Showdown Hold'em table

J6o does not meet the 4x raising criteria per published optimal strategy, so check to see the flop.

With J6o on a 9-high board, we have only one overcard and no draw. Our equity against a random dealer hand is below the threshold for a profitable 2x raise; checking preserves the option to fold on the river if we don't improve, minimizing expected loss.

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AKs is a premium hand and falls within the optimal 4x raising range (any ace, K2s+).

J4s is not in the optimal 4x raising range (requires J8s+), and raising 3x would be speculative with a weak suited jack; checking preserves the option to raise later if the flop improves the hand.

J4 suited with a gutshot straight draw and backdoor flush on a 9s7c8d board is too weak to raise 2x; checking preserves the option to fold on the river if we miss, minimizing expected loss.

A5o is in the optimal 4x range (any ace).

6c 7s is not in the optimal 4x raising range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo), so checking is correct.

Weak pair of sixes with no strong draw; checking preserves the option to see the turn and river before committing more chips, and avoids a likely negative-EV raise.

J2o is not in the optimal 4x raising range (requires J8s+ or JTo+), so checking preserves chips and allows a decision on the flop.

J2o has no pair and only backdoor straight possibilities; raising 2x would be -EV.

J2o on A-T-9-6-4 board gives only Ace-high with J kicker, no pair, no draw. Dealer qualifies with pair or better, and even if dealer misses, our high card is weak. Folding loses only the ante and blind, saving the play bet.

7-3 offsuit is far below the optimal preflop raising range, so I check to avoid committing extra chips and preserve the option to raise or fold later.

We have a pair of sevens on the flop. In standard optimal strategy, any pair or better is a raise 2x on the flop after checking preflop. Although our kicker is weak, the expected value of raising is positive compared to checking and facing a river decision.

76s is not in the optimal 4x raising range, so check to see the flop and potentially raise 2x if the flop is favorable.

Bottom pair with backdoor straight potential; standard flop raise.

A5o falls within the published optimal 4x range (any ace, 33+, etc.), so raising 4x maximizes expected value.

K7o is in the optimal 4x raising range (K5o+).

65o is not in the optimal 4x raise range and is too weak to raise 3x; checking preserves chips for better opportunities.

We hold an open-ended straight draw with no pair or overcards. Raising 2x would cost 20 chips with negative expected value, while checking lets us see turn and river for free and decide optimally on the river.

We have a flush (A-Q-7-6-5 hearts). Against a random dealer hand, our flush wins about 85% of the time, and the expected value of raising is positive compared to folding.

J8o is below the optimal 4x raise threshold (requires JTo+), so checking preflop preserves equity.

With J8o on a K-high flop and no draw, checking preserves the option to fold on the river if we don't improve, avoiding a larger loss.

K9s is in the optimal 4x raising range per published strategy.

87 suited is not in the optimal 4x raise range (pairs 33+, any ace, K2s+, etc.), and raising 3x is not warranted for a medium suited connector; checking lets us see the flop before investing more.

With 8d7d on a board of TcJc2sAd6s, our best hand is Ace-high. We beat only dealer hands with no pair and worse kickers, but we lose to any pair, any better Ace-high, and Broadway draws with KQ. The probability of winning is too low to justify risking an additional 10 chips; folding loses only the 20 chips already posted.

Any ace falls in the optimal preflop raise 4x range against the house dealer, maximizing expected value.

J9o is not in the optimal preflop 4x raising range (requires JTo or better). Checking preserves the option to raise later when more information is available.

With J9o on a 3d5h7d board, we have no pair and only backdoor straight draws. The expected value of raising 2x is negative compared to checking and preserving the option to fold on the river if we don't improve, as the optimal river strategy will allow us to minimize losses with weak hands.

Hand is too weak for a preflop raise; check to see flop.

Flopped a pair of threes. Even with a weak kicker, any pair is a value raise on the flop according to optimal strategy, as it yields positive expected value against the dealer's random holding.

94 offsuit is not in the optimal 4x range and is too weak to raise 3x; check to see the flop.

Holding 9-high with no pair and no draw on a J-5-3 board, raising 2x would be -EV. Checking allows us to see the turn and river for free and only invest on the river if we improve.

With 4d 9c on a board of Jh 5c 3d 2c 3s, our hand is a pair of threes with J-9-5 kickers. Enumerating all 990 dealer hands, we win 72, tie 9, and lose 909. EV of raising 1x is -26.09 chips, worse than folding's -20, so fold is optimal.

J6o is well below the optimal 4x range (J8s+/JTo+), so checking preserves the option to raise later if the board improves the hand.

J6o misses the flop completely with no draw; checking avoids putting more chips at risk with a weak hand.

Our hand is exactly the board's two pair (fives and threes) with no improvement. Dealer always has at least that, so we cannot win; we only tie or lose. Raising risks 30 to win 0 when we tie, and lose 30 when dealer improves (84.8% chance). Folding loses 20, which is better.

Pocket aces are a premium hand; optimal strategy dictates a 4x raise preflop.

T8s is below the published optimal 4x range (J8s+), so checking is the highest-EV play, preserving the option to raise later if the board improves.

Pair of eights with backdoor flush draw; equity against random dealer hand is about 60-65%, well above the ~44% needed to make a 2x raise profitable. Raising now captures maximum value.

3d4h is not in the optimal 4x range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo) and too weak to raise 3x; checking preserves chips for later streets.

Our hand is only a pair of queens with Ace kicker, but no cards to improve. Dealer qualifies automatically with board pair, and any dealer hand containing an Ace, Jack, 7, any pair, or any card higher than 7 gives dealer a better hand. The probability of winning is well below 25%, so raising is negative EV.

KJo is in the published optimal 4x preflop range (K5o+), so raising 4x maximizes expected chips.

Ace-Queen offsuit is a premium hand and falls within the optimal preflop 4x raising range (any ace, all pairs 33+, and numerous suited connectors). Raising 4x maximizes expected value.

JTo is in the optimal 4x raising range according to the published strategy.

KQo is in the published optimal 4x raising range (K5o+), so raising 4x maximizes expected value.

T6o is not in the optimal preflop raise range; checking preserves the option to raise on later streets if the board improves our hand.

Holding T6o with no pair or draw on an A-Q-7 flop, checking is better than raising 2x to minimize expected loss.

With Th-6h on a Qh-7c-Ac-7d-Kd board, the player has only a pair of sevens with A-K-Q kickers. Against a random dealer hand, this is a slight underdog (about 48% equity) and raising 1x risks an additional 10 chips to win a small net profit when ahead, while losing the full 30 when behind. Folding limits the loss to the 20-chip ante+blind, which is the better expected value in this marginal spot.

54o is not in the optimal preflop raise range; checking allows me to see the flop and potentially raise later if I hit a strong draw or pair.

With a gutshot straight draw and no pair, the hand is too weak to raise 2x on the flop. Checking preserves the option to fold on the river if we don't improve, minimizing losses.

With only a pair of sevens and A-8-5 kickers, we beat only 12 of 990 dealer hands and tie 20; raising loses about 28.8 chips on average, worse than folding's loss of 20.

Ad4s is any ace, optimal 4x raise per published table.

Jh5h is not in the optimal 4x raising range (J8s+ required), so check to see the flop.

J-high with no draw on this board is far too weak to raise; optimal play is to check and decide on the river.

We have two pair Q and 7 with J kicker. Dealer qualifies and any Ace or King kicker, or full house, beats us. With many unknown high cards left, we are not favored to win the 1x bet.