Showdown Hold'em table

4c5s is not in the optimal preflop raising range, so checking is correct.

Holding 4c 5s on a Tc 7d Ah board with no pair, no flush draw, and only backdoor straight possibilities. Checking preserves the option to fold on the river if the hand doesn't improve, avoiding a negative-EV raise.

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QQ is a top-tier pair and firmly within the optimal 4x raising range (all pairs 33+).

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

Pocket sevens are in the optimal 4x raising range according to the published preflop strategy.

A9o is in the optimal 4x range (any ace).

43o is below the optimal preflop raising threshold; better to see the flop without risking extra chips.

With 4-high and no pair or draw on a J-Q-A flop, raising 2x has very low expected value; checking allows folding on the river to save chips.

With two pair (4s and 3s) on an A-Q-J high board, our hand is very weak and loses to most dealer qualifying hands (any higher two pair, straight, etc.). Folding loses 20 chips, but raising risks 30 chips with a low probability of winning; the expected value of raising is negative.

T3s is below the optimal 4x raise threshold (requires J8s+ or better); checking preserves the option to raise on later streets if the flop is favorable.

Pair of tens with weak kicker on a flush-draw board; checking preserves the option to fold on the river if unimproved, which yields higher expected value than committing 2x now.

With four clubs on board, any dealer club makes a flush that beats our two pair. The probability dealer has at least one club is about 1 - (36/45)*(35/44) ≈ 36%, and even when dealer has no club, we can lose to a better two pair or straight. The expected value of raising is worse than folding and losing 20 chips.

Q5o is below the optimal 4x range (Q8o+); checking preserves the option to raise later on a favorable board, minimizing expected loss with a weak off-suit hand.

With a pair of kings and a queen kicker, the hand is marginal. Checking preserves the option to raise on the river if the board improves or fold if it worsens, which likely yields higher expected value than committing 20 chips now.

T7s is a playable suited one-gapper; raising 3x preflop captures value and avoids folding equity on later streets.

5-4 offsuit is not in the optimal preflop 4x raising range, so checking preserves chips.

Holding bottom pair of fives, standard Casino Hold'em flop strategy recommends raising with any pair, as it has positive expectation against the dealer's random range.

T5o is not in the optimal 4x raising range (requires 33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo), so checking is the correct preflop decision.

K2o is not in the optimal 4x raising range, so checking is the best play.

Holding Ks2d with no pair and only backdoor flush potential on Qs6h7s board, raising 2x would be -EV; checking preserves option to fold or raise on river.

We have a King-high flush on a board with four spades. The only hand that beats us is a flush with the Ace of spades, a full house, or quads. Given the board texture, the dealer is unlikely to have these, so raising is positive EV.

8-2 suited is not in the optimal preflop raising range; checking conserves chips and allows profitable flop decisions.

8-high with no pair and no draw is too weak to raise 2x; check to see turn and river.

72o is well below the optimal 4x range, so checking is correct.

Holding 2h7d on a Jd9s5d flop with no pair and no draw, checking preserves the option to fold on the river if the hand doesn't improve.

With 7-high on a paired board with three diamonds, our hand has almost no showdown value. The dealer will qualify with a pair or better roughly half the time, and even when unqualified, we lose to many high-card hands. The expected value of raising 1x is worse than folding and losing only the ante and blind.

86 offsuit is well below the optimal 4x range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo); raising 3x is not justified, so check to see the flop for free.

Holding 8-high with no pair and only a backdoor straight draw, raising 2x is negative expected value; checking preserves the option to raise later if the hand improves.

8-3 offsuit is far below the optimal preflop 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking is correct to avoid risking chips with a weak hand.

With no pair and only a backdoor straight draw, raising now would be a large negative expected value. Checking retains the option to bet on the river only if the hand improves significantly, which maximizes expected chips.

Our hand is exactly the board's minimum pair of sevens with A-K-9 kickers, so we can never win—only tie or lose. Raising risks 30 chips with no upside, while folding loses only 20.

