BvB 3-Bet Pot Deep Dive: 9♥ 5♦ 3♣ Rainbow at 100bb Cash

The blind-vs-blind 3-bet pot is one of the most complex and frequently misplayed spots in 100bb cash games. When the board comes 9♥ 5♦ 3♣ rainbow — one of the driest possible textures — both players face a deceptively nuanced decision tree that most regulars get wrong.

This deep dive breaks down every decision point from preflop through the river using solver-verified data. Whether you're the 3-bettor in position or the caller out of position, you'll walk away with a complete strategy for this board texture — and every board like it.

Want to run this analysis on your own spots? Solver+ gives you access to precomputed GTO solutions for thousands of common spots, and Postflop+ lets you train these decisions against a GTO bot until they're automatic.

1 The Setup: Preflop Ranges

SB opens to 3bb. BB 3-bets to 9.6bb. SB calls. The pot is 19.2bb with 90.4bb behind for each player — an SPR of 4.71.

BB's 3-bet range is polar — premiums at the top, suited connectors and bluffs at the bottom. SB's calling range is condensed — hands too strong to fold but not strong enough to 4-bet (JJ+ and AK 4-bet).

SB (OOP Caller) — Condensed Range

SB's range is built for boards like this. With no JJ+ or AK (those 4-bet), the range is heavy on pocket pairs (22–TT), suited broadways (KQs–AQs), offsuit broadways (KQo–ATo), suited connectors (54s–T9s), and suited aces (A2s–A9s). It's a middle-heavy range that connects well with low-to-mid boards.

BB (IP 3-Bettor) — Polar Range

BB's range is wider (229 weight vs 196) and much more polar. It contains AA, KK, QQ, JJ at the top — hands SB cannot have — and a wide assortment of offsuit bluffs (A2o–A7o, K5o–K9o, T7o, J8o) at the bottom. Mid pairs like 77–TT are at 0.5 weight (mixing 3-bet vs call).

2 Board Analysis: 9♥ 5♦ 3♣ Rainbow

This is one of the driest possible flop textures. No flush draws. Almost no straight draws (only 46 has an open-ender). The board is low, disconnected, and rainbow — a Type B board where the default strategy is "small bet or check."

3 Pot Geometry: Planning Across Streets

At SPR 4.71, how many streets of value can each hand type extract? The answer depends on which flop sizing BB chooses — and this choice shapes the entire hand tree.

Pot Progression by Line

4 BB's Flop Strategy: The Two-Sizing Dynamic

After SB checks (which happens 98.3% of the time — treat it as always), BB faces the most important decision of the hand: bet size selection.

BB c-bets 58.6% of the time using two distinct sizes, and checks back 41.4%. This is not a range-bet spot. Each sizing serves a fundamentally different purpose.

BB's flop range split on 9♥5♦3♣ in Solver+ — three distinct actions with the range grid color-coded by frequency

5 SB's Defensive Strategy

How SB responds depends entirely on which sizing BB chose. The check-raise frequency is 2.6× higher against the small bet — a critical structural feature that punishes indiscriminate range-betting.

Want to practice these defense frequencies until they're second nature? Postflop+ lets you play these exact spots against a GTO opponent and tracks where your frequencies diverge from optimal.

6 The Three Paths: Post-Flop Decision Tree

Three dominant paths emerge from the flop, each creating a fundamentally different dynamic for the rest of the hand.

SB checks (98.3%)
│
├── BB bets 80% pot (33.2%)
│   ├── SB folds (44.8%) — offsuit overcards, weak suited
│   ├── SB calls (46.9%) — sets, pairs 55-88, top pair, suited connectors
│   └── SB raises (8.2%) — TT (90%), A9s (97%), semi-bluffs
│       └── Turn: BB barrels overpairs on bricks, checks on overcards
│
├── BB bets 25% pot (25.4%)
│   ├── SB folds (16.8%) — only KJo, QJo, KQo
│   ├── SB calls (62.1%) — wide: all pairs, draws, broadways
│   └── SB raises (21.1%) — TT, 33, 76s, A9s, K9s, semi-bluffs
│       └── Turn: Wide ranges, thin value decisions
│
└── BB checks (41.4%) — KQs, AJs, ATs, 76s, 87s, K8o, T3s, 77, 88
    └── Turn: SB probes aggressively — BB's range is capped

7 Turn Strategy by Path

Path A: After 80% C-Bet Path B: After 25% C-Bet Path C: After Check-Back Path D: After SB Check-Raise

Pot ~49.92bb · Stacks ~75.04bb · SPR ~1.50

BB's range is polarized (overpairs + bluffs). SB's range is condensed and strong (sets, pairs, connectors). SB almost never donks — CHECK ≥78% on every card.

