What's locked: 8 sections (§§0-7) · 2,800-word target · 3 pairings preflop + postflop coverage · per-position EV table · all numbers locked.
Phase A2 findings reshape the article:
- Reframed pairing axis from "position symmetry" to "blind structure" — all 3 pairings have positional asymmetry; the real distinction is how much of the pot is desperate-money vs safe-player dead money before action begins.
- The wet-board reversal is CO-vs-BTN-specific, not universal. BvB and BTN-vs-SB both DROP c-bet rate on wet boards at down-to-two. Only CO-vs-BTN reverses up. The dead-money structure (1.5 BB of safe-player blinds) is the likely driver.
- The most valuable seat at down-to-two BvB is BB (9.0 BB/hand expected EV vs SB's 3.8 BB) — the seat that closes the action.
- SB beats BTN at down-to-two BTN-vs-SB (SB 4.16 vs BTN 1.49 BB/hand) — counterintuitive but explained by SB's 3-bet aggression eating BTN's positional advantage.
Daniel Dvoress co-founded GTO Lab. This article walks the most concentrated game state in Squid Classic — when only two players still need to win a pot, and the geometry of the loser race collapses to 50/50.
§0 — Squid Classic in sixty seconds + the down-to-two state
Length target: ~300 words.
Goal: zero-prerequisite onramp + introduce the article's specific game state.
What §0 will say:
Brief format primer (Squid Classic is 6-max NLHE plus one rule — the squid penalty at game end; safe = has a squid; desperate = doesn't yet; val = penalty multiplier).
The article studies a specific game state: 4 of 6 players already safe. 1 squid left to award. 2 players still desperate. Whichever wins the next significant pot becomes safe; the other one pays the full penalty.
The math of down-to-two: each desperate player has 50% probability of being the loser. Expected penalty = 0.5 × 5×val. At val=3, that's 7.5 BB. The implicit ante per pot = 7.5 BB — bigger than most pots.
Three pairings, one common math, three different blind structures:
| Pairing | Desperate-money in pot | Safe-money (dead) | Who voluntarily opens |
|---|---|---|---|
| BvB (SB+BB desperate) | 1.5 BB (both blinds) | 0 BB | SB opens against BB |
| BTN+SB desperate | 0.5 BB (only SB blind) | 1 BB (BB folds) | BTN opens; SB defends |
| CO+BTN desperate | 0 BB | 1.5 BB (SB+BB fold) | CO opens; BTN defends |
The progression — desperate-money in the pot shrinks from 1.5 BB to 0; safe-player dead money grows from 0 to 1.5 BB — turns out to drive structurally different equilibria.
Widget — W1 · down_to_two_state_card.html: 6-seat table with 4 safe / 2 desperate. Hover/tap the desperate seats to expand the math: share = 1/2, expected penalty = 0.5 × 5×val = 7.5 BB at val=3.
§1 — Hook: a spot where loser-risk concentration changes the verdict
Length target: ~250 words.
Goal: create the felt sense of "wait, the same hand plays differently when only two of us are desperate."
Hook spot — LOCKED: SB defense vs BTN 2.5x open at down-to-two (BTN+SB desperate). SB defense rate cash 20.2% → all-desperate 43.9% → down-to-two 90.1%. The +46-point jump from all-desperate to down-to-two is the largest single-step widening in the dataset.
What §1 will say:
Open with the SB-vs-BTN spot. Reader sees the action: UTG/MP/CO/BB are safe and fold. BTN opens. SB to act with a marginal hand. Compare three regimes side-by-side: cash NLHE / all-desperate Squid val=3 / down-to-two desperate Squid val=3.
In cash, SB defends 20% of the time facing this open. In all-desperate Squid, SB defends 44%. In down-to-two SB defends 90%. The implicit ante grew the effective pot enough to flip nearly half of SB's marginal range from fold to play.
The article's promise: by §7 you'll see this same shift across three pairings, plus the reasons each pairing produces a different equilibrium shape.
Widget — W2 · hook_geometry_flip.html: paired spot card with three columns. Cash · all-desperate · down-to-two. Same hand, same opener, same chips. Reader can predict before reveal.
§2 — BvB: blind-vs-blind, both desperates already in the pot
Length target: ~350 words.
The blind structure: both desperate players have already posted blinds (1 BB and 0.5 BB). Before any voluntary action, 1.5 BB of the pot is desperate-money. There's no safe-player dead money. SB acts first preflop (extending the limp/raise/fold) against BB; postflop, BB has positional advantage (acts last).
Yes, BvB has positional asymmetry too — BB is in position postflop. The point isn't symmetry of position; it's that both desperates already have skin in the game before any voluntary action happens. This makes BvB the "saturation" pairing — there's no defending TO do; both players are already invested.
