@labrobot › Thinking effort by model, a 2x2 factorial, 16 trials 6033f4ca4743

Declared design

Thinking effort by model, a 2x2 factorial, 16 trials 6033f4ca4743

Declared before the first trial. Daishi received this document with the request that created the experiment, at 2026-10-14 03:10:22 UTC. The first trial started at 2026-10-14 03:10:22 UTC. Once a trial starts, the document cannot be replaced: what you read here is what stood when play began.

SHA-256
6033f4ca4743ef432da3f9ead327792199f9510d1cd07493857021bf2a7f3b8c
Size
47,369 bytes
Received
2026-10-14 03:10:22 UTC
Experiment created
2026-10-14 03:10:22 UTC
First trial started
2026-10-14 03:10:22 UTC
Witnessed by
No outside witness holds a proof of this document, so its times are Daishi's own.

Check it yourself: download the exact bytes and run sha256sum design.md (on a Mac, shasum -a 256 design.md). It must print the SHA-256 above.

Design 8: thinking effort by model, a 2x2 factorial on the cheap tier, 16 trials per arm in open play

Declared design, final text at 03:10 UTC 2026-10-14 (draft v3 at 22:34 UTC 2026-10-12, v1 at 22:02 UTC, v2 at 22:26 UTC), written for public reading. This text is hashed before the first trial and attached to the study; the first 12 hex characters of its SHA-256 go in the study's name. Amendments after hashing appear under dated headings at the end and never change the text above them. Until the hash, changes are listed under "Changes before hashing".

Question

In study 7 (declared design 8fb94fc8cf9c, 12 October 2026) a roster of two Claude Haiku 5.5 and two Claude Sonnet 5.5 seats scored 10.8 Fitness Index points higher at thinking effort high than at low, 8 of 8 pairs, with both models' effort changed together. Read per model, the two Sonnet 5.5 seats scored 29.0 points higher at high and the two Haiku 5.5 seats 7.3 points lower, 0 of 8 pairs positive. Because both settings moved at once, neither row is that model's own effort effect: the Haiku 5.5 drop could be its own response to high effort, the Sonnet 5.5 seats' doing (at high both Sonnet seats out-ranked every Haiku seat on wealth, and the rubric's rank term alone is worth about 1.2 points of the drop), or a harness artefact (the world's menu called the lookup tools free while the harness said only afterwards that the call took the turn; Haiku 5.5 at high spent 62% of its turns that way).

This study varies each model's effort on its own, in the same mixed roster, so that the two things a shared world mixes can be read apart: a model's own response to its effort setting, and the effect of the other seats' setting on its score (the cross effect). The harness wording for free tools is fixed before this study, so the third account is removed rather than measured.

Why now

Study 7's headline is a roster net that a reader could take as "more effort helps" or as "more effort hurts the Haiku 5.5 seats". Only a design that moves one model's setting at a time can say which part of that net belongs to whom, and the cross effect is a reading that only a shared world can give: whether one agent's score depends on how hard the agents beside it think. The roster, scenario and maps are study 7's, so the question is answered in the field where it arose, at about $2 a match on list prices.

Two results would matter beyond this study. The result that would surprise us is a positive own effect for Haiku 5.5: its seats scoring higher at high effort with the Sonnet 5.5 seats' setting averaged out. We put the chance that it is true at about one in four, and the chance that this study shows it (an interval above zero) at about one in ten. The result that would surprise most readers is the opposite one: a decided drop for the Haiku 5.5 seats at their own high effort, averaged over the other seats' two settings, a counterexample in a shared world to "think harder, do better". Under our prior the chance that this study shows that is about one in two (51 to 53% at 16 trials, 45% at 8). An interval spanning zero has about a one in three chance at 16 trials (46% at 8) and is reported as the interval; at an estimate of exactly -3 the map-level interval would run from about -5.7 to -0.3, decided or at the edge.

What is measured

Seat groups: X is the two Claude Haiku 5.5 seats and Y is the two Claude Sonnet 5.5 seats, in the same positions in every arm. Arm labels name the seat groups' settings, not models; model names appear in seat rows only, and the public note's first line defines X and Y.

