# Heads-up premium pairs: selected study evidence Article: https://gtogecko.com/blog/heads-up-premium-pair-study Retrieved and analyzed September 30, 2026. These files publish selected results and three explanatory range views, not complete proprietary solver trees. ## Model and question Heads-up no-limit Hold'em, equal starting stacks before posting 0.5/1 bb blinds, no ante, catalog rake zero, chip EV. BTN is the small blind and acts first preflop. The catalog labels these heads-up artifacts MTT/ChipEV; the app aliases eligible no-ante heads-up models into Spins. No ICM or bounty utility is used. Opening options are fold, limp to 1 bb, raise to 2 bb, and shove to the starting stack. At 10 bb, BB can check or shove after a limp; a small isolation raise is unavailable. At 25 bb a 3 bb raise is available. Native trees change with depth; this is not a controlled stack-only intervention. After exploring 10/20 bb, we registered two primary tests on QQ/KK/AA at 8/10/12/15/20/25 bb: whether limp EV exceeds shove EV, and whether limp is within 0.1 bb of the highest stored action EV in every row. Depths 8/12/15/25 were held out. Depths 30/35 were separate boundaries; requested 40 bb was absent. JJ/TT are separate neighboring-hand checks. We retrieved 78 decision nodes, containing 13,182 hand-class rows. ## What survived validation The 10 bb QQ–AA limp-versus-shove comparison is a conditional observation from the saved model. The important limp, limp/shove and open-shove response nodes have no positive-reach action played at least 5% more than 0.1 bb below another stored action. Independent Monte Carlo showdown calculations reproduce all three 10 bb shove values within sampling uncertainty. Limp EV still depends on the source's unverified postflop continuation. The broader registered rule is **unresolved**. The raw 0.05/0.1/0.2 bb limp screens pass 15/17/18 of 18 rows, but that arithmetic is not a validated strategy verdict. The apparent 25 bb AA exception reaches a flagged response after limp/raise 3/reraise 7 in 17.7413% of counterfactual AA-limp deals. The AA continuation reraises 7 at 72.62% after BB raises 3. Global rarity of that branch does not bound its importance for this proposed action. An independent 25 bb AA all-in estimate is 4.440982 bb (95% Monte Carlo interval 4.434663–4.447300), versus stored 4.38056 bb. We did not substitute that estimate into the original solution or infer the cause of the discrepancy. Values at 25 bb and deeper remain diagnostic output, not validated recommendations. The audit found 204 frequency/EV action flags across later nodes, none at roots. At 10 bb all 13 flags are behind the rarely used min-raise. Its raw EV is shown for completeness, not to certify equivalence to limping. At 35 bb, one flagged node has 4.0478% global reach; not all flags are negligible. The consistency screen is not an exploitability or convergence certificate. ## Files and denominators - `selected-hands.json`:40 selected root hand/depth rows, original action frequencies and EVs, derived gaps and per-row validation notes. Action order: fold, limp, min-raise, shove. - `summary.json`:descriptive QQ–AA averages and raw threshold fractions at each depth. All are arithmetic summaries subject to the limits above. - `range-views.json`:three 10 bb range views: BTN/SB opening, BB facing limp, BB facing open shove. All 169 classes enter each view with full own reach. BB fold after a limp is a zero-frequency terminal placeholder and is omitted from its displayed options. - `range-composition.json`:selected 10/25 bb marginal composition and AA-compatible BB responses. The 25 bb composition describes saved policies only. - `all-in-crosschecks.json`:selected independent simulation results, sample sizes, seeds and formula inputs; no full proprietary response export. - `verify.py`:local consistency verifier for selected files. It does not re-solve poker or independently validate the database. - `MANIFEST.sha256`:checksums of this public bundle excluding the manifest itself. Pair/suited/offsuit classes contribute 6/4/12 exact combinations before card removal. Whole-range displayed percentages use marginal class reach times that multiplicity. They are not automatically two-player occurrence frequencies. With one exact AA combination removed, BB has 1,225 compatible combinations. At 10 bb, BB's shove-after-limp mass is 475.7072 and its call-versus-shove mass 382.0064:38.83324% versus 31.18420%. These are separate policies held as exported, not causal evidence. The exact suits are interchangeable for these suit-symmetric preflop class inputs. EVs use folding at the root decision as 0. The posted SB 0.5 bb is sunk. For stack S, a called shove returns `2*S*equity-(S-0.5)` relative to folding; an uncontested shove returns 1.5 bb. Thus `EV=(1-p_call)*1.5+p_call*(2*S*equity-(S-0.5))`. Each independent all-in row samples 1,000,000 legal boards and exact villain combinations weighted by the stored call policy, with fixed seeds. Eval7 0.1.11 evaluates hands; PokerKit independently agreed on 1,000 sampled showdowns. Intervals describe simulation sampling uncertainty only, not original solver error or strategic optimality. ## Limits Original solver version, achieved convergence, stopping condition and postflop abstraction were unavailable. Integer export scales are 0.0001 for frequency/reach and 0.00001 bb for EV; these are storage precision, not solve accuracy. Reconstructed reaches agree within 0.0001. A 0.02 bb discussion band identifies near-ties without asserting precision. We compare local stored actions, not a complete changed policy against an adapting opponent. Related depths and hand classes are not independent experiments. No human behavior, win-rate or guaranteed outcome is measured. No conclusion transfers automatically to antes, ICM, bounties, cash rake or multiway pots. The header is original AI-generated editorial artwork. The table, chart and grids are deterministic figures derived from the selected numerical data.