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What is every hand worth on a 9 6 2 monotone flop?

On a 9 6 2 monotone flop, the three sets lead with unusually modest edges over a random hand, and holding a single high heart often matters more than the ranks in your hand.

9 6 2 monotone

Monotone boards

Equity vs one random hand

99 83.3%
66 82.7%
22 81.9%
AA 79.6%

Notable hands on 9 6 2 monotone

HandFlopsEquityWhy it matters
99 set 83.3% Top set, yet the board refuses to let even this be a lock.
66 set 82.7% Middle set, packed in tight with the other two.
22 set 81.9% Bottom set. Even this deserves respect and caution in equal measure here.
AA overpair 79.6% The best overpair, better still when one of them is the ace of hearts.
KK overpair 77.6% A strong overpair that very much wants its king to be a heart.
96s two pair 75.5% Top two pair from a hand nobody chooses to play.
92o two pair 74.2% Two pair out of pure junk, comfortably in front of a random hand anyway.
A9o pair 72.3% Top pair, and sometimes the nut flush draw riding along with it.
AKo nothing yet 55.0% The big-card flagship, scraping out a small edge unless it brought a heart.
JTs nothing yet 45.7% Suited, connected, useless: when it is not in hearts, this board gives it nothing.

9 6 2 in one suit is the strange twin of the driest board in poker. Strip the hearts away and this is a disconnected nothing-flop; with them, every hand becomes two hands: the version holding a heart and the version holding none. No straight threatens anyone, the ranks barely interact, and the entire conversation is about one suit.

Sets still finish on top, nines, sixes, and deuces, but look how modest their lead is. A monotone flop is the great compressor of equity, because so many random hands arrive holding a live flush card or two. The junk two pair hands, 96 and even 92, do fine, and the real currency beneath the made hands is a single high heart: top pair with A9 is strong partly because its ace is sometimes the ace of hearts, stapling the nut flush draw onto the pair.

The suit rules deserve one careful sentence. A suited hand here is a flopped flush only when it is suited in hearts, which any suited class is only a fraction of the time, and a hand like 87 suited in spades is just high-card nothing with a backdoor apology. Every suited row averages those lives together, so read it as a blend, never a promise.

The stall-outs are the famous big cards. AK without a heart is just two overcards, and the class overall keeps only a small edge. KQ is a genuine coin flip, and JT suited is an underdog. The mistake on monotone flops is bluffing and calling by rank instead of by suit: the hand that continues profitably here is not the prettiest one, it is the one holding the right heart. Check your suits before your ranks and you are ahead of most of the table.

All 169 hands on 9 6 2 monotone

Equity of every starting hand class against one random opponent hand on 9 6 2 monotone, averaged over the class's possible suit combinations. Sorted best to worst within each group.

Suit note: on this board a suited hand only has flush potential when its suit matches the board's. The figures average over all suit combinations of each class.

Pairs

HandFlopsEquity
99 set 83.3%
66 set 82.7%
22 set 81.9%
AA overpair 79.6%
KK overpair 77.6%
QQ overpair 75.6%
JJ overpair 74.0%
TT overpair 72.5%
88 65.4%
77 63.5%
55 55.5%
44 52.8%
33 51.0%

Suited

HandFlopsEquity
96s two pair 75.5%
92s two pair 74.0%
62s two pair 72.0%
A9s pair 65.9%
K9s pair 65.2%
Q9s pair 64.6%
T9s pair 64.4%
J9s pair 64.3%
98s pair 63.1%
97s pair 62.7%
95s pair 61.9%
94s pair 61.2%
93s pair 61.2%
A6s pair 57.2%
K6s pair 56.7%
AKs 56.2%
Q6s pair 56.2%
T6s pair 55.9%
J6s pair 55.8%
AQs 55.7%
86s pair 55.3%
76s pair 55.3%
ATs 55.2%
AJs 55.1%
A8s 54.6%
A7s 54.0%
65s pair 53.6%
64s pair 52.9%
87s 52.8%
63s pair 52.8%
A5s 52.7%
KQs 52.0%
A4s 51.9%
A3s 51.9%
KTs 51.9%
KJs 51.6%
K8s 50.5%
K7s 50.0%
QTs 48.9%
QJs 48.8%
K5s 48.6%
T8s 48.5%
K4s 47.9%
K3s 47.8%
Q8s 47.6%
A2s pair 47.5%
T7s 47.4%
K2s pair 46.8%
Q7s 46.4%
Q2s pair 46.3%
T2s pair 46.0%
JTs 45.7%
82s pair 45.7%
J2s pair 45.5%
72s pair 45.3%
Q5s 45.1%
52s pair 44.7%
J8s 44.6%
85s 44.4%
Q4s 44.2%
Q3s 44.1%
42s pair 43.8%
32s pair 43.7%
J7s 43.4%
75s 42.7%
J5s 41.9%
54s 41.1%
J3s 41.0%
53s 41.0%
J4s 40.9%
T5s 39.5%
43s 39.3%
T4s 39.2%
T3s 39.2%
84s 37.1%
83s 37.1%
74s 35.3%
73s 35.3%

Offsuit

HandFlopsEquity
96o two pair 75.5%
92o two pair 74.2%
A9o pair 72.3%
62o two pair 71.9%
K9o pair 71.4%
Q9o pair 70.6%
J9o pair 69.5%
T9o pair 69.4%
98o pair 67.6%
97o pair 67.0%
95o pair 65.9%
94o pair 64.9%
A6o pair 64.7%
93o pair 64.5%
K6o pair 63.9%
Q6o pair 63.1%
J6o pair 61.9%
T6o pair 61.8%
86o pair 61.0%
76o pair 60.2%
65o pair 58.4%
64o pair 57.4%
63o pair 56.9%
A2o pair 56.0%
AKo 55.0%
K2o pair 54.9%
Q2o pair 54.0%
AQo 53.9%
AJo 53.0%
J2o pair 52.9%
T2o pair 52.9%
ATo 52.7%
82o pair 52.0%
A8o 51.5%
72o pair 51.2%
A7o 50.5%
52o pair 50.1%
KQo 49.8%
42o pair 48.9%
KJo 48.7%
KTo 48.7%
A5o 48.7%
32o pair 48.7%
87o 48.0%
A4o 47.5%
A3o 47.0%
K8o 46.6%
K7o 45.8%
QJo 45.4%
QTo 45.4%
T8o 44.2%
K5o 43.9%
Q8o 43.4%
T7o 42.7%
K4o 42.6%
K3o 42.2%
JTo 41.7%
Q7o 41.6%
J8o 39.9%
Q5o 39.7%
85o 38.7%
Q4o 38.7%
Q3o 38.2%
J7o 38.1%
75o 36.7%
J5o 36.2%
J4o 34.9%
54o 34.4%
J3o 34.4%
53o 33.9%
T5o 33.2%
T4o 32.6%
T3o 32.4%
43o 32.0%
84o 30.1%
83o 29.9%
74o 28.1%
73o 27.8%

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