Showdown Hold'em table

54 offsuit is outside the published optimal 4x range (no pair, no ace, and too weak to raise 3x), so checking preserves the option to raise later if the board improves.

Board pair means I am currently behind essentially every dealer holding; only a straight or two pair saves me. Checking keeps the option to fold a miss on the river and raise 1x only if I improve.

J4 offsuit is well below the published preflop 4x range (J8s+ or JTo), so checking preserves the option to raise later with more information.

J4 offsuit on a 7-3-2 rainbow flop has no pair, no draw, and little equity, so checking keeps the river fold option instead of putting 2x more at risk.

6-4 offsuit is well below the published 4x range and has poor high-card and straight potential, so checking preserves the option to raise later only if the board improves.

Flopped trip sixes is well ahead of the dealer’s two random cards, so the 2x raise has strong positive EV versus checking.

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

43o is far below the published preflop 4x range (33+, Ax, K5o+, Q8o+, JTo), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

A5 suited is in the published optimal 4x range (any ace), so I raise the maximum preflop.

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

J2o is well below the published preflop 4x range (JTo+ or J8s+), so checking preserves the option to raise later with a better board.

Jack-high with no pair and no flush or straight draw on A-6-4 is too weak to put a 2x play bet in. Check and reassess on the river.

Q3 offsuit is outside the published optimal 4x range (Q8o+), so checking preserves the option to raise 2x on the flop or 1x on the river if the board improves.

Q3 offsuit has no pair and no draw on a rainbow 8-9-4 flop, so a 2x raise is -EV. Check and keep the option to fold on the river if the hand does not improve.

T7 offsuit is below 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 a better board.

Bottom pair with a ten kicker and no draw is too weak to lock in a 2x flop raise; checking keeps the river option to raise if I improve or fold if I don't.

Q7 offsuit is below the published optimal 4x range (Q8o+ or Q6s+), so checking preserves the option to raise later with more information.

K7o is in the published optimal 4x range (K5o+), so I raise the maximum preflop.

A3s is in the published optimal 4x range (any ace), so I raise the maximum preflop.

J4 offsuit is well below the published preflop 4x range (J8s+ or JTo), so checking preserves the option to raise later with a better board.

Jack-four offsuit has no pair and no draw on a paired 3-3-9 board, so a 2x raise is negative EV. Check to see the river and only continue if the hand improves.

65s is below the published 4x range (J8s+), so I check and keep the option to raise 2x if the flop connects.

Four hearts give a strong flush draw with enough equity to raise 2x now rather than check and decide on the river.

53 suited is below the published optimal preflop 4x range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise later with more information.

53s has no pair and only a backdoor flush on K72, so a 2x raise is -EV. Check keeps the river option to raise if I improve or fold if I miss.

Board kings mean the dealer always qualifies, and 5-3 only makes KK-J-7-5, which loses to 957 of 990 dealer holdings. Raising 1x is about -29 EV versus -20 for folding.

Pocket fives are in the published optimal 4x range (33+), so I raise the maximum preflop.

Js6s is below the published 4x range (J8s+), and a 3x raise is dominated by either 4x or a check, so I check and keep the option to raise later.

Js6s on 3sAcQh is ace-high with only a backdoor flush and no pair. Checking preserves the river fold option; a 2x raise has no made hand or real draw to justify it.

Ace-queen-jack high beats most non-qualifying dealer holdings and ties some jack-high hands, so a 1x raise is about 1.5 chips better than folding the ante and blind.

T7s is below the published preflop 4x range (J8s+), so checking preserves the option to raise later with a made hand or strong draw.

Two pair (tens and sevens) is a strong made hand on the flop, so I raise 2x to get more money in while ahead rather than check down to a 1x river decision.

JTo is in the published optimal preflop 4x range, so I raise the maximum rather than check.

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

JTs is in the published optimal 4x range (J8s+), so raising the maximum preflop is the correct play.

Q5 offsuit is below the published 4x range (Q8o+ or Q6s+), so checking preserves the option to raise later with more information.

Queen-high with no pair and no draw on 9-3-8 is too weak to raise 2x; checking keeps the river fold option if I miss.

AKo is in the published optimal 4x range (any ace, and K5o+), so I raise the maximum preflop.

T2o is outside the published optimal 4x range (no pair, no ace, and too weak offsuit), so checking preserves the option to raise later only if the board improves.

Ten-high with only a backdoor diamond draw has too little equity to commit a 2x raise; checking preserves the option to raise or fold on the river.

Pocket jacks are in the published optimal 4x range (33+), so I raise the maximum preflop rather than check.

56s is below the published optimal 4x range (Q6s+/J8s+), so checking preserves the option to raise 2x on a favorable flop or fold cheaply on the river.

87 offsuit is below the published 4x range (no pair, no ace, and not K/Q/J strength), so I check and keep the option to raise later if the board improves.

9-4 offsuit is well below the published optimal 4x range (no pair, no ace, and neither suited nor high enough), so checking preserves the option to raise later if the board improves.

94o on Q87 rainbow has no pair, no flush draw, and no one-card straight draw, so raising 2x has negative EV. Check to keep the river fold option.

9-2 offsuit is far below the published preflop 4x range (33+, any ace, K5o+/K2s+, Q8o+/Q6s+, JTo/J8s+), so checking preserves the option to raise later or fold the river.

No made hand beyond the board pair of fours, and only a slim backdoor club draw, so checking preserves the option to raise or fold on the river.