Turn Card Impact on BB's Strategy:

Turn Card	BB Effect	SB Effect	BB Action
Brick (2,4,8)	Neutral	Neutral	Barrel 60-75% pot with QQ+, TT, K9o. Equity bluff with AKo/AKs.
Ace	Kills QQ/JJ/TT	Improves SB's Ax	Barrel AA only. Check everything else.
King	Improves KK, K9	Improves SB's Kx	Barrel KK. QQ/JJ/TT must check.
Queen / Jack	Mixed	Both improve	Barrel the improved hand only. TT in trouble.
9, 5, 3 (pairs)	Some trips	Quads/trips for SB	Bet trips for value. Check overpairs cautiously.
7, 6	Minimal	Two pairs/straights for 76s/87s	Size down slightly. SB improved more.

The Nut-Donation Principle: Every bet is a donation into villain's nuts. When the turn gifts SB new nut combos (A, K, Q, J), your big bet donates into a range that just got stronger. On overcards: size down or check. On bricks: maintain the plan.

BB's turn range split on 9♥5♦3♣ 2♥ brick after 80% flop c-bet in Solver+

Pot ~28.80bb · Stacks ~85.60bb · SPR ~2.97

Both ranges are wider. BB's value range is thinner and SB's calling range is more diverse. SB is even more passive than Path A — CHECK ≥99% on overcards and bricks.

BB Hand	Turn Action	Sizing	Notes
99 (set)	Barrel ~70%	50-66% pot	Build pot for river stacking
AA	Barrel ~60%	50-66% pot	Not vulnerable but wants to build pot
KK	Barrel ~55%	50-60% pot	Must deny equity to SB's Ax overcards
QQ/JJ	Barrel ~50%	50-60% pot	Same overcard problem as the flop
T9s	Barrel ~40%	33-50% pot	Top pair thin value
54s	Check ~60%	—	One-and-done equity denial on flop

When BB doesn't have the nut advantage but wants to deny equity, a micro-denial bet (20–30% pot) is the right play on brick turns. It's a micro-commitment that advances equity without building an unnavigable pot.

BB's Turn Barrel Frequencies (after SB checks, which is ≥98%):

BB continues barreling 47-64% with a clear preference for 80% pot sizing.

Turn Card	BB Check	Bet ~25%	Bet ~80%	Overbet ~135%	Total Barrel
5♣ mid pairs	36%	1%	61%	2%	64%
Q♣ overcard	41%	—	58%	1%	59%
K♦ overcard	42%	1%	56%	1%	58%
9♠ top pairs	43%	3%	54%	1%	57%
J♣ overcard	44%	—	55%	1%	56%
A♥ overcard	47%	6%	38%	9%	53%
2♥ brick	49%	1%	34%	16%	51%
6♠ straight	49%	19%	31%	1%	51%
7♥ straight	53%	7%	36%	4%	47%
4♦ gutshot	53%	1%	45%	1%	47%

SB's Response to 80% Barrel:

Fold

54.2%

Call

41.3%

All-in

4.6%

SB's Response to 135% Overbet:

Fold

69.4%

Call

18.4%

All-in

12.2%

Pot 19.20bb · Stacks 90.40bb · SPR 4.71

BB's range is capped — no overpairs, no strong top pair (those all bet the flop). SB's range is completely uncapped. This is the highest-leverage node in the hand tree.

