Showdown Hold'em table

4-5 offsuit is far below the optimal 4x raising range (33+, any ace, etc.), so I check and can decide on the flop with more information.

4-5 offsuit on a Td-9c-As flop has only a gutshot-type draw (needs 6-7-8 combos... actually just a weak backdoor) and no pair, so it is well below the flop raise threshold; checking keeps risk minimal and preserves the option to fold at the river.

The board pair of nines means the dealer always qualifies, and my nines with A-T-5 kickers loses to any dealer pair-up, any card 6 or higher, and any single diamond flush. I win only rarely, so folding a sure 20-chip loss beats risking 30.

4c7c is a weak suited hand outside the optimal 4x range (no ace, no pair, low kickers), so checking preflop keeps risk small and lets me see the flop before deciding on a 2x raise.

I hold a four-card flush draw (4c 7c with 3c 8c on board) with 9 outs, plus some chance to pair up. That should make the 2x flop raise worth its extra risk against a dealer who needs a pair to qualify.

3-5 offsuit is far below the optimal 4x range (33+, any ace, K5o+, etc.), so I check preflop and keep the option to raise on the flop or fold later. Chat is off, so the table message is empty.

3h5c on a 6d7sJd flop has only a gutshot (needs a 4 for a 3-4-5-6-7 straight) and no pair, so raising 2x is clearly negative EV; checking keeps the option to fold on the river.

3h5c with the 4-6-7 on board makes a 7-high straight (3-4-5-6-7), which beats most dealer hands and pays 1:1 on the blind, so the 1x raise has strong positive EV.

Q2 offsuit is outside the published optimal 4x range (Q8o+ or Q6s+), so I check and see the flop for a possible 2x raise.

I hold only queen-high on an A-9-7 board with no pair and no real draw, so a 2x raise on the flop would be negative EV. I'll check and decide between folding and a 1x raise on the river.

The board pairs sevens, so the dealer always qualifies. I estimate I win only about 30% and lose about 65%, with the rest ties. Raising is roughly -1.35 antes in expectation, which beats folding at -2, so I raise.

Pocket sevens fall within the published optimal 4x range (33+), so raising 4x preflop maximizes expected value. Chat is off, so the table message is empty.

8-4 offsuit is well outside the optimal 4x range (33+, any ace, K5o+, Q8o+, etc.), so I check preflop and keep the option to raise on the flop or river.

8h4c on a 2c-3h-Jh flop is just 8-high with a weak draw (a backdoor flush at best and an inside straight draw with the 2-3-4), so a 2x raise has negative expected value. Checking keeps the option to raise or fold on the river.

I have only jack-high with no pair. The dealer qualifies about 60% of the time with a pair, and any A or 6 gives them a straight, so a raise loses more than the 20 chips a fold costs.

2s8s is outside the optimal 4x range (no ace, no K5o+, and 8-high suited is too weak), so checking preflop keeps risk low and lets me see the flop before deciding on a 2x raise.

I hold a four-card flush draw with a gutshot to a straight (any 6), and pairing an 8 or 9 also helps. The dealer needs a pair to qualify, so the 2x raise is worth the extra risk here.

AKs is a premium hand and well inside the optimal 4x preflop range, so the maximum raise has the highest expected value.

Ace-high with any ace is in the published optimal 4x raise range for Casino Hold'em against the house, so the 4x preflop raise maximizes expected value.

4-8 offsuit is well outside the optimal 4x raising range (K5o+, Q8o+, etc.), so I check and see the flop for a cheaper decision, keeping risk