Showdown Hold'em table

9-3 offsuit is well below the published preflop 4x range (no pair, no ace, and neither king/queen/jack strength), so checking preserves the option to raise later with more information.

T9s is below the published 4x range (J8s+ / JTo), so check and keep the flop 2x option if the board helps.

87o 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.

Pair of sevens beats about 42% of dealer holdings and ties 6%, so a 1x raise loses about 11 chips in expectation versus 20 for a fold.

23 offsuit is far below the published 4x range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

9d3d is suited but well below the published optimal 4x range (no pair, no ace, and not a strong king/queen/jack hand), so checking preserves the option to raise later if the board improves.

9d3d has no pair and no real draw on As-7c-6s, so a 2x raise is not justified. Check and reassess on the river.

Board is aces and sixes; my nine kicker beats most dealer holdings, and dealer always qualifies. Raising wins about 702 of 990 matchups and is clearly +EV versus folding.

5-8 offsuit is well below the published 4x range (no pair, no ace, and neither card is high enough), so checking preserves the option to raise later if the board improves.

Bottom pair of fives with no flush or straight draw is too weak to raise 2x; checking keeps the option to raise 1x or fold on the river.

98o is below the published optimal 4x range (JTo+ offsuit), so checking preserves the option to raise later with a better board.

93 suited is below the published preflop 4x range (no pair, no ace, and weaker than Q6s+/J8s+), so checking preserves the option to raise later with a better board.

9c3c has no pair and no real draw on Qc-8d-As, so a 2x raise is -EV. Check and reassess on the river.

Q4 offsuit is below the published preflop 4x range (Q8o+), so checking preserves the option to raise on later streets if the board improves.

Pair of fours with only a backdoor heart draw is too weak to commit a 2x raise; checking keeps the option to raise 1x or fold once the river is known.

Q9o is in the published optimal 4x range (Q8o+), so I raise the maximum preflop rather than check.

74o is well below the published 4x range (no pair, no ace, and neither king/queen/jack strength), so checking preserves the option to raise later if the board improves.

Pair of sevens with an ace on the board is too weak to raise 2x; checking preserves the option to raise 1x or fold once the river is known.

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

K8 suited is in the published optimal 4x range (K2s+), so I raise the maximum preflop.

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

Board pair of eights with a nine kicker and no draw is too weak to raise 2x; checking preserves the option to fold or raise 1x on the river.

Board is queens and eights with a jack kicker, so my 9-4 can only tie or lose. Ties occur in 423 of 990 dealer holdings (42.7%), so calling loses about 17 chips on average versus 20 for a fold.

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

Pair of deuces still wins against every non-qualifying dealer hand and a few weaker pair-of-twos kickers, so a 1x raise loses less in expectation than folding the ante and blind.

8-3 offsuit is far below the published 4x range, so checking preserves the option to raise 2x only if the flop improves the hand.

83o on A76 has no pair, no flush draw and only thin runner-runner straight chances, so equity is too low to commit a 2x raise; checking preserves the option to fold on the river if I miss.

Ace-high J-8-7-6 loses to about 908 of 990 dealer holdings. Raising 1x is worth about -24 chips versus -20 for folding, so fold.

Ad2d is any ace, which is in the published optimal preflop 4x range, so I raise the maximum.

A8o is in the published optimal 4x range (any ace), so I raise the maximum preflop rather than check.

23s is well below the published optimal 4x range (33+, suited broadways and stronger), so checking preserves the option to raise later if the board improves.

I have a king-high diamond flush and the board pair means the dealer always qualifies. Only about 56 of 990 dealer holdings beat a flush, so a 1x raise is clearly +EV versus folding.

T8o is below the published optimal 4x range (JTo+, Q8o+, etc.), so checking preserves the option to raise later with more information.

97o 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 later if the board improves.

No pair and only a backdoor spade draw against a king-high board; the dealer never folds, so a 2x raise has no bluff value and is -EV. Check to see the river for free and raise only if the hand improves.

54o 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.

T8o is below the published preflop 4x range (JTo+, Q8o+, suited broadways and pairs), so checking preserves the option to raise later with a made hand or strong draw.

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

8-3 offsuit is far below the published preflop raise range, so checking keeps the option to raise later only if the board improves.

8-3 offsuit on 7-2-4 has no pair and no draw, so a 2x raise is -EV. Check and keep the river fold option.

Pocket deuces are below the published 4x range (33+), so I check and keep the option to raise 2x if the flop gives me a set or a strong draw.

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

Q3o is below the published 4x range (Q8o+), so checking preflop is the +EV default and keeps the option to raise or fold later.