SB Turn Probe Frequencies by Card:

Turn Card	Check	Bet 40%	Bet 95%	Bet 150%
Brick (2♥)	58%	23%	15%	4%
A♥ overcard	98%	—	1%	—
K♦ overcard	77%	15%	7%	1%
J♣ overcard	51%	34%	14%	1%
7♥ straight	37%	24%	11%	29%
6♠ straight	35%	21%	21%	23%
9♠ pairs top	46%	17%	17%	20%

Maximum aggression on straight-completing cards: 7♥ and 6♠ see 63–65% probe frequencies with 23–29% at 150% pot. SB holds 76s, 87s, 98s and can overbet credibly. On bricks, SB probes ~42% at smaller sizes.

SB's turn probe split after BB's check-back on 9♥5♦3♣ 2♥ in Solver+ — four sizes plus check

SB Probe Hands (Brick Turn):

Hand	Probe Freq	Sizing	Logic
TT	60-75%	33-50% pot	Hidden overpair. Value probe against capped range.
99, 55, 33	65-85%	25-33% pot	Sets. Small value probe. No protection needed.
A9s, K9s	70-85%	33-50% pot	Top pair. Aggressive probe against capped range.
88, 77	50-65%	25% pot	Equity denial micro-bet. Deny BB's overcard outs.
76s, 65s	55-65%	25-33% pot	Gutshot + overcards (76s) / pair + gutshot (65s). Good probe hands with equity.
KQs, AJs	40-60%	25-33% pot	Semi-bluff probe. Strong candidates for probing a capped range.

Path D Turn: After SB Check-Raised the Flop

SB's XR ranges and BB's responses are covered in Section 5. Here we focus on turn continuation after the raise.

XR vs 80% Pot (SPR 0.55) XR vs 25% Pot (SPR ~2.0)

Turn After XR vs Big Bet — Effectively Committed

Pot ~8,064 with ~4,432 behind. SPR 0.55. Nearly every hand either jams or check-folds.

Hand	Turn Action	Logic
TT	Jam any turn	Must deny before overcards arrive. Only loses to sets.
A9s	Jam bricks, check overcards	Strong TPTK. Check A/K/Q turns that scare.
K9s	Jam bricks	Top pair. Fold to 3-bet if BB came over the top on flop.
JTs	Jam on gin cards (Q, 8)	Check-fold blanks. Semi-bluff budget spent.
AJs	Jam if A or J lands	Check-fold blanks. Bluffing budget exhausted.
A5s / A2s	Jam if A or wheel card hits	Give up on blanks.

Turn is simplified at SPR 0.55: No thin value, no block betting — the pot is too committed for nuance. Jam value, check-fold missed semi-bluffs.

Turn After XR vs Small Bet — Room to Maneuver

Pot ~3,600 with ~7,360 behind. SPR ~2.04. Genuine decisions about barrel sizing and card impact.

SB's Turn Continuation by Hand:

Hand	Turn Action	Logic
TT	Barrel 60-75% pot on bricks	Check overcards. Still the must-protect overpair.
A9s	Barrel bricks for value	On A turn → bet big (two pair). Check bad overcards.
33, 99	Barrel 50-66% on any turn	Three streets of value. Can slow-play bricks to let BB catch up.
76s	Barrel on 4 (straight completes)	Check-evaluate blanks — 7-high has minimal SDV. Give up on overcards.
K9s	Barrel bricks 50-60% pot	On K turn → bet big (two pair). Cautious on A turn.
A4s	Barrel if A hits or straight completes	Check-fold blanks. Ace blocker helps as bluff.
Q9s	Barrel bricks cautiously 33-50%	Check overcards.
66	Barrel selectively	Check most turns for SDV.

Turn Card Impact After XR vs Small:

Turn Card	SB Strategy	Logic
Brick (2,4,8)	Barrel 60-70% with TT/A9s/sets/K9s. Semi-bluff 76s on 4/8.	Nothing changed. SB's range advantage holds. Apply pressure.
Ace	Barrel A9s (now two pair). Check TT/K9s. A4s improves.	Ace helps SB's A9s and A4s but hurts TT badly. Polarize: bet improved hands, check the rest.
King	Barrel K9s (now two pair). Check most others. TT cautious.	K benefits K9s dramatically. SB can overbet with K9s for value.
Queen / Jack	Barrel TT for protection. Sets continue. Semi-bluffs check.	Overcards threaten TT — must continue denying. 76s loses value as a barrel.
6 or 7	76s barrels big (two pair/straight). All value continues.	Best card for SB's semi-bluff region. 76s becomes nutted.
9, 5, 3 (pairs board)	Sets → quads/full house (bet big). TT/A9s check cautiously.	Board pairing favors SB's set-heavy XR range enormously.

