Showdown Hold'em table

J6 offsuit is outside the published 4x range (J8s+ or JTo), so checking preserves the option to raise later with more information.

Jc6s misses 3d9s5s with only a backdoor spade draw, so a 2x flop raise is -EV. Check and reassess on the river.

Board pair of nines means the dealer always qualifies, and Jc-6s only makes nines with a jack kicker. That wins about 156 of 990 holdings and loses about 825, so a 1x raise is worse than folding the ante and blind.

Ace-King suited is in the published optimal 4x range (any ace, K2s+), so I raise the maximum preflop.

J4 suited is below the published 4x range (J8s+), so checking preflop is the correct default and preserves the option to raise on later streets.

J4 has only a gutshot to a jack-high straight and a backdoor flush on 7-8-9. Checking preserves a river fold when I miss and a 1x raise only if I improve.

Board pair means the dealer always qualifies, and Jc plays as a kicker over the bare Q-9-8. Exact enumeration of the 990 holdings shows raising 1x loses less than folding.

A5o is any ace, which is in the published optimal 4x preflop range.

67 offsuit is outside the published 4x range and has little preflop equity, so I check and wait for a better flop or river decision.

Pair of sixes with a weak kicker and no strong draw is not worth a 2x flop raise against a random dealer hand; check and reassess on the river.

Pair of sixes still has positive equity versus a fold: exact river enumeration loses to 528 of 990 holdings, ties 6, and wins 456, for about -9.2 chips versus -20 for folding.

J2 offsuit is well below the published preflop 4x range (J8s+ or JTo), so checking preserves the option to raise later if the board improves.

Jack-high with no pair and no meaningful draw on T94 rainbow is too weak to raise 2x; check and reassess on the river.

Ace-high with a jack kicker loses to every qualifying dealer hand and to most unpaired king or queen holdings, so a 1x raise is about one chip worse than folding.

7-3 offsuit is far below the published 4x raising range, so checking preserves the option to raise later only if the board improves.

Pair of sevens with a weak kicker on a king-high board is too marginal to commit a 2x raise; checking preserves the option to fold on the river if we do not improve.

Pair of sevens beats a large share of dealer holdings, including every non-qualifying hand. Calling is far less costly in expectation than folding the ante and blind.

67s is outside the published optimal 4x range (no pair, no ace, below K/Q/J thresholds), so check and reassess on later streets.

Pair of sevens on a king-high board with no flush draw is too weak to commit a 2x raise; checking keeps the river fold-or-raise option.

Pair of sevens wins about 445 of 990 dealer holdings and ties 6, so the 1x raise loses less than folding the ante and blind.

Ad5o is in the published optimal 4x range (any ace), so I raise the maximum preflop.

K7 offsuit is in the published optimal 4x range (K5o+), so I raise the maximum preflop.

65o is outside the published optimal 4x range (no pair, no ace, and not a qualifying king/queen/jack hand), so checking preserves the option to raise later with more information.

Open-ended straight draw (4-5-6-7) is a standard +EV flop raise versus the house; the 2x play bet is justified by straight equity plus pair outs and the ante/blind already posted.

J8 offsuit is outside the published 4x range (needs J8s+ or JTo), so checking preserves the option to raise later with a better board.

Jack-high with no pair and no draw on Kd-3d-2c is too weak to raise 2x; checking keeps the option to fold or raise 1x on the river.

Ace-king high loses to every qualifying dealer hand, and the non-qualifying runouts are not frequent enough to justify risking the extra play bet. Folding loses only the ante and blind, which is better than raising.

K9 suited is in the published optimal 4x range (K2s+), so I raise the maximum preflop.

87s is below the published optimal 4x range (J8s+), so checking preserves the option to raise later with more information.

8d7d on Tc Jc 2s is only a gutshot with no pair or flush draw, so a 2x raise is -EV. Check and reassess on the river.

Ace-high with 8-7 kickers loses to 861 of 990 dealer holdings, and the 1x raise is worth about -22 chips versus -20 for folding.

Ace-4 offsuit is in the published optimal 4x range (any ace), so I raise the maximum preflop.

