every scenario, and the suite-wide answer is an average over that curve. + +That is why one scenario, measured to any precision, cannot settle it, and why +the follow-up is **8 scenarios x 12 runs rather than 50 runs of one**. A bigger +version of this probe buys a tighter figure for a single point on a curve whose +*shape* is the unknown. The measurement below is one point, and it is reported +as one. + +It also means a lopsided scenario returning a *high* self-discordance is the +strong form of the result, and a balanced one returning a high figure is the +weak form - the opposite of the intuition, and the way this was first framed +here and had to be corrected. + **Measured, and not settled.** 24 runs of `4v4-civil-war-bv10000-s825243000` at seed 1, same weights, no exploration, **zero timeouts and zero defaults**, on a machine under load the whole time. @@ -432,13 +450,13 @@ point estimate crossed the threshold from above to below as data arrived. That is exactly the number that would have been retracted had it been reported as a finding at 12 runs, and it is why it was not. -**The lopsidedness makes the result stronger, not weaker.** `2p(1-p)` is -maximised at p = 0.5, so a scenario one side wins 74% of the time should have -*low* self-discordance - and it still comes out at 0.386 against a between-bot -0.426. Only about **0.04** of the between-bot discordance is unexplained by the -same configuration disagreeing with itself. That is a scenario chosen without -regard to balance, not a cherry-picked coin flip, and the margin left for -"signal" is thin. +**This point sits low on the curve and still comes out high**, which is the +strong form described above. At p = 0.739 the scenario is well off the p = 0.5 +peak, so `2p(1-p)` should be small here - and it is 0.386 against a between-bot +0.426, leaving only about **0.04** unexplained by a configuration disagreeing +with itself. A balanced scenario sits *higher*. So the curve runs the wrong way +for paired comparison: this is close to a best case, not a worst one, and it was +chosen without regard to balance rather than picked for it. The repeat count settles the plan rather than being chosen: the low end of the self-discordance interval only clears 0.426 at about **50 decided runs** of one -- 2.51.2