The key difference between the two XR paths: vs the big bet, SB's range is narrow (TT + A9s dominated) and the pot is committed — turn play is automatic. Vs the small bet, SB's range is wider and includes sets + semi-bluffs with SPR ~2.0 remaining — turn play involves genuine decisions about barrel sizing, card impact, and whether semi-bluffs continue or give up.

8 River Strategy: Solver Data & Heuristics

At the river, every hand falls into exactly one of five classes. The classification determines your mandatory play — there's no judgment call, just execution.

River by Path — Solver Data

Path A: After 80% C-Bet Path B: After 25% C-Bet Path C: After Check-Back Path D: After SB Check-Raise

Path A River: After BB Bet 80% Flop, SB Called

Two sub-scenarios depending on what happened on the turn. When BB checks the turn, their range is capped — no overpairs or strong value stayed passive. SB's range is uncapped.

Both Check Turn → SB Acts BB Triple-Barrels → SB Defends BB Triple-Barrels (Solver Data) BB Facing SB's River Bet (Path A)

SB's River Action After Both Check Turn (Pot ~49.92bb, Stacks ~75.04bb):

Board: 9♥ 5♦ 3♣ 2♥ (brick turn)

River Card	Check	Bet ~40%	All-In	Pattern
2♦ double brick	39%	60%	—	Best probe card — nothing changed, BB's capped range can't call
K♦ overcard	62%	37%	1%	Medium bet, less polarized
A♥ overcard	71%	4%	25%	Polarized — SB has Ax that improved, goes all-in or gives up
7♠ straight	54%	23%	23%	Split sizing — straights jam, thin value bets small
4♦ connects	88%	1%	12%	Check-heavy — 4 connects draws, gives BB combos
T♣ overcard	91%	4%	5%	Near-pure check — T improves BB's TT

Board: 9♥ 5♦ 3♣ 7♥ (straight-completing turn)

River Card	Check	Bet ~40%	All-In
6♠ completes	36%	60%	4%
8♦ completes	38%	48%	15%
A♥ overcard	79%	2%	19%
2♦ brick	62%	38%	1%

Key Pattern: Sizing Is Polarized

SB uses either ~40% pot or all-in with almost nothing in between. This is the hallmark of a range-vs-capped-range river: SB has the nuts or nothing. Straight-completing rivers (6♠, 8♦ after 7♥ turn) see 62-64% continuation — SB holds 76s, 87s, 98s and barrels credibly.

When BB Triple-Barrels (Flop 80% → Turn Barrel → River Bet):

SB's calling range has been filtered to sets, strong pairs, and the best bluff-catchers. This is the most polarized river spot in the entire hand tree.

SB Hand	Class	vs 66% Pot	vs Pot Bet	vs Overbet	Blockers
99, 55, 33	A/B — Nuts	Call/Raise	Call/Raise	Call	Blocks 9x/5x/3x value
TT (rare)	B — Thick	Call	Call	Call cautiously	Blocks TT combos
Q9s, T9s	C/D — Bluff-catcher	Call if unblocks bluffs	Fold lean	Fold	Blocks QQ/TT value
88, 77, 66	D — SDV	Fold	Fold	Fold	No positive blockers
76s, 65s (bricked)	E — Air	Bluff if no SDV	Bluff	Bluff	Unblocks BB's folds
AQo, KQs	D — SDV	Fold	Fold	Fold	Blocks value = negative

Blocker Selection Guide (SB's Calling Decisions):

Holding	Effect	Action
A 9	Blocks BB's 9x value (K9, Q9, T9)	Call more
An A	Blocks BB's AA	Call more
A K	Blocks BB's KK	Call slightly more
A Q	Blocks QQ but also QTo bluffs	Neutral
A J	Blocks JJ and JTo bluffs	Fold lean

BB Acts on River After Triple-Barrel Line (SPR ~0.83):

Board: 9♥ 5♦ 3♣ 2♥. BB bet 80% flop → barreled turn → acts on river. Only sizing is all-in.

