Three Retreats

Extending the Squad Sim Report along two axes: retreat scale/schedule (S26 → W26 → S27) and the recursive warm-invite run-up that fills them · deterministic Monte Carlo · 2026-07-05

The experiment

Question. The v2 report simulated one retreat: the 35-person S26 field. Two things it didn't model: (1) the next two retreats are bigger and shaped differently — W26 (60 people, Thu night → Wed morning) and S27 (85 people, 10 days, Fri → Sun) — and (2) rosters don't appear by fiat: attendees declare potential best friends during the run-up, and naming someone outside the circle triggers a warm invite, recursively, until the retreat fills.

Naming model. Declaration is fat-tailed: 70% of people are light namers (Poisson 0.7) and 30% are super-connectors (Poisson 4.0) — ≈1.69 namings per attendee overall. (The brief's "average attendee names 0.7" can't be the overall mean alongside "30% name 4," so it's modeled as the light-namer rate.) Each naming points outside the current invitee list with probability 50%; outside names accept 70% of the time and start declaring their own. S26's 35 attendees seed W26's 12-week run-up; W26's 60 seed S27's. Declared PBFs become forced best-friend-potential edges in the arrival field; everyone else is bucketed by the v2 calibration, with familiarity gated by invite-graph distance.

Schedules. Same daily template as v2 (lunch pods of 6 · afternoon 1:1 walks · dinner pods · evening circles of 9, closing check-in), different envelopes: S26 = 6 full days (25 small slots), W26 = 5 (21), S27 = 8 + a mid-retreat rest day (29). Re-sorts every 2 days; strangers you actually met become judgeable — so wanted lists grow during the retreat. FAIR-deficit matcher throughout.

The run-up: a subcritical cascade that still fills

R₀ = 1.69 namings × 50% outside × 70% accept ≈ 0.59 — each attendee recruits ~0.6 more. That's subcritical: warm growth dies out rather than explodes. But a dying cascade from a big seed still sums: 35 seeds → 35/(1−0.59) ≈ 85 total descendants; 60 seeds → ≈146. So the chain works — barely for W26, comfortably for S27.

Mean invited count across the 12-week run-up (40 runs). W26 hits 60 around week 2 with an average of just 0.9 organizer top-up invites; S27 reaches 85 by ~week 3 with 0 — and turns away a mean waitlist of 23 (W26: 11).

Who the cascade brings

W26

S27

seed alumni 1 hop out 2 hops 3+ hops top-up

W26 is 58% S26 alumni, 28% one hop out; only 12% arrive ≥2 hops from anyone you've retreated with. S27 is even more alumni-weighted (71%) because 60 seeds nearly fill 85 on their own.

Arrival safety. 11% of W26 arrivals (8% at S27) have exactly one warm edge: the person who named them. Another 10% / 13% arrive with no declared-PBF edges at all (seeds who named no one and were named by no one — real people still carry secure ties). The first-night design owes these people an anchor.

What has to be true for warm growth to work

Sweeping the two beliefs the model rests on — how often namings point outside the circle (p_out) and how often outsiders say yes:

	accept 50%	accept 70%	accept 90%
30% named outside	R₀ 0.25 W26 45/60 · S27 77/85	R₀ 0.35 W26 49/60 · S27 83/85	R₀ 0.46 W26 56/60 · S27 84/85
50% named outside	R₀ 0.42 W26 53/60 · S27 84/85	R₀ 0.59 ★ W26 59/60 · S27 85/85	R₀ 0.76 W26 60/60 · S27 85/85
70% named outside	R₀ 0.59 W26 58/60 · S27 85/85	R₀ 0.83 W26 60/60 · S27 85/85	R₀ 1.06 W26 60/60 · S27 85/85

Cell = mean organic roster at top-up time (20 runs each). Green: both retreats fill organically · amber: one fills · red: both need top-ups. ★ = default assumption. Only the most optimistic cell (70% outside × 90% accept, R₀ 1.06) goes supercritical — everywhere else growth is a burn-down of the seeds' enthusiasm, not an epidemic.