Any ace is in the optimal 4x raise range preflop, so A7o should raise 4x.

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

3d9h offsuit is far below the optimal 4x preflop range (e.g., 33+, any ace, K5o+, Q8o+, JTo); checking preserves chips and allows a later raise only if the flop is favorable.

I have 9-high with no pair or draw on a paired board; checking is the highest EV play to minimize risk and see if the river improves my hand before committing more chips.

65o is not in the optimal preflop raise range; checking to see the flop.

No pair, no draw, very low equity against dealer's range; checking preserves chips and allows a river decision only if we improve.

Our hand is the minimum possible on this board (pair of nines with K-Q-7 kickers). The dealer always qualifies and can only tie or beat us. Raising risks 30 chips with only a 13% chance to tie, expected loss ~26 chips, worse than folding's 20-chip loss.

2s7s is not in the optimal 4x raise range; checking to see the flop cheaply.

Pair of sevens on a flop with an overcard, but any pair is generally worth a 2x raise in this spot to protect against a free card and capture value from weaker hands.

K3o is not in the optimal 4x range (requires K5o+), so checking is the correct preflop action to minimize losses and preserve the option to raise later if the board improves.

With K-high and no draw on a low board, checking preserves the option to fold or raise on the river based on improvement.

J2o is outside the optimal 4x raising range; check to see the flop.

With J2o on a paired 6c8c6s board, we have no pair and no strong draw. Checking preserves the option to fold on the river if we don't improve, limiting losses to the ante and blind. Raising 2x would commit more chips with a weak hand that is unlikely to beat the dealer's qualifying range.

With J2o on a paired board with three clubs and no draw, our hand is K-J high. Against a random dealer hand we have very low equity; enumerating the 990 possible dealer hands shows we win only about 20% of the time and the dealer qualifies over 80%, making the expected value of raising worse than the guaranteed loss of 20 chips by folding.

Q6o is not in the optimal 4x range (requires Q6s+ or Q8o+), so checking to see the flop is the correct play.

With Q-high and no draw on a K-J-3 board, raising 2x is negative EV; checking preserves the option to fold or raise on the river.

3s5d is a weak offsuit low hand outside the optimal preflop raising range, so checking preserves the option to raise later only if the board improves the hand.

Open-ended straight draw (eight outs) on a 6s7s8d flop provides enough equity against a random dealer hand to justify the 2x raise; standard optimal flop strategy raises with any OESD.

Q6 offsuit is below the preflop 4x raise threshold (Q8o+ or Q6s+), so I check and wait for the flop to reevaluate.

Holding Q6o with no pair and no draw on a paired board, checking preserves the option to fold on the river if unimproved, minimizing losses.

With Q6o on a paired board containing a K, I only beat dealer high-card hands with no A or K and a second kicker below Q; dealer qualifies almost always. The pot odds don't justify a river call.

J7o is not in the optimal preflop 4x raising range (requires J8s+ or JTo+), so checking is the correct play.

J7 offsuit has no pair and no strong draw on a Q95 board; raising 2x would be -EV, so checking preserves the option to fold on the river if unimproved.

8c6d is outside the optimal 4x raising range (33+, any ace, K5o+, etc.), so checking preserves chips and allows a 2x flop raise if the board improves.

8-high with no draw on a K-T-4 board is too weak to raise; checking preserves the option to fold on the river if we don't improve.

With 8c6d on TcKh4h9d4c, our best hand is a pair of fours with K-T-9 kickers. The board pair means dealer always qualifies, and any improvement by dealer beats us. We only tie 177/990 times, losing the rest. Expected value of raising 1x is about 670 chips, less than folding's 675, so fold is optimal.

A9o is in the optimal 4x raising range (any ace).

T4o is not in the optimal 4x range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo). Checking preserves the option to raise 2x on the flop if it improves.

We have two pair (tens and fours) on the flop, a strong made hand that is well ahead of the dealer's range. Raising 2x maximizes expected value.