River Card	BB CHECK	BB ALL-IN
A♥ overcard	48%	52%
K♦ overcard	25%	75%
T♣ overcard	22%	78%
7♠ straight	39%	61%
4♦ connects	44%	56%
2♦ double brick	32%	68%

Key Pattern: Shove Frequency by River Card

T♣ and K♦ trigger the highest shove frequencies (75-78%) — these overcards don't improve SB's calling range. A♥ is the lowest shove at 52% because the Ace improves some of SB's remaining hands (A9s, A5s).

BB Responds to SB's River Bet (After Both Check Turn):

Board: 9♥ 5♦ 3♣ 2♥. Both checked turn → SB bets ~40% pot on river → BB responds.

River Card	SB Bet Size	BB Fold	BB Call	BB Raise/AI
K♦ overcard	~40%p	39%	36%	24%
7♠ straight	~40%p	54%	29%	17%
2♦ double brick	~40%p	62%	17%	21%

Key Pattern: BB's Delayed Aggression

BB folds 39-62% overall. The 2♦ brick triggers the highest fold frequency (62%) — BB's capped range has nothing to call with on a blank runout. BB raises 17-24% with sets and two-pair that checked back the turn for deception.

Path B River: After BB Bet 25% Flop, SB Called

SB checks the turn ≥98% of the time. The river plays out very differently depending on whether BB barreled or checked behind on the turn.

Both Check Turn → SB Acts River BB Barrels Turn → SB Calls → River BB Acts After x/x Turn

Both Check Turn (2♥ brick) → SB Acts on River

Pot 28.80bb, stacks 85.60bb. BB's turn check capped their range — SB can probe with value.

River Card	Check	Bet ~40%	Bet ~95%	All-In	Pattern
T♣ overcard	30%	42%	28%	—	Strongest bet card — T doesn't help BB's capped range
7♠ straight	37%	38%	19%	6%	Draw-completing — SB's straights arrive
2♦ double brick	52%	29%	19%	—	Standard — nothing changed, moderate bet
A♥ overcard	66%	—	4%	30%	Polar — 30% all-in or give up. A9s/AJs improved to nuts.
K♦ overcard	71%	28%	—	—	Small-only — SB block-bets with Kx and medium pairs
4♦ connects	86%	—	—	14%	Check-heavy with all-in kicker — nuts shove, rest give up

SB's Block Bet Ladder (this check-through line):

SB Hand	Equity	Block Bet Size	Logic
Pair of 3s (A3s)	~55%	10% pot	Weakest thin value. Beats only air.
Pair of 5s (65s, 54s)	~58%	15-20% pot	Slightly stronger. Beats air + weak pairs.
97s (TP weak kicker)	~62%	25% pot	Solid thin value.
T9s (top pair)	~65%	25-33% pot	Stronger thin value.
Q9s (TP good kicker)	~68%	33% pot	Transitioning toward standard bet.
K9s (TP strong kicker)	~72%	33-50% pot	Thick value territory.
A9s (TPTK)	~78%	50% pot	Standard value bet, not a block.
99 (set)	~90%+	66-100% pot	Class A. Max value extraction.

The most commonly missed play at NL100-500: Block-betting thin value on low boards. Pairs of 3s and pairs of 5s on 9-high boards should block-bet but are almost always checked.

Bluff Selection — The Inversion Rule:

Prefer hands with one overcard + busted backdoor over two overcards. Two-overcard hands (KQo) have too much SDV to waste as bluffs AND they block the opponent's folding range.

BLUFF SUITCASE ORDER (fill from the bottom up):

1st Busted gutshots with no pair — A4s that missed, pure air

2nd Overcard hands with zero SDV — QJo that bricked everything

3rd Only if suitcase isn't full: weak pairs with marginal SDV (44, 22)

BB Barrels 80% Turn → SB Calls → SB Acts on River

Board 9♥5♦3♣ 2♥. Pot ~74.37bb, stacks ~62.61bb. SPR ~0.84 — effectively committed. The only sizing is check or shove.