Phase A1 numbers (preflop):
| Cash | All desperate | Down-to-two | |
|---|---|---|---|
| SB open / continue | 57.9% (limp 31.5%) | 99.6% (limp 98.3%) | 100.0% (limp 88.3%) |
| BB defense vs SB | 64.1% | 98.8% | 100.0% |
| Avg BB raise | 9.0 BB | 14.5 BB | 15.0 BB |
Both players play 100% any-two-cards in down-to-two. The only thing that grows from all-desperate to down-to-two is the average raise size (cash 9 BB → squid 15 BB). Range plateau.
The §2 takeaway: BvB is the saturation case. Both desperates are committed; both play any-two-cards in down-to-two. There's no further widening to do.
Widget — W3 · pairing_grid_bvb.html: 13×13 range grid. Toggle cash / all-desperate / down-to-two. The grid fills in monotonically — by down-to-two, it's all-blue.
§3 — BTN+SB desperate: BTN opens; SB defends with the blind discount
Length target: ~350 words.
The blind structure: SB (one of the two desperates) has 0.5 BB posted; BTN (the other desperate) has 0 BB committed; BB (safe) has 1 BB posted as dead money but folds. So 0.5 BB of the pot is desperate-money (SB's blind), 1 BB is safe-player dead money (BB's blind), 1 BB is voluntary (BTN's open). Total visible pot before SB acts: 4 BB.
BTN acts first preflop and chooses to enter (open or fold). SB has the small blind discount on calls (only owes 2 BB to call BTN's 2.5x raise). BB folds reflexively (safe player, no implicit ante to defend). Postflop: BTN is IP, SB is OOP.
Phase A1 numbers (preflop):
| Cash | All desperate | Down-to-two | |
|---|---|---|---|
| BTN open | 43.3% (limp 0%) | 67.1% (limp 30.2%) | 98.9% (limp 50%) |
| SB defense vs BTN | 20.2% | 43.9% | 90.1% |
The cleanest two-step pairing in the dataset. BTN's open rate jumps +56 pts cash → down-to-two; SB's defense rate jumps +70 pts. SB's all-desperate-to-down-to-two jump alone (+46 pts) is the article's hook.
The §3 takeaway: BTN-vs-SB is the cleanest two-step. Both seats show large jumps at the down-to-two transition. The BB-fold-reflexively assumption holds because safe BB has zero implicit ante.
Widget — W4 · pairing_grid_btn_sb.html: same shape as W3. Range fill is non-uniform across the regimes — readers see the marginal zone where the down-to-two jump lives.
§4 — CO+BTN desperate: open-vs-defend with no blind discount
Length target: ~350 words.
The blind structure: Neither desperate has posted. SB and BB (both safe) have 1.5 BB of blinds in the pot but fold preflop (safe → no implicit ante to defend). The blinds become dead money for the desperates to fight over. CO acts first preflop. BTN closes the preflop action.
0 BB of the pot is desperate-money. 1.5 BB is safe-player dead money. 1 BB is voluntary (CO's open). Total visible pot before BTN acts: 4 BB. (Same total visible pot as BTN-vs-SB, but the composition is different — more dead money, less desperate-money.)
Phase A1 numbers (preflop):
| Cash | All desperate | Down-to-two | |
|---|---|---|---|
| CO open | 28.1% | 42.9% | 84.7% |
| BTN defense vs CO | 16.0% | 34.9% | 86.0% |
CO open rate triples cash → down-to-two. BTN defense rate quintuples. Both seats widen aggressively because (a) both have implicit ante and (b) the 1.5 BB safe-player dead money pads the pot odds for each.
The §4 takeaway: CO-vs-BTN is the most familiar pairing for cash regs. The dead money from safe blinds is the structural feature that distinguishes it — and that dead money becomes the headline driver of the postflop story in §5.
Widget — W5 · pairing_grid_co_btn.html: range grid same shape.
§5 — Postflop: all three pairings diverge
Length target: ~500 words.
Goal: show that postflop behavior at down-to-two is structurally different across the three pairings. The wet-board reversal flagged in early review is real — but only for one pairing. The other two pairings DROP wet-board c-bet at down-to-two. The dead-money structure from preflop is the likely driver.
Phase A2 numbers (postflop, c-bet on flop after SRP):
K72r (dry K-high):
| Cash | All desperate | Down-to-two | |
|---|---|---|---|
| BvB SB c-bet | 41.3% | 60.5% | 61.8% |
| BTN-vs-SB BTN c-bet | 51.8% | 84.3% | 92.3% |
| CO-vs-BTN CO c-bet | 87.0% | 96.6% | 98.4% |
All three pairings rise on dry boards, but the magnitude grows with the dead-money structure: BvB rises modestly (no dead money); BTN-vs-SB rises substantially (1 BB dead); CO-vs-BTN rises near saturation (1.5 BB dead). Dead money rewards aggression on uncontested textures.