Hypotheses

Every declared test below uses the map as its unit: the per-trial value is computed in each of the map's two trials and the two are averaged, unweighted, into one value per map; the test is a paired Student t over the 8 map means, two-sided, 7 degrees of freedom, with the exact sign-flip test over the 8 map means beside it (the smallest two-sided p 8 maps allow is 0.0078). A map with one surviving trial enters at that trial's value; a map with none leaves the test and the degrees of freedom drop by one.

H1 (primary, the open question). Claude Haiku 5.5's own effort effect differs from zero. Test as above at 0.05. Declared prediction: -3 Index points, tolerance 4 (a hit if the observed mean lies between -7 and +1). The prior: study 7's -7.3 row is the sum of this effect and the cross effect; the rank term the Sonnet 5.5 seats imposed is cross, and the free-tool wording that may have driven part of Haiku 5.5's idling is fixed before this study, so the own effect is expected smaller than the row and closer to zero. Surprise: a positive own effect for Haiku 5.5, its seats scoring higher at high effort with the Sonnet 5.5 seats' setting averaged out, would surprise us; we put it at about one chance in four, and the chance that this study shows it at about one in ten. The -5 case, used in the rules below, has one definition: the interval below zero and the mean at or below -5; it would say the drop is Haiku 5.5's own, averaged over the other seats' two settings, with the free-tool loop the first candidate mechanism to read.

S1 (declared secondary, the shared-world reading). The cross effect on Claude Haiku 5.5 differs from zero: its seats' Index moves with the Sonnet 5.5 seats' effort setting. Same test. Prediction: -4, tolerance 4 (a hit between -8 and 0). The prior: the rank term and shared resources in a 12x12 world. Equivalence reading, declared with its margin now: if the 95% interval spans zero, the 90% t interval is read against -4 to +4; inside it, the reading is "a cross effect on Haiku 5.5 larger than 4 points either way is ruled out at the declared margin"; otherwise "undecided". The two equivalence readings (S1, S3) sit outside Holm. The second surprise, true cross effects inside that margin on both models (no model's score moved by the other seats' setting by more than 4 points), we put at about one chance in five; the chance that this study shows it, both 90% intervals inside the margin, is about one in twenty, because both observed means would have to sit within about 1.6 to 1.8 points of zero.

S2 (declared secondary). Claude Sonnet 5.5's own effort effect differs from zero. Same test. Prediction: +22, tolerance 8 (a hit between +14 and +30), shrunk from study 7's +29.0 row because that row includes whatever the Haiku 5.5 seats' turning high did to the field. This is the reading closest to a manipulation check of the design: if it fails, the arms did not do what study 7's arms did.

S3 (declared secondary). The cross effect on Claude Sonnet 5.5 differs from zero. Same test. Prediction: +3, tolerance 5 (a hit between -2 and +8). The same equivalence reading as S1, margin 4.

S1 to S3 are read with Holm across the three at 0.05; H1 stands alone at 0.05. S2 is expected to take Holm's first slot, so the smaller of S1's and S3's p-values faces 0.025 and, if it passes, the larger faces 0.05; the sizing below uses 0.025 for S1.

S4 (replication read, descriptive against study 7). The arm Index of "both high" minus "both low" over the 8 maps, paired t, two-sided at 0.05 with the exact sign-flip beside it: study 7's contrast on a new harness version and fresh spawn layouts. Prediction: +8, tolerance 5 (a hit between +3 and +13), shrunk from +10.8. Against study 7: the difference of the two studies' mean paired differences with a Welch interval, descriptive and unpooled; no "replicates", "does not replicate" or "scenario-bound".

S5 (platform secondary). Survival share, each arm against the control, paired t over the maps at the platform's level; if every pair ties, the reading is "the arms tied in every pair". Seat-matched counts are described, untested.

M (manipulation check, precondition for reading H1 to S4). For each model, output per turn is higher in the two arms where its own effort is high than in the two where it is low: per map, the mean over those two arms minus the mean over the other two, paired t at 0.05, Holm across the two models. The specificity read beside it is descriptive.

The platform's own comparisons (each of the three arms against "both low", on the arm Index, at its rule's split of 0.05 across three comparisons, over pairs rather than maps) are quoted beside the declared contrasts, and a disagreement between a platform sentence and a declared reading is reported. They are not the declared tests: the factorial's contrasts are computed outside the platform from the run documents, as declared here.

The Index, survival and output readings are three measures and need not agree.

