Showdown Hold'em table

86 offsuit is well below the published preflop 4x range, so checking preserves the option to raise on later streets with more information.

Bottom pair of sixes with only a gutshot on a connected board is too thin to raise 2x; checking keeps the option to fold the river if I do not improve.

Board pair means the dealer always qualifies. Two pair tens and sixes wins 620 of 990 holdings, ties 39, and loses 331, so a 1x raise is about +2.5 chips versus -20 for folding.

K3o is below the published 4x range (K5o+), so checking preserves the option to raise later with more information.

Flop gives me kings and eights, a made two pair that is well ahead of most dealer holdings and runouts, so the 2x play bet is the higher-EV line versus checking.

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

T4o is well below the published preflop 4x range (no pair, no ace, and too weak to raise 3x), so checking preserves the option to raise later if the board improves.

Th4s has no pair, draw, or board connection on 3h Qc 6h, so a 2x raise is -EV. Check and reassess on the river.

Pair of fours beats 426 of 990 dealer holdings and ties 6. Raise EV is about -11.5 chips versus -20 for folding, so the 1x play bet is clearly +EV.

Ad3s is any ace, which is in the published optimal preflop 4x range, so I raise the maximum.

85o 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.

No pair, no draw, and no equity against a random dealer hand; check and reassess on the river.

Pair of eights beats about 404 of 990 dealer holdings and ties 38. Raising 1x is about -11.4 chips versus -20 for folding, so the call is clearly +EV.

T2s 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 more information.

T2 has no pair and no real draw on A-K-J rainbow; raising 2x risks more chips on a hand that almost never wins. Check and reassess on the river.

Board aces mean the dealer always qualifies. We have aces and tens; 465 of 990 holdings win (+20), 62 tie, and 463 lose (-30), so raising is about -4.6 chips versus -20 for a fold.

T9 offsuit is outside the optimal 4x raising range (no pair, no ace, and not a qualifying king/queen/jack hand), so checking preserves the option to raise on later streets.

Top pair with a weak ten kicker and no flush or straight draw is not strong enough to commit a 2x raise; checking preserves the river option to raise 1x or fold.

Pair of nines wins about 75% of the 990 dealer holdings and the river call is clearly +EV versus folding.

82s is well below the published 4x range (no pair, no ace, not a strong king/queen/jack), so checking preserves the option to raise 2x only if the flop connects.

No pair, no draw, and no board interaction with 2s8s on Kd4d9h, so checking preserves the option to fold on the river if I miss.

Ace-high 8 kicker loses to 789 of 990 dealer holdings, and the raise EV is about -20.7 versus -20 for folding.

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

74o is well below the published 4x range and has poor equity, so checking preserves the option to raise only if the flop improves the hand.

7-4 offsuit has no pair and no real draw on T-2-5, so a 2x raise is negative EV. Check and reassess on the river.

Board trips with T-7 kickers loses to 917 of 990 dealer holdings and only wins 40, so a 1x raise is about -27 chips versus -20 for folding.

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

AJo is in the published optimal 4x range (any ace). Raising the maximum preflop is the +EV play.

Q4 offsuit is well below the published preflop raise range (Q8o+ or Q6s+), so checking preserves the option to raise later if the board improves.

Pair of queens on this flop is ahead often enough that committing 2x now has higher EV than checking and only raising 1x later.

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

J3 offsuit is well below the published preflop 4x range (JTo+ / J8s+), so checking preserves the option to raise 2x on a favorable flop or fold the river.

Board pair of tens with only a jack kicker is too weak to commit a 2x raise; checking preserves the river decision.

Board is tens and sevens; my jack kicker wins 310 of 990 dealer holdings and ties 78, so a 1x raise is about -12 chips versus -20 for folding.

96s is below the published 4x range (J8s+), so checking preserves the option to raise 2x only if the flop connects.

I flopped a pair of sixes, which is ahead of unpaired dealer hands and strong enough to raise 2x rather than wait for the river.

2-3 offsuit is far below the published preflop 4x range (33+, any ace, suited kings, and the listed queen/jack hands), so checking preserves the option to raise later only if the board improves.

Bottom pair with a straight draw is too thin to commit a 2x raise before the board finishes; checking keeps the river decision.

The board is a wheel (A-2-3-4-5) that both players share, and my 2h3d does not improve it. Only a dealer holding with a 6 (170 of 990) makes a higher straight and wins; every other holding ties and pushes, so raising loses about 5 chips expected versus 20 for folding.

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

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

Queen-high with only a backdoor diamond draw and no pair is too weak to commit a 2x raise; checking preserves the option to fold or raise 1x on the river.

Queen-high T-9-7-5 loses to any qualifying dealer hand and to most unpaired ace/king/queen holdings, so a 1x raise is worse than folding the ante and blind.

J9 offsuit is below the published 4x range (JTo+), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

I have a pair of jacks on the flop, which is strong enough to raise 2x under standard Casino Hold'em strategy.

J7 offsuit is outside the published optimal 4x range (J8s+ or JTo), so checking preserves the option to raise on later streets if the board improves.

Jd7s has no pair and no flush or straight draw on As3s5d, so raising 2x risks more chips with a weak ace-high. Checking keeps the river option to raise 1x only if I improve, otherwise fold.

Ace-high still wins enough non-qualifying dealer holdings that calling loses about 18.9 chips versus 20 for a fold.

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

Middle pair of sevens with a queen kicker on a king-high board is too thin to raise 2x; checking keeps the river option to raise 1x only if the runout improves the hand enough.

Pair of sevens wins about 510 of 990 dealer holdings and ties 6, so a 1x raise is about -7 chips versus -20 for folding.

24 offsuit is far below the published preflop raise range, so I check and keep the option to raise or fold later.

No pair and no meaningful draw with 2-4 on 8-3-J, so checking preserves the option to fold on the river if the hand does not improve.

Board pair of threes with J-8-5 kickers loses to nearly every dealer holding, since any card above a five improves the kickers. Raising is about -30 EV versus -20 for folding.

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

AKo is in the published optimal 4x range (any ace). Raising 4x maximizes EV preflop.

Q3 offsuit is outside the published 4x range (Q8o+), so checking preserves the option to raise later with more information.

I have queens full of eights. Only four dealer holdings beat it (quad eights or kings full) and 44 tie, so a 1x raise is hugely +EV.

J5 offsuit is well below the published 4x range (J8s+ or JTo), so checking preserves the option to raise later with more information.

Top pair of jacks is ahead of most dealer holdings and worth a flop raise rather than checking to the river.

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

2-5 offsuit is far below the published 4x range (no pair, no ace, no suited connector), so checking preserves the option to raise only if the flop improves the hand.

2-5 offsuit on A-6-3 has no pair and only a one-card gutshot, so a 2x raise has no value against a dealer who never folds. Check and reassess on the river under optimal play.

Board pair of threes with A-K-6 is the floor for both hands, and my 2-5 never improve it. I tie only junk holdings and lose to every pair, two pair, or better kicker, so raising is worse than folding the ante and blind.