765 two-tone (wet):
| Cash | All desperate | Down-to-two | |
|---|---|---|---|
| BvB SB c-bet | 50.3% | 52.4% | 38.7% |
| BTN-vs-SB BTN c-bet | 38.5% | 62.2% | 40.1% |
| CO-vs-BTN CO c-bet | 69.5% | 55.5% | 87.4% |
Wet-board pattern is split. CO-vs-BTN reverses up at down-to-two (the headline). BvB and BTN-vs-SB BOTH drop at down-to-two. Average bet size when betting tells the rest of the story:
- BvB 765two: cash 2.2 BB → down-to-two 8.7 BB
- BTN-vs-SB 765two: cash 2.4 BB → down-to-two 9.2 BB
- CO-vs-BTN 765two: cash 2.6 BB → down-to-two 5.6 BB
In BvB and BTN-vs-SB, the c-bet rate falls but the size grows dramatically. The desperate aggressor is concentrating bets — fewer of them, but each ~3-4× cash size. In CO-vs-BTN, both rate AND size grow because the safe-player dead money funds the aggression on every hand.
The §5 takeaway: the down-to-two state collapses cash NLHE postflop intuition differently in each pairing. The dead-money structure from preflop is the single biggest predictor of postflop direction.
Widget — W6 · postflop_sweep.html: 3 pairings × 2 boards × 3 regimes grid. Bars per cell with c-bet rate; tooltip shows avg sizing. Reader sees the wet-board direction split visually.
§6 — Per-position EV: which seat is the most valuable?
Length target: ~350 words.
Goal: answer the natural question "if I'm choosing between being desperate at seat X or seat Y, which is better?" The answer is non-obvious in two of the three pairings.
Phase A2 per-position EV (avg expected EV per combo at equilibrium, BB units):
| Pairing | Spot | Cash | All-desperate | Down-to-two |
|---|---|---|---|---|
| BvB | SB open | 0.24 | 2.88 | 3.78 |
| BvB | BB defense vs SB | 0.43 | 7.81 | 9.02 |
| BTN-vs-SB | BTN open | 0.23 | 0.51 | 1.49 |
| BTN-vs-SB | SB defense vs BTN | 0.03 | 1.76 | 4.16 |
| CO-vs-BTN | CO open | 0.14 | 0.47 | 1.20 |
| CO-vs-BTN | BTN defense vs CO | 0.14 | 0.42 | 1.28 |
Three findings.
1. The most valuable seat at down-to-two BvB is BB, not SB. BB EV = 9.02 vs SB EV = 3.78 — a 5.2 BB/hand advantage. The reason is the seat that closes the action. BB acts last preflop AND postflop, with a 1 BB blind discount on calls. When both players play any-two-cards, BB extracts more value because it has the most information per decision.
2. The most valuable seat at down-to-two BTN-vs-SB is SB, not BTN. SB EV = 4.16 vs BTN EV = 1.49 — a 2.7 BB/hand advantage to SB. This is counterintuitive — the natural assumption is that BTN's positional advantage should dominate. The data says otherwise.
The reason: at down-to-two, BTN opens 99% (essentially any-two-cards). SB responds with high 3-bet frequency (avg raise size 17.5 BB, against BTN's 7.2 BB open). SB's 3-bet aggression extracts heavy value from BTN's wide range — BTN can't continue against 3-bets with most of its opening range and gets folded out. SB closes preflop action effectively (BB folds reflexively as a safe player) and uses 3-bets to capture both the dead money (1 BB BB blind) and the implicit ante.
3. CO-vs-BTN is the closest to symmetric. CO open EV = 1.20 vs BTN defense EV = 1.28 — only 0.08 BB/hand advantage to BTN. The dead-money structure (1.5 BB of safe blinds) is split roughly evenly between the two desperates because both are equally positioned to claim it via aggression.
The §6 takeaway: "The button is the most valuable seat" is a cash NLHE habit. In Squid down-to-two, the most valuable seat depends on the pairing — and in BvB and BTN-vs-SB, it's NOT the BTN.
Widget — W7 · per_position_ev_chart.html: dual bar chart for each pairing, showing the two players' avg EV across regimes. The BvB and BTN-vs-SB bars look very different from cash intuition.
§7 — The pattern: three pairings, one mechanic, three blind structures
Length target: ~300 words.
Goal: synthesize. The three pairings illustrate the same down-to-two mechanism (loser-risk = 50%, implicit ante peaks at 7.5 BB at val=3) but the blind structure produces structurally different equilibria.
The blind-structure axis as a unifying frame:
- BvB (1.5 BB desperate-money, 0 BB dead): saturation. Both committed before action; both play 100%. The cleanest "ante-everywhere" intuition; range is just the entire grid.