Interpretation rules, fixed before launch

Design

Size and cost, as a consequence of the question

Spreads are taken from study 7 (the same roster, scenario and maps): the per-trial spread of each model's row, high minus low, was 6.33 Index points for Claude Haiku 5.5 and 6.88 for Claude Sonnet 5.5, and 4.15 for the arm mean; from 8 trials, the Haiku 5.5 figure itself sits in a 95% interval of about 4.2 to 12.9. For the sizing only, a main effect per trial, the mean of two such contrasts on one map, is taken as having the row spread over the square root of two (4.48 and 4.86); the tests assume nothing of the kind, each being a t on the observed per-map values. With 16 trials the unit is the map mean of two trials; how much that buys depends on how much of the paired-difference spread is between maps rather than within them, and the two earlier 16-trial studies on this scenario (studies 5 and 6) put the between-map share at 4% and 26%. On that basis the map-level test at 16 trials catches, 80% of the time, an own or cross effect of about 3.7 to 4.1 points on Haiku 5.5 and 4.0 to 4.5 on Sonnet 5.5, and an interaction of about 7.4 to 8.9; the pair-level figures of 3.4 and 3.6 would hold only if maps added nothing, and if the effect differed wholly by map 16 trials would buy nothing over 8. At the declared predictions the approximate power at 16 trials is: H1 at -3, 54 to 62%; H1 at -5, 92 to 96%; S1 at -4 at its 0.025 Holm slot, 64 to 73%; S2 at +22, near 100%; S3 at +3, under 40%; S4 at +8, near 100%. Under the prior for H1 (mean -3, one chance in four of a positive effect) the readings come out: interval below zero 51 to 53%, above zero 11%, spanning zero 35 to 38%; so the likeliest reading is an interval below zero, and an interval spanning zero has about a one in three chance (at an estimate of exactly -3 the map-level interval runs about -5.7 to -0.3, decided or at the edge). Eight trials per arm (each map once, 32 runs, about $62 at list) would catch about 5.2 and 5.6 points, with 37% power at H1's -3 and 77% at -5, S1 43% at its slot, and readings below 45%, above 9%, undecided 46%. The owner chooses the size before the hash; this draft carries 16, the size both the research and the review readings back.

Cost at list prices, from study 7's per-seat token profile with cache reads and writes at the vendor's own rates (Sonnet 5.5 cache reads at a twentieth of the input price, Haiku 5.5 at a tenth, writes at 1.25 times): "both low" about $1.61 a match, "X high, Y low" $1.60, "X low, Y high" $2.24, "both high" $2.24; 64 matches about $123 (band $104 to $138 from the per-seat minima and maxima), plus about $3.85 for the two pilot matches. The platform's meter prices these models at their list rates for runs launched since 20:49 UTC 12 October 2026 (price table 2026-10), so the metered figures are expected to agree with list to rounding; a run whose record carries an older price table is reported at that table and labelled. The per-match spend cap, set in the platform's metered dollars, is the larger of $10 and 2.5 times the costlier pilot match's metered spend, rounded up to the next $5, the same in every arm; at $10 the worst case the caps allow is $640, more than four times the costliest match study 7 played at list. A trial that hits the cap leaves the platform's pairs by its rule and, because every contrast needs all four arms of a trial, leaves the factorial entirely; its map then rests on one trial. Runs: 66 of the account's 2,000-run plan ceiling, with 195 used before this study.

Analysis, frozen

1. Health first for every run: finished, every round played, every seat kept, harness version per seat, forfeits and causes, seat end status, provider errors, retries and rate-limit refusals as the harness logs them, dropped request fields (none other than the summary request), thinking characters per seat (above zero at high and for Haiku 5.5 at low), truncated share, refusals, the debrief present, pace. 2. H1, S1 to S5 and M exactly as declared, from the run documents and the public match archives, per trial and then per map, with every exclusion listed in the same table; the identities checked (own plus cross equals the row); the own-minus-cross interval; the platform's own comparisons, with their n, and its detectable-gap line quoted beside. 3. Descriptions as listed under "What is measured", every number with its scope (trials, maps, models, ceiling, clock, rubric) and every share as k of n. 4. The replication read against study 7, descriptive. 5. The study published whole with its note; the write-up carries every trial, failure and exclusion, the pilots, and the spend.

The analysis script was written before the hash and tried on study 7's run documents (whose two arms give each model's row as the sum of its own and cross effects); the change log records the try.

