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What is every hand worth on a 7 7 7 trips flop?

On a 7 7 7 trips flop, any hand containing the last seven makes quads, every pocket pair plays as an instant full house, and everyone else is fighting a pure kicker war over the board.

7 7 7

Trips boards

Equity vs one random hand

A7o 100.0%
72o 100.0%
AA 94.9%
KK 91.5%

Notable hands on 7 7 7

HandFlopsEquityWhy it matters
A7o quads 100.0% Four sevens with an ace on the side. The deck cannot produce a better hand.
72o quads 100.0% The case seven makes quads even for the worst hand in poker. Poetry.
AA full house 94.9% Sevens full of aces, the biggest full house and the best realistic holding here.
KK full house 91.5% Sevens full of kings, second rung on the boat ladder.
88 full house 77.3% A modest pair, a made full house, and a comfortable favorite.
22 full house 62.9% Sevens full of deuces: technically a boat, practically the nervous kind.
AKo nothing yet 69.8% No pair required. The board is the hand, and these are the best kickers.
A2s nothing yet 63.9% Even a ragged ace wins the kicker war more often than not.
JTs nothing yet 46.7% Suited and connected mean nothing when everyone already has trips. A slight underdog.
32o nothing yet 25.2% The worst kickers in the deck, fighting over a board that plays itself.

Three sevens on the flop is a poker curiosity with a real lesson inside. Start with the strangest fact: pocket sevens cannot exist here. Three of the four sevens are on the board, so no player can hold two more, and the quads belong instead to anyone holding the single seven left in the deck. A7 offsuit, 72 offsuit, it makes no difference: one seven means four sevens.

Behind the quads, the full houses line up by rank. Every pocket pair is a made full house, sevens full of that pair, sorted strictly by size: sevens full of aces at the top, kings next, all the way down to sevens full of deuces, which wins less than its label suggests because every higher pocket pair and the case seven have it beat, and even an unpaired opponent can outdraw it by pairing a bigger card.

Everyone without a pair or a seven is playing the purest kicker war in poker. The board hands trips to every player at the table, so the winner between two unpaired hands is simply whoever holds better side cards. That is why AK is a solid favorite with no pair at all, why a lone ace carries real weight, and why small connected hands like JT suited, with neither high cards nor a live draw, quietly slip below even money.

People go wrong by forgetting what the board already gave everyone. Players see trips in their hand reading and feel strong, but the trips belong to the table, not to them, and a naked queen-high holding is just queen high with extra steps. Sizing logic flips too: almost nothing improves or falls behind on later streets, so the pot is mostly decided the moment the cards are dealt. When a flop comes 7 7 7, count your kickers, respect any raise, and remember that exactly one seven is out there somewhere.

All 169 hands on 7 7 7

Equity of every starting hand class against one random opponent hand on 7 7 7, averaged over the class's possible suit combinations. Sorted best to worst within each group.

Pairs

HandFlopsEquity
AA full house 94.9%
KK full house 91.5%
QQ full house 88.4%
JJ full house 85.4%
TT full house 82.6%
99 full house 79.7%
88 full house 77.3%
66 full house 73.5%
55 full house 70.8%
44 full house 68.1%
33 full house 65.4%
22 full house 62.9%
77 blocked n/a

Suited

HandFlopsEquity
A7s quads 100.0%
K7s quads 100.0%
Q7s quads 100.0%
J7s quads 100.0%
T7s quads 100.0%
97s quads 100.0%
87s quads 100.0%
76s quads 100.0%
75s quads 100.0%
74s quads 100.0%
73s quads 100.0%
72s quads 100.0%
AKs 70.1%
AQs 68.8%
AJs 67.8%
ATs 66.8%
A9s 66.2%
A8s 65.7%
A6s 65.3%
A5s 64.8%
A4s 64.4%
A3s 64.2%
A2s 63.9%
KQs 61.3%
KJs 60.2%
KTs 59.3%
K9s 58.9%
K8s 58.4%
K6s 57.8%
K5s 57.4%
K4s 57.3%
K3s 57.0%
K2s 56.5%
QJs 53.4%
QTs 52.4%
Q9s 52.0%
Q8s 51.4%
Q6s 50.7%
Q5s 50.5%
Q4s 50.3%
Q3s 49.9%
Q2s 49.5%
JTs 46.7%
J9s 46.2%
J8s 45.9%
J6s 44.6%
J5s 44.4%
J4s 43.9%
J3s 43.7%
J2s 43.4%
T9s 41.5%
T8s 41.2%
T6s 40.0%
T5s 39.2%
T4s 38.6%
T3s 38.6%
T2s 38.1%
98s 38.0%
96s 36.6%
95s 35.8%
94s 34.7%
86s 34.4%
93s 34.3%
92s 34.1%
85s 33.3%
84s 32.5%
65s 32.1%
83s 31.4%
64s 31.1%
82s 31.0%
63s 30.0%
54s 29.9%
62s 28.8%
53s 28.8%
43s 28.3%
52s 27.6%
42s 27.2%
32s 26.9%

Offsuit

HandFlopsEquity
A7o quads 100.0%
K7o quads 100.0%
Q7o quads 100.0%
J7o quads 100.0%
T7o quads 100.0%
97o quads 100.0%
87o quads 100.0%
76o quads 100.0%
75o quads 100.0%
74o quads 100.0%
73o quads 100.0%
72o quads 100.0%
AKo 69.8%
AQo 68.4%
AJo 67.4%
ATo 66.5%
A9o 65.9%
A8o 65.6%
A6o 64.8%
A5o 64.6%
A4o 64.0%
A3o 63.9%
A2o 63.5%
KQo 60.8%
KJo 59.7%
KTo 58.8%
K9o 58.1%
K8o 57.9%
K6o 57.4%
K5o 56.9%
K4o 56.4%
K3o 56.2%
K2o 55.9%
QJo 52.6%
QTo 51.6%
Q9o 51.1%
Q8o 50.5%
Q6o 50.1%
Q5o 49.7%
Q4o 49.1%
Q3o 48.9%
Q2o 48.8%
JTo 45.7%
J9o 45.2%
J8o 44.6%
J6o 43.5%
J5o 43.1%
J4o 42.9%
J3o 42.6%
J2o 42.2%
T9o 40.3%
T8o 39.9%
T6o 38.7%
T5o 37.7%
T4o 37.5%
T3o 37.1%
T2o 36.7%
98o 36.4%
96o 35.0%
95o 34.2%
94o 33.2%
86o 32.8%
93o 32.8%
92o 32.6%
85o 31.8%
84o 30.8%
65o 30.5%
83o 29.6%
64o 29.3%
82o 29.3%
63o 28.4%
54o 28.2%
53o 27.2%
62o 27.1%
43o 26.6%
52o 25.8%
42o 25.5%
32o 25.2%

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