River Card	Check	All-In	Pattern
A♥ overcard	51%	49%	Only shove card — A9s improved to trips, A5s/A3s made two pair
K♦ overcard	100%	—	Pure check
7♠ straight	100%	—	Pure check
T♣ overcard	100%	—	Pure check
2♦ double brick	100%	—	Pure check
4♦ connects	91%	9%	Near-pure check — rare shove with nutted hands only

Deep-Street Pot Geometry Confirmed

At SPR ~0.84, SB's range is already defined — hands that called the turn barrel are sets and strong pairs that want to check-call BB's potential third barrel, not lead into it. Only the Ace triggers a shove (49%) because it dramatically improves SB's calling range.

BB Acts on River After x/x Turn (SB Checks to BB):

Board: 9♥ 5♦ 3♣ 2♥. BB bet 25% flop → SB call → x/x turn → SB checks river → BB acts. Pot 28.80bb, stacks 85.60bb.

River Card	BB CHECK	BB BET ~35%p	BB BET ~90%p	BB ALL-IN
A♥ overcard	68%	4%	27%	1%
K♦ overcard	57%	2%	40%	1%
7♠ straight	59%	2%	39%	—
4♦ connects	47%	45%	5%	3%
T♣ overcard	63%	6%	26%	5%
2♦ double brick	61%	4%	30%	5%

Key Pattern: Sizing Selection by River Card

K♦ is BB's best bet card (43% total, 40% at 90% pot) — the King doesn't improve SB's range. 4♦ is uniquely a small-bet card (45% at 35% pot) because it connects draws and BB wants thin value. All other river cards default to 90% pot as the primary sizing.

Path C River: After BB Check-Back — Three Solver Scenarios

Path C produces the widest ranges and most varied river spots. The solver was queried on three distinct scenarios.

Scenario 1: x/x/x/x Scenario 2: SB Probed → BB Called Scenario 3: 9♠ Pairs Board BB Acts After Calling SB's Turn Probe BB Acts After x/x/x/x

Both check flop AND turn (x/x/x/x). SB acts on river.

Board: 9♥ 5♦ 3♣ 2♥. Pot 19.20bb, stacks 90.40bb. Ranges are very wide — this is thin-value paradise.

River Card	Check	Bet 40%	Bet 95%	Bet 150%
K♦ overcard	51%	43%	6%	—
J♣ overcard	56%	44%	—	—
T♣ overcard	53%	26%	14%	7%
A♥ overcard	72%	18%	1%	10%
7♠ straight	63%	15%	3%	17%
4♦ connects	89%	10%	—	1%

K♦ and J♣ are the best probes (43-44% bet, mostly small). A♥ and 4♦ are check-heavy.

SB probed 40% pot on 2♥ brick, BB called. SB acts on river.

Pot 34.56bb, stacks 82.72bb. This is the critical line — SB continues far more often than "one-and-done."

River Card	Check	Bet 40%	Bet 95%	All-In
7♠ straight	15%	49%	29%	7%
T♣ overcard	34%	52%	15%	—
2♦ double brick	38%	54%	8%	—
K♦ overcard	64%	36%	—	—
A♥ overcard	68%	1%	25%	6%
4♦ connects	81%	—	1%	18%

"One-and-Done" Probe is NOT GTO

SB continues on 5 of 6 river cards tested, often above 50%. The solver strongly disagrees with giving up after probing. Key patterns:
7♠ = strongest continuation — 85% bet across all sizes (7% all-in). Straight completers are the best barrel cards.
T♣ and 2♦ = strong continuations — 62-67% bet. Run-outs that don't change the board favor the aggressor.
K♦ = small-only continuation — 36% bet, all at 40% pot.
A♥ = polar — 32% bet, but skips small sizing (25% at 95%, 6% all-in).
4♦ = check-heavy — 81% check. The 4 connects too many draws.

SB's river range split after probe→call on brick runout in Solver+ — continuation far from "one-and-done"

Both check turn, 9♠ pairs the board. SB acts on river.

Board: 9♥ 5♦ 3♣ 9♠. Pot 19.20bb, stacks 90.40bb. Paired board makes both ranges more cautious.

River Card	Check	Bet 40%	Bet 95%	Bet 150%	All-In
K♦ overcard	56%	36%	7%	—	2%
A♥ overcard	70%	29%	—	—	1%
7♠ straight	77%	6%	8%	2%	8%
2♦ brick	81%	5%	9%	5%	—

SB probes less overall (19-44%). K♦ is still the best probe river (44%). Paired board reduces aggression across all cards.

