# Multiway c-bet transfer: method and selected data Research date: September 29, 2026. Article: https://gtogecko.com/blog/multiway-cbet-transfer-study ## Question and setup What happens in stored three-way action values when we reuse an exact hand's heads-up check/small-bet/large-bet mix? Six-handed NLHE cash, 100 bb starting stacks, no ante, opener raises to 2.5 bb. Heads-up: SB folds, BB calls, 5.5 bb flop pot. Three-way: SB and BB call, 7.5 bb pot. Active stacks are 97.5 bb behind. Catalogue rake is 5% capped at 4 bb; original solver settings are unavailable. Both blinds have only a check before the opener acts. These files cannot test whether allowing leads would change the opener's decision. Mapping: heads-up bet 4.1 bb to three-way bet 5.6 bb; heads-up bet 1.8 bb to three-way bet 2.5 bb; check to check. These are approximately 75%/33% pot sizes. The transferred action frequencies, not old absolute wager amounts, define the experiment. BTN's entering range is identical within every native pair. Blind ranges, pot and bet amounts change together; this does not isolate the effect of the extra caller. Primary: 12 unpaired rainbow BTN boards, four discovery and eight held out. One discovery pair was inspected for schema before registration. Four additional BTN paired/two-tone boards and four matched CO board pairs are separate boundaries. All 40 requested files were retrieved afresh and used. 7,053 positive-reach primary exact hand/board rows, 4,706 held out; 10,921 rows including boundaries. No missing matching hero combos or excluded cases. ## Calculation and interpretation For each hand h, q is the normalized heads-up frequency vector, E is the three-way stored action EV vector in bb, and gap = max(E) - sum(q[a] * E[a]). This is a one-decision arithmetic screen against unchanged stored continuations. It is not a full-strategy evaluation, re-solve, opponent-adaptation experiment or exploitability estimate. Do not multiply it by 100 and label it bb/100. Probabilities were stored to two decimals; totals 0.99/1.01 were renormalized to 1. Raw EV units divide by 10. EV values are compared only within the same decision node; no absolute EV difference between native pots is interpreted. Positive hero reach weights form each within-board denominator. These are marginal weighted-combo summaries, not real deal occurrence probabilities. Across-board means give each selected board equal weight. No representativeness of all flops or independence of hand rows is claimed. The preregistered test required at least 95% of marginal mass to have gap at most 0.1 bb on every held-out board. Seven of eight held-out boards pass; 8s 3h 2d fails (5.342677% above 0.1 bb). Across all 12 primary boards, 11 pass. At 0.05 bb none passes; at 0.2 bb all pass. These thresholds are editorial screens, not universal mistake definitions or numerical accuracy guarantees. An independent Decimal implementation reproduces the 20 paired summaries. A post-analysis source-rounding envelope varies each HU probability within +/-0.005, constrained to sum to 1, then expands the gap interval by 0.001 bb for two ordinary EV rounding errors. The 8s 3h 2d failure remains. This only tests an assumed rounding model; original convergence is still unknown. ## Material model-quality limitation Original solver/version, abstraction, achieved accuracy and stopping reason are unavailable. None of the 20 three-way opener nodes has an action used at least 5% more than 0.1 bb below its best stored alternative. However, a bounded audit through two response levels finds material subsequent strategy/EV disagreements, including reachable branches. Those root checks do not validate the continuations or certify accurate root EVs. The observed BTN frequency reduction, CO reversals and selected stored-EV calculations are reproducible. A claim about equilibrium safety, actual loss from adopting a complete strategy, or causal explanation would require better-validated solves. Multiway guarantees cannot be inferred from heads-up zero-sum theory. ## Public files - board-summary.json: all 20 paired summaries, including distributions, native mix diagnostics and threshold sensitivity. - selected-hands.json: four selected exact-hand comparisons; all action frequencies and EVs. - range-views.json: five illustrative 169-class views. Classes aggregate exact suits by marginal weight; entry weight=class mass/legal combos after board removal. Filled strategy segments show conditional action frequency. Opponent entry grids only mark presence, not calls or strength. - range-composition.json: two boards' current made-hand category masses for hero and opponents. These are not runout equities or jointly compatible matchup probabilities. - verify.py: standard-library audit of selected arithmetic, frequency sums, range mass/entry weights and category totals. - MANIFEST.sha256: hashes of these selected public artifacts. Full proprietary trees, internal access details and private logs are excluded. The original image is AI-generated editorial artwork, not numerical evidence. ## Primary context - https://blog.gtowizard.com/playing-in-position-against-two-callers/ -- different 100bb LJ chip-EV frequency/sizing study, not replication of this cash transfer test. - https://blog.gtowizard.com/now_live_3_way_solving_nodelocking_2_0_and_50k_icm_ft_sims/ -- an example limiting blanket small-bet claims. - https://piosolver.com/docs/viewer/numbers_in_piosolver/ -- distinguishes marginal ranges, matchup frequencies and action EVs. - https://blog.gtowizard.com/understanding-nash-distance/ -- strategy/EV disagreement and numerical accuracy context, not a certificate for these exports.