Showdown Hold'em table

K2o is below the published 4x range (K5o+ or K2s+), and a 3x raise is not justified with this weak offsuit king. Checking preserves the option to raise later if the board improves.

Pair of twos plus a king-high flush draw is ahead of most non-pairing dealer hands and has solid improvement equity, so committing 2x now is better than checking and only getting 1x when the draw or pair holds up.

K6o is in the published optimal preflop 4x range (K5o+), so I raise the maximum.

Kd2s is offsuit and below the published 4x range (K5o+), but king-x offsuit in this spot is a standard 3x raise rather than a check.

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

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

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

T3 offsuit is well below the published 4x range (no pair, no ace, and not a suited or offsuit broadway combo), so checking preserves the option to raise later if the board improves.

47 offsuit is well below the preflop raising range, so I check and keep the option to raise or fold later.

98o 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.

98 offsuit on A-4-6 with two diamonds has no pair and no real draw, so a 2x raise is not justified. Check and reassess on the river.

6-9 offsuit is outside the published optimal 4x range (pairs 33+, any ace, and the listed king/queen/jack hands), so checking is correct preflop.

6-9 offsuit on A-Q-8 has no pair and no flush or straight draw, so a 2x raise is -EV. Check and reassess on the river.

7-4 offsuit is well below the published preflop 4x range (no pair, no ace, no suited/connected strength), so checking preserves the option to raise later only if the board improves.

T7s is outside the published 4x range (below J8s+), and 3x is not used when 4x is the value raise, so check to see the flop before committing more.

Pair of fives with a ten kicker and only a backdoor club draw is too weak to raise 2x; check and reassess on the river.

8s3s is well below the published 4x range (no pair, no ace, and not a strong king/queen/jack hand), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

8s3s has no pair and no heart draw on a three-heart board, so a 2x raise is -EV. Check and decide on the river.

Jack-high loses to 945 of 990 dealer holdings, and the 1x raise is worth about -25 versus -20 for folding, so the extra play bet is not justified.

T8o is below the published preflop 4x range (JTo+ / suited broadways and pairs), so checking preserves the option to raise 2x on a favorable flop or 1x on the river.

89o is outside the published optimal 4x range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so I check and defer the raise decision to a later street.

Ace-high with only backdoor runner-runner possibilities has too little equity against this coordinated board to justify a 2x raise; checking keeps the river fold option.

Ace-high with a nine kicker beats every non-qualifying dealer holding that lacks a nine and ties those that have one. Exact enumeration of the 990 holdings shows calling loses about 19 chips in expectation versus 20 for a fold.

3c7s is far below the published optimal 4x range (no pair, no ace, no suited/connected strength), so checking preserves the option to raise later only if the board improves.

3c7s completely missed Ks-4h-8d with no pair and no draw, so a 2x raise has no equity justification. Check and reassess on the river.

8-6 offsuit is well below the published 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.

6-8 offsuit has no pair and no draw on 9-2-3, so raising 2x commits extra chips with little equity. Checking keeps the river fold option.

Board queens mean the dealer always qualifies, and my QQ-9-8-6 loses to 873 of 990 holdings. Raising is about -24 chips versus -20 for folding.

Q9o is inside the published optimal 4x range (Q8o+), so I raise the maximum preflop.

A7o is in the published optimal 4x range (any ace), so I raise the maximum preflop rather than check.

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

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

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

J5s is below the published preflop 4x range (J8s+), so checking preserves the option to raise 2x on a favorable flop.

Js5s on 8d4h6d is only a gutshot plus one overcard with no flush draw, so raising 2x is not justified. Checking keeps the river option to raise 1x if I improve or fold if I miss.

J9 suited is in the published optimal 4x range (J8s+), so I raise the maximum preflop.

Q7 offsuit is below the published optimal 4x range (Q8o+ or Q6s+), and 3x is dominated by 4x when raising is correct, so checking is best.

Top pair of queens on the flop is ahead of most dealer holdings and is a standard 2x raise; checking only to raise 1x later gives up value since I will rarely want to fold this hand.

8-3 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.

8-3 offsuit on 5-T-7 rainbow has no pair and no draw, so a 2x raise is -EV. Check and keep the river option to fold if unimproved.

Ad4d is any ace, which is in the published optimal preflop 4x range, so I raise the maximum.

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

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

T8o is outside the published optimal 4x range (no pair, ace, king, queen, or jack-ten), so checking preserves the option to raise later if the board improves.