J9 offsuit is below the published preflop 4x range (JTo+ for offsuit jacks), so checking is the correct default.

J9 offsuit misses 3-5-7 with no pair, flush draw, or straight draw, so a 2x raise is not justified. Check and reassess on the river.

Jack-high loses to any dealer pair and to most higher high-card hands, so the 1x raise is worse in expectation than folding the ante and blind.

36o is well below the published preflop 4x range (no pair, no ace, and neither card is high enough), so checking preserves the option to raise later only if the board improves.

Pair of threes with no flush or straight draw is too weak to raise 2x; check and reassess on the river.

I have trip threes with a 9-6 kicker, and the board pair means the dealer always qualifies. Only about 74 of 990 holdings beat me and 3 tie, so a 1x raise is worth about +16 chips versus -20 for folding.

4-9 offsuit is well below the published preflop 4x range (no pair, no ace, and neither card is high enough). Checking keeps the option to raise 2x on a favorable flop or fold on the river.

No pair, no draw, and only 9-high against a jack-high board, so a 2x raise has negative equity. Check and reassess on the river.

Board pair means the dealer always qualifies, and 4d9c is only threes with a nine kicker. Only 72 of 990 holdings win and 9 tie, so a 1x raise is about -26 versus -20 for folding.

J6 offsuit is well below the published 4x range (JTo+), so checking preserves the option to raise later if the board improves.

Jack-high with no pair, no flush draw, and no straight draw on 5-9-3. Raising 2x is -EV; check and reassess on the river.

Board is two pair fives and threes, so I hold that with a jack kicker. Exact enumeration shows a 1x raise loses about 16.5 chips versus 20 for a fold, so raising is the better call.

Pocket aces are the strongest starting hand and are in the published optimal 4x range, so I raise the maximum.

T8s is below the published 4x range (J8s+), and a 3x raise is worse than 4x with a positive-EV hand, so check and reassess on later streets.

Pair of eights plus a four-flush has enough equity and improvement chances to raise 2x on the flop.

3-4 offsuit is well below the published preflop 4x range (no pair, no ace, and neither king, queen, nor jack). Checking preserves the option to raise 2x on a favorable flop or fold on the river.

34 offsuit on a paired queen flop has almost no equity and few ways to improve past the dealer, so checking preserves the option to fold on the river.

Board pair of queens with A-J-7 means my 3-4 never win and only tie if the dealer has two unpaired cards six or lower (129/990). Raising is about -6 chips versus folding the ante and blind.

KJo is in the published optimal preflop 4x range (K5o+), so raise the maximum.

AQo is in the published optimal 4x range (any ace), so I raise the maximum preflop.

JTo is in the published optimal preflop 4x range (J8s+ or JTo), so I raise the maximum.

KQo is in the published optimal 4x range (K5o+), so raising the maximum preflop is the correct play.

T6 offsuit is outside the published 4x range (no pair, ace, or qualifying broadway), so checking preserves the option to raise later with a made hand.

Ten-high with no pair and no draw on an ace-queen board has too little equity to put in a 2x raise; check and reassess on the river.

My hand is exactly the board pair of sevens with A-K-Q kickers, so I can only tie or lose. About half of dealer holdings also play the board and tie, which returns the ante and blind; that is better than folding for a sure loss of both.

4-5 offsuit is well below the published optimal 4x range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise later with a better board.

4c5s on Ac7c8s is only a gutshot with no pair or flush draw, so raising 2x is -EV. Check to keep the river option.

Board pair of sevens means the dealer always qualifies and almost always has ace-eight kickers or better; only 3-4 specifically loses to my five kicker, so a 1x raise is worse than folding.

Any ace is in the published optimal 4x preflop range, so A4o raises the maximum.

J5s is below the published optimal 4x range (J8s+), and a 3x raise is dominated by 4x, so checking is correct.

Jh5h on Q72 rainbow has no pair and no draw, so a 2x raise is -EV; check and reassess on the river.

Board is queens and sevens, so I have QQ77J and the dealer always qualifies. Against the 990 holdings I win 483, tie 90 and lose 417; the 1x raise is about -2.9 chips versus -20 for a fold.