The three retreats, side by side

	S26	W26	S27
People / full days	35 / 6	60 / 5	85 / 8
Small-format slots	25	21	29
Walks per person	6	5	7
Strangers at arrival	67%	85%	89%
Wanted list, arrival → close	6.5 → 15.3	6.4 → 23.4	7.3 → 34.8
Contact coverage (of 10)	9.7	9.7	9.8
Coverage p10	92%	92%	94%
Mutual-PBF pairs getting a walk	82%	84%	83%
Experience mean	21.5	28.5	33.3
Experience p10	2.8	22.0	26.2
Worst person (mean)	-26.4 (Peter)	15.4 (Peter)	19.7 (Peter)

The depth budget collapses before contact does — once

"Did I share small-format time with everyone I'm drawn to?" saturates at every scale (coverage ≈ 9.7/10, and the bottom decile actually improves with scale: 92% → 92% → 94%). What collapses is walks per wanted person — and it's a step function, not a slide: 39% at S26 drops to 21% at W26 (−46%), then barely moves at S27 (20%). The one-time cost is leaving the small fully-judged regime. The mechanism is that longer/bigger retreats grow the demand side faster than the walk supply: wanted lists multiply 2.3× over the retreat at S26, 3.7× at W26, 4.8× at S27 as re-sorts convert strangers.

solid = walks availablemid = wanted at arrivallight = wanted by close

The tail inverts: the small retreat is the risky one

Counter-intuitively, S26 — smallest, longest-known field — has by far the worst floor. When 33 of 34 others are judgeable and ~19% of judged ties are "not drawn," veto collisions become unavoidable in a 25-slot week; the matcher runs out of clean placements for the most-vetoed people. At 60/85, the field is 85%–89% strangers at arrival: vetoes are sparse and easy to route around, so nobody craters — but the highs are also blander early on. Two sharpenings: single reps at S26 blow out to −179 (≈7× worse than the averaged floor of −26 — quarantine and isolation penalties stack in unlucky weeks), and the worst person is the same real persona (Peter) at all three scales — a structural, identifiable matching problem, not noise.

−300 (dashed)+52 · person-rep totals, shared scale

What this changes about the design

The recruiting levers are substitutes — fix whichever leg is weak, and R₀ alone doesn't tell you which. Moving p_out 30→70% adds ~13 organic W26 seats when acceptance is weak but ~4 when it's strong (and vice versa for acceptance). At matched R₀, acceptance converts better: (50% out × 70% accept) fills 59.4 while (70% × 50%) fills 58.3, and a higher-R₀ cell can fill worse. If declarations already point outward, invest in the invite experience; if the circle names inward, prompt "who isn't here yet?"
New-face fraction is set by the capacity ratio, not by luck. Hop-0 share equals seed/capacity almost exactly (58.3% at W26 = 35/60; 70.6% at S27 = 60/85) — so choosing capacity is choosing how alumni-heavy the room feels, before any invite dynamics play out.
Warm growth alone fills W26 only barely — plan a small top-up list, not a big one. Default assumptions leave ~1 seat to fill by hand; pessimistic ones (30% outside, 50% accept) leave ~15 of 60. Watch the week-6 count: the trajectory's shape is nearly linear, so mid-run-up pace predicts the finish.
S27 has an admissions problem, not a recruiting problem. Organic demand never falls short in any rep (top-up exactly 0; mean waitlist ~23 behind 85 seats): the third retreat needs an overflow process, not a backfill process, and the cascade could be deliberately damped without endangering fill.
Anchor the namer bond on night one. ~8–11% of arrivals know exactly one person — their namer. Seat them together at arrival dinner; the matcher can take over from day 1.
At 60+, ration re-sort demand or grow the walk supply. Wanted lists end at ~23 (W26) and ~35 (S27) against 5–7 walks; walks cover ~20% of the list versus ~39% at S26. Options: second daily walk slot at S27 (it has the calendar room), or make pods the honest primary format and reserve walks for mutual-PBF pairs (the matcher already gets 83% of those pairs at least one walk at 85).
The dignity floor matters most at the smallest retreat. The at-risk population from the v2 report (Peter et al.) craters hardest precisely where everyone knows everyone; deficit-weighting and veto-quarantine are S26 features first, scale features second.

Caveats

The 0.7/4.0 mixture is an interpretation of an internally-inconsistent brief (see Naming model); overall namings ≈1.69/person is the load-bearing number.
Synthetic attendees are jittered copies of the 35 real personas — real people dominate both tails (Peter is worst at all three scales partly by construction).
Coverage counts "shared ≥1 small slot," a low bar; the depth budget section is the honest capacity metric.
Filler fractions use post-decay pair quality and aren't comparable to the v2 report's filler numbers; the cross-retreat trend (0.88 → 0.86 → 0.78) is what's meaningful.
The sensitivity grid's S27 arm seeds from an idealized synthetic 60-roster rather than a chained W26 run at the same parameters.
Everyone attends everything (no appetite modeling); vetoes stay fixed once assigned.

Simulation: multi_retreat.py (deterministic, verified) · extends the Squad Sim Report (v2) and the Circle Sort vocabulary · seeds 3000/5000-series · 40/25/15 reps per retreat