BB Acts on River After Calling SB's Turn Probe:

Board: 9♥ 5♦ 3♣ 2♥. x/x flop → SB probed 40% turn → BB called → SB checks river → BB acts. Pot 34.56bb, stacks 82.72bb.

River Card	BB CHECK	BB BET ~35%p	BB BET ~90%p	BB ALL-IN
A♥ overcard	63%	4%	22%	11%
K♦ overcard	56%	3%	30%	12%
7♠ straight	63%	1%	35%	2%
4♦ connects	56%	3%	40%	1%
T♣ overcard	64%	2%	26%	9%
2♦ double brick	62%	1%	27%	10%

Key Pattern: BB's Delayed Value After Calling Probe

4♦ is BB's best bet card (44% total, mostly at 90% pot). K♦ triggers 42% betting with 12% all-in — overcards that improve BB's range. All river cards use 90% pot as the primary sizing, with all-in reserved for the strongest holdings.

BB Acts on River After x/x/x/x (Both Check Flop AND Turn):

Board: 9♥ 5♦ 3♣ 2♥. Both check flop AND turn → SB checks river → BB acts. Pot 19.20bb, stacks 90.40bb.

River Card	BB CHECK	BB BET ~35%p	BB BET ~90%p	BB BET ~150%p	BB ALL-IN
A♥ overcard	49%	30%	16%	3%	3%
K♦ overcard	51%	24%	21%	4%	—
7♠ straight	58%	16%	26%	—	—
4♦ connects	50%	46%	1%	1%	2%
T♣ overcard	59%	9%	31%	1%	—
2♦ double brick	58%	15%	20%	7%	—

Key Pattern: Wide Sizing Spread After Four Checks

4♦ is the small-bet card (46% at 35% pot). A♥ has the broadest sizing spread — 51% betting across all sizes as AA finally fires after checking twice. T♣ is a medium-bet card (41% total, 31% at 90% pot). With deep stacks and wide ranges, BB uses the full sizing menu.

SB's River Hand Table (After Probe → Call Line, Brick Run-Out):

SB Hand	Class	River Action	Sizing	Notes
99, 55, 33	A — Nuts	Value bet	66-100% pot	Max value. BB called probe with medium hand.
TT	B — Thick	Value bet	50-75% pot	Strong overpair. BB cannot have better.
A9s	B — Thick	Value bet	50-66% pot	TPTK. Beats BB's entire calling range.
K9s	B/C	Value bet	33-50% pot	Thin value territory. Size by equity.
Q9s	C — Thin	Block bet	25-33% pot	Mandatory block bet.
T9s	C — Thin	Block bet	25% pot	Thinnest value. Small block.
88, 77, 66	D — SDV	Check	—	Too weak to get called by worse.
76s (gutshot)	D — SDV	Check	—	7-high with busted gutshot. Marginal SDV — don't bluff.
KQs (missed)	E — Air	Bluff	50-75% pot	Blocks KK value. Good bluff.
QJo (missed)	E — Air	Bluff	50-66% pot	Bottom of range. Fill suitcase.
A6s (missed)	E — Air	Bluff	50-66% pot	Blocks AA value.

BB's River Strategy (IP, After Calling SB's Turn Probe):

BB Action When Checked To	Hands	Notes
Bet for value	Any top pair or better	Standard value bet at 66-75% pot
Check back	Overcards that floated (KQs), low suited hands (76s, 87s), pure air	SDV — end the hand for free
Bluff (rare)	Hands that unblock SB's folds	Solver bluffs at low frequency with total air that can't win at showdown

Path D River: After SB Check-Raised the Flop

The river after a check-raise depends entirely on which flop sizing SB raised against. The two paths diverge dramatically.

XR vs 80% Pot (Committed) XR vs 25% Pot (SPR ~2.0)

SPR was 0.55 entering the turn — most hands resolved before the river.