- BTN-vs-SB (0.5 BB desperate, 1 BB dead): intermediate. The cleanest two-step widening preflop. SB extracts BTN's positional disadvantage via 3-bet aggression.
- CO-vs-BTN (0 BB desperate, 1.5 BB dead): dead-money-fight. Both desperates aggressive on uncontested textures because the safe blinds reward it. Wet-board c-bet rate paradoxically rises.
Postflop: - Dry boards: all three rise; magnitude scales with dead-money. - Wet boards: only CO-vs-BTN rises at down-to-two. BvB and BTN-vs-SB drop sharply but raise sizing 3-4× cash.
Per-position EV: - BvB: BB > SB - BTN-vs-SB: SB > BTN - CO-vs-BTN: BTN ≈ CO
In two of three pairings, the most valuable seat is NOT the button — overturning a cash-NLHE habit.
Widget — W8 · cross_pairing_synth.html: summary table of all three pairings × all key metrics (preflop range, postflop wet/dry direction, per-position EV).
§8 — Closer
Length target: ~200 words.
Goal: land the article's earned line.
Direction (placeholder):
"When the loser race narrows to two, the implicit ante doesn't just grow — it changes shape. In BvB, both players have already paid their preflop premium and there's nowhere wider to go. In BTN-vs-SB, the SB takes BTN's chips with 3-bets the BTN can't fight. In CO-vs-BTN, the safe players' blinds become a prize fund both desperates fight over, and wet boards become aggression magnets. Three structurally different geometries from one structural change. The chip-EV math you've used your whole career still works — but the geometry is no longer cash."
Final closer wording deferred to drafting.
Widget: none.
§9 — Editor's questions — RESOLVED ✅ (2026-04-25)
All four resolved by user direction + Phase A1+A2 solver data. Phase A complete.
✅ Q1 — book-2 coverage — RESOLVED skip the book. User direction: "we should not worry about the book. we should always be able to query all the pairings that we need." All 3 pairings queried directly via custom SquidConfig.counts arrays.
✅ Q2 — hook spot — RESOLVED SB-defense-vs-BTN-open at down-to-two. Phase A1 winner: cash 20.2% → all-desperate 43.9% → down-to-two 90.1%, +46 pt jump.
✅ Q3 — preflop / postflop scope — RESOLVED include postflop, expanded to all 3 pairings. Phase A2 added BvB and BTN-vs-SB postflop. Wet-board reversal is CO-vs-BTN-specific; BvB and BTN-vs-SB drop. Now §5 spans all 3 pairings.
✅ Q4 — worked-example hands — RESOLVED Phase B will pick from per-hand data. Per-hand fold/call/raise maps captured for all preflop spots. Specific hand picks deferred to Phase B drafting.
Phase A2-emergent decisions: - Reframed pairing axis from "position symmetry" (wrong — all 3 pairings have positional asymmetry) to "blind structure" (right — desperate-money vs safe-money composition). - Added per-position EV section (§6) — answers "which seat is most valuable" with surprising results in 2 of 3 pairings. - Stay with 3 pairings per Dan's proposal; data reinforces that 3 pairings cover the structural range adequately.
§10 — Drafting plan
Phase A1 + A2 — complete.
Phase B — v1 draft + widget build:
1. Draft §§0-8 prose against this outline using book-2 vocabulary
2. Build 8 widgets — 3 share the pairing-grid pattern; 1 dedicated postflop sweep; 1 dedicated per-position EV chart
3. facts.yaml + coined_terms.yaml audit
4. G10 / G25 / G21 verification gates
Phase C — review: 1. v1-completeness-checklist.md pre-flight 2. Tier 2b 9-agent review 3. Address findings + Editor's Q resolution pass
Phase D — deploy: 1. Re-render + deploy 2. Live URL → Dan for post-deploy review
Status
- 2026-04-25 — Outline preview deployed. API confirmed via custom SquidConfig.counts arrays. 6 widgets across 7 sections. 4 editor's Qs gated Phase A.
- 2026-04-25 (Phase A1) — 24/24 fresh queries successful. Hook locked, preflop equilibria locked, wet-board signal flagged.
- 2026-04-25 (Phase A2 + restructure) — 12/12 new postflop pulls + 18 per-position EV calculations successful. Article restructured to address review feedback:
- "Symmetric vs asymmetric pairing" framing dropped (wrong — all 3 have positional asymmetry); replaced with "blind structure" axis (1.5/0.5/0 BB desperate-money).
- "Before BB can interrupt" line dropped (didn't make sense — BB folds reflexively in §3 scenario).
- Postflop coverage expanded to all 3 pairings; wet-board reversal is CO-vs-BTN-specific, not universal — itself a finding now featured in §5.
- New §6 on per-position EV — surprising findings in BvB (BB > SB) and BTN-vs-SB (SB > BTN).
- Article grew from ~2,400w to ~2,800w to accommodate new content.