Showdown Hold'em table

7-4 offsuit is far below the published preflop 4x range (33+, any ace, suited kings/queens/jacks in range), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

74 offsuit has no pair and no draw on 6-9-3; raising 2x risks more chips on a hand that is usually behind, so check and decide at the river.

King-high 7-4 loses to almost every dealer holding; the rare chop or win does not cover the extra play-bet loss when the dealer qualifies, so folding the locked ante and blind is better.

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

76o 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.

Pair of sevens on a low, unpaired board is a made hand worth a flop raise for value; dealer often misses or fails to outdraw it.

T5s is below the published preflop 4x range (J8s+), so checking preserves the option to raise 2x on a favorable flop.

5d Td on 7c Ah 4h is ace-high with no pair and no flush or straight draw. Checking keeps the option to fold on the river if I miss, instead of committing a 2x play bet with air.

K9o is in the published optimal 4x range (K5o+), so raise the maximum preflop.

Q9 suited is in the published optimal 4x range (Q6s+), so raising the maximum preflop is the correct play.

Q7 offsuit is below the published optimal 4x range (Q8o+ or Q6s+), so checking preflop is the correct play.

T3s is suited but below the published optimal 4x range (J8s+), so checking preflop preserves the option to raise 2x on a favorable flop.

Q4 offsuit is outside the published optimal 4x range (Q8o+ or Q6s+), so checking preserves the option to raise later with more information.

Queen-high with only a gutshot to a five is too weak to raise 2x; checking keeps the option to raise 1x if a five or strong pair arrives and fold otherwise.

T3o is well below the published 4x range (no pair, no ace, and not a qualifying king/queen/jack hand), so checking preserves the option to raise 2x on a favorable flop or fold the river.

Board pair only with a ten kicker and no real draw; checking keeps the river fold option instead of committing 2x with a weak hand.

A2s is in the published optimal 4x range (any ace), so I raise the maximum preflop.

9-4 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 2x on the flop or 1x on the river.

A2o is in the published optimal 4x range (any ace), so I raise the maximum preflop.

94s is outside the published optimal 4x range (no pair, no ace, and below the king/queen/jack thresholds), so checking preserves the option to raise 2x on a favorable flop.

No pair or strong draw on the flop with 9-4 of clubs, so checking preserves the option to fold on the river if the hand does not improve.

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

J5 offsuit is below the published preflop 4x range (JTo+ or J8s+), so checking preserves the option to raise later with a better board.

J5o has no pair and only backdoor draws on Q97, so a 2x raise is -EV; check and reassess on the river under optimal play.

Q2 offsuit is outside the published optimal preflop 4x range (Q8o+ or Q6s+), so checking preserves the option to raise later with more information.

Queen-high flush draw with no pair has no fold equity against the dealer, and missing often makes a 2x raise worse than checking to keep the river fold-or-raise option.

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

Q8s is in the published optimal preflop 4x range (Q6s+), so I raise the maximum.

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

3-7 offsuit is far below the published preflop raising range, so checking preserves the option to raise 2x on the flop or fold on the river.

3-7 offsuit on 4-Q-5 has no pair and only a gutshot, so raising 2x commits extra chips with poor equity. Checking keeps the river option to fold if I miss.

The board gives both of us two pair, fives and fours with a queen kicker, so the dealer can only tie or win. The dealer fails to improve in about 41% of holdings, making a 1x raise worth about -17.8 chips versus -20 for folding.

J6s is below the published optimal 4x range (J8s+), so checking preflop is the correct play.

Jack-six has no pair and only backdoor straight and flush possibilities on this king-high flop, so a 2x raise is not justified. Check and reassess on the river.

Jacks and sevens is ahead of most of the 990 dealer holdings, and raising 1x has clearly higher EV than folding the ante and blind.

K6o is in the published optimal 4x range (K5o+), so raising four times the ante is the correct preflop play.

Any ace is in the published optimal 4x range, so I raise the maximum preflop with Ah4s.

Q3 offsuit is below the published 4x range (Q8o+ or Q6s+), so checking preflop preserves the option to raise 2x on a favorable flop or fold on the river.

Queen-high with no pair or draw on K-6-2 is too weak to raise 2x; check and reassess on the river under optimal play.

9-3 offsuit 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 if the board improves.

3-9 offsuit on J-8-5 has no pair, no flush draw, and almost no straight equity, so a 2x raise is -EV. Check and reassess on the river.

River high-card J-9 loses to 957 of 990 dealer holdings, and the 1x play bet is -EV versus folding the ante and blind.

3-6 offsuit is far below the published 4x range (no pair, no ace, and neither suited nor connected enough). Checking keeps the ante and blind in play and preserves the option to raise 2x only if the flop improves the hand.

K2o is below the published 4x range (K5o+ or K2s+), so checking preflop preserves the option to raise 2x on a favorable flop or fold the river.

T9 offsuit is below the published optimal 4x range (JTo is the cutoff for offsuit broadways), so checking preserves the option to raise on later streets.