After SB's flop XR and a turn jam or call, remaining stacks are minimal. The river is almost always an all-in or a trivial decision. If somehow both players check the turn (rare at this SPR), the river plays out simply:

SB Hand	Class	River Action	Notes
TT	A/B — Nuts	Jam remaining stack	SB's overpair — always gets it in. Only loses to sets that slow-played.
A9s	B — Thick	Jam remaining stack	TPTK. Ahead of BB's entire continuing range except overpairs.
K9s	B/C	Jam if improved, check if not	On K river → jam (two pair). On blanks → thin jam at this SPR.
JTs (bricked)	E — Air	Jam as bluff if missed	Busted straight draw. Last chance to represent the overpair line. Only bluff if straight bricked.
AJs (bricked)	D/E	Check-fold	A-high has marginal SDV at this pot size. Not enough to bluff with.

In practice, this river rarely happens. At SPR 0.55, the turn action (jam or fold) resolves 90%+ of hands. The remaining river spots are trivial: if you have value, put it in. If you have air, your last bluff chance is a small remaining stack shove.

SPR ~2.0 entering the turn → ~0.8-1.2 entering the river after a turn barrel.

This path produces meaningful river decisions. After SB's flop XR (to ~1,200) and a turn barrel (~50-66% pot), the pot is ~7,200-8,400 with ~3,600-5,200 behind. SB's range is polarized between value that barrelled and semi-bluffs that continued.

SB's River Strategy (After XR Flop → Barrel Turn → River):

SB Hand	Class	River Action	Sizing	Notes
33, 99 (sets)	A — Nuts	Jam	All-in	Three streets of value complete. Jam remaining stack on any river.
TT	A/B — Nuts	Jam on blanks, check overcards	All-in / Check	On A/K/Q river, TT loses to improved hands. Check and evaluate. On bricks, jam for value.
A9s	B — Thick	Value bet / Jam	66-100% pot	On A river → two pair, jam. On blanks → value bet. On K/Q → cautious bet.
K9s	B/C	Value bet on K, block bet on blanks	50-66% pot	On K river → two pair, jam. On blanks → thin value at 50%. On A → check.
Q9s	C — Thin	Block bet on blanks	33% pot	Thin value. Beats BB's bluff-catchers but loses to overpairs that called.
76s (hit straight)	A — Nuts	Jam	All-in	If 4 arrived on turn or river → nutted. Jam for max value.
76s (missed)	E — Air	Bluff or give up	66-100% pot	Busted gutshot. Best bluff candidate — unblocks BB's folds and blocks nothing.
A4s (missed)	E — Air	Bluff	66-100% pot	Busted draw with ace blocker. Blocks AA in BB's range → good bluff.
66 (missed)	D — SDV	Check-fold	—	Underpair with SDV. Don't turn into a bluff — 6-high beats nothing if called.

BB's River Defense (After Calling XR + Turn Barrel):

BB Hand	River Action	Notes
AA, KK	Call any sizing	Top of range. Beats TT, A9s, K9s. Only loses to sets.
QQ, JJ	Call on blanks, fold on A/K	Ahead of SB's bluffs. On A/K rivers, SB's value range improves — tighten up.
TT	Marginal call	Splitting with SB's TT, behind sets. Blocker to TT value is positive — call lean.
99 (set)	Call / raise	Nutted. Snap call or raise for max value.
T9s (top pair)	Fold to jam, call small	Facing a polarized range. T9s is a bluff-catcher at best. Fold to large sizing.

River After XR vs Small: The Polarization Payoff

SB's check-raise on the flop set up a three-street value plan for sets and TT, with semi-bluffs (76s, A4s) as the natural bluff candidates. By the river, the range is cleanly polarized: nuts or air. Sets and TT jam for value. Missed draws either bluff (if they have good blockers) or give up. There's very little thin value — the XR path compresses the hand into a binary decision.

Solver-Based River Calling Framework

Before calling any river bet, evaluate using pot odds and blocker logic — not just hand strength:

Position-Dependent River Play: OOP vs IP

9 Quick Reference Cheat Sheet

Board Texture Classification

When you see similar boards at the table, classify them immediately using this framework:

Common Misconceptions

Analysis based on GTO solver data for 100bb cash BvB 3-bet pots (flop 3♣5♦9♥). All frequencies are solver-derived. Run these spots yourself with Solver+.