Showdown Hold'em table

K2 offsuit is below the published 4x range (K5o+), so checking preserves the option to raise later with more information.

Bottom pair of twos with only a backdoor club draw is too weak to commit a 2x raise; checking keeps the river option to raise if I improve or fold if I do not.

A6o is in the published optimal 4x range (any ace), so I raise the maximum preflop.

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

9-high with no pair, flush draw, or straight draw on T-3-5 has too little equity to commit a 2x play bet; check and reassess on the river.

J8 offsuit is outside the published 4x range (J8s+ or JTo), so checking preflop is the higher-EV line.

T2s is outside the published 4x range and too weak to justify a 3x raise, so I check and keep the later decision.

Ten-high with no pair and no draw has little equity, so checking preserves the option to fold on the river if the board does not improve.

Board pair means the dealer always qualifies, and my jack-ten kicker only wins 112 of 990 holdings and ties 33. Raising loses about 23.3 chips in expectation versus 20 by folding.

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

K9o is inside the published optimal 4x range (K5o+), so I raise the maximum preflop rather than check.

T4 offsuit is well below the published preflop raise range, so checking preserves the option to raise 2x only if the flop improves the hand.

Pair of tens with a four kicker on an ace-high board is too weak to raise 2x; checking keeps the river option to fold or raise 1x if the hand improves.

J7s is below the published 4x range (J8s+), so checking preflop is the higher-EV line and preserves the flop decision.

Jack-high with no pair and no draw on an ace-high flop is too weak to raise 2x. Checking preserves the option to raise 1x or fold once the river is known.

98o is outside the published 4x range (no pair, no ace, and below the K/Q/J thresholds), so I check and keep the option to raise 2x on the flop or fold on the river.

9-8 offsuit has no pair, no flush draw, and no one-card straight draw on A-T-3. Raising 2x commits extra chips with little equity, so check and reassess on the river.

23 offsuit is well below the published 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise later if the board improves.

Pair of twos still wins whenever the dealer fails to qualify, and that happens often enough that a 1x raise loses less than folding the ante and blind.

T8o is outside the published 4x range and too weak to raise 3x for value, so I check and keep the option to raise or fold later.

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

T9 offsuit is below the published optimal 4x range (JTo+), so checking preflop is the correct play.

No pair and no real draw on K-6-4; 9-T high is too weak to put in a 2x raise, so check and keep the river decision.

Q6 offsuit is below the published 4x range (Q8o+ or Q6s+), and a 3x raise is a worse price on the same marginal hand. Check to see the flop before committing more.

Q6 offsuit has no pair and no draw on K95 rainbow, so equity is too thin to commit a 2x raise. Checking keeps the river option to fold if I miss.

King-queen high beats 244 of 990 dealer holdings and ties 9, all versus non-qualifiers. Raising returns about -18.5 chips versus -20 for folding, so the 1x play bet is the higher-EV line.

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

J8 offsuit is outside the published 4x range (J8s+ or JTo), and a 3x raise is not the value size for this hand, so check and reassess on the flop.

Jack-high with no pair and no flush or straight draw on a three-club board is too weak to put two more antes in. Check and reassess on the river.

My best hand is ace-high (A-Q-J-7-5), so I only profit when the dealer also fails to qualify and has a worse kicker. That is too rare to offset the extra ante lost whenever the dealer pairs or better, so a sure -20 from folding beats raising.

K4s is in the published optimal preflop 4x range (K2s+), so I raise the maximum.

J6 offsuit is outside the published optimal 4x range (J8s+ or JTo), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

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

6-2 offsuit is far below the published preflop 4x range (no pair, no ace, and neither suited nor high enough), so checking preserves the option to raise later only if the board improves.

62 offsuit completely missed this flop with no pair and no draw, so a 2x raise has negative expectation. Check and reassess on the river under optimal play.

Ace-high AKQJ6 loses to 917 of 990 dealer holdings and only wins 40, so a 1x raise is about 5 chips worse than folding.

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

QTo is in the published optimal 4x range (Q8o+), so I raise the maximum preflop rather than check.

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

43 offsuit is well below the published preflop 4x range (no pair, no ace, and not a suited or high connector), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

43 offsuit has no pair, flush draw, or straight draw on Q-K-5, so a 2x raise has poor equity against the dealer. Check and reassess on the river.

K2o is below the published 4x range (K5o+ or K2s+), so checking is the correct preflop action.

King-high with only a gutshot to Broadway has too little equity to commit a 2x play bet; check and decide on the river.

9s2s is well below the published optimal 4x range (J8s+ and stronger), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

68o is well 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.

54o is well below the published optimal 4x range (no pair, no ace, no suited connector), so checking preserves the option to raise 2x on a favorable flop or fold the river.

5-4 offsuit has no pair, no flush draw, and no straight draw on T-7-7. Checking preserves the option to fold on the river unless the board improves the hand enough to call.

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