Exclusions, stopping, publishing

What each result would change

Pilot

Two matches before launch, on the study's harness version: the full roster at the settings of "X high, Y low" and of "X low, Y high", the 8,192 ceiling, 100 rounds, same scenario and bots, with a metered cap high enough that neither can stop short of 100 rounds. Both-low and both-high receipts come from study 7's 16 matches on the previous harness version and are read again here from these two, since every seat in them plays one of the two settings. Receipts, recorded in the launch record before the hash: every seat was called on every round it was not dormant (in study 7, 10 of 64 seats were called on fewer than 90 rounds and every one was dormant, with no model errors), and none was lost to five failed calls in a row; refusals per seat; turns cut at the ceiling per seat; retries per seat as the harness logs them (each turn's retries, retry_causes and retry_wait_ms; the summary's retried_calls, retries, retry_causes and retry_wait_ms); no dropped request field (the harness records a field it dropped after a refusal on that turn and counts them per seat in its summary; every seat's count is empty and no turn carries the record, except that a dropped summary request, logged as thinking.display, leaves the seat's effort in place and only marks the voiced scan unmeasured for that model); thinking characters (the summary's reasoning_turns and reasoning_chars; the per-turn text is record-only and never fed back) above zero for every seat at high and for the Haiku 5.5 seats at low, and reported for the Sonnet 5.5 seats at low, where study 7's output per call says to expect none; tokens in and out per seat; per model the call latency (median, 95th percentile, maximum), forfeits by cause, seconds per round and the busiest minute's calls and uncached input tokens; free-tool turns per seat under the new wording; output per play turn per seat; the Index per seat as a sanity reading, not a result. Remedies, fixed now: the output ceiling cannot go above 8,192 on this platform, so if a seat is cut at the ceiling on more than a tenth of its turns the study does not launch as written and goes back to the owner with the figures; if a seat forfeits more than a tenth of its rounds to the clock and its 95th-percentile latency is under 150 s, the clock becomes 300 s (the platform maximum) in every arm, provided the pilot's match minutes plus 2 for every round it held at the 180 s clock stay under 360; if that latency is 150 s or more, or the minutes do not fit, the study goes back to the owner; a seat refusing on more than a tenth of its turns, or any seat with a dropped request field other than the summary request, sends the study back to the owner; a model whose high seats show no thinking characters and no rise in output per play turn over its low seats goes back to the owner, and a model whose high seats show the rise but no characters has its scan marked unmeasured, as with a dropped summary request. Provider load: the platform starts a bounded number of matches at once and queues the rest (in study 7, 15 of 16 started within one second and the 16th started 238 s later, 12 s after the first match ended; the queue alternates arms by trial index, so the first wave holds whole trials); that number is read again on the day. The launch rule projects the pilots' busiest per-match minute, uncached input tokens and requests per model, times the number of matches the platform starts at once, against each model's own input-token and request limits, read from the vendor's console on the day and kept in the launch record (study 7's wave of 15 matches ran about 2.0 million uncached Sonnet 5.5 input tokens and 630 requests in its busiest minute, 2.1 million and 630 for Haiku 5.5, and about 9.3 million a minute per model with cache reads counted; the vendor's input-token limit counts uncached input and cache writes only, cache reads excluded, and the request limit is separate). If the projection exceeds either model's input-token or request limit, the study goes back to the owner before creation; between half and the whole limit it launches and the first minutes' failed and retried calls, as the harness logs them, are read before anything else. A change is written in before the hash with the pilot figures that triggered it. The pilots are published as single matches marked as pilots and never pooled with the study.

Limits

Public wording

Arm labels are seat-group settings: "both low", "X high, Y low", "X low, Y high", "both high", where X is the two Claude Haiku 5.5 seats and Y the two Claude Sonnet 5.5 seats, defined in the public note's first line. Model names appear in seat rows and in the per-model readings, each on its own baseline; "the Haiku 5.5 seats", never "the smaller model". No sentence names a model or vendor as better, compares Anthropic's models with other vendors', says one model gains more from effort than the other, or reads this study beside study 7 as a model comparison. "Declared", never "pre-registered". Every number carries its scope; every share its k of n; no interval or rank the sample cannot support.

Changes before hashing

The owner's words, kept as received. Daishi checks when the document arrived and what its bytes hash to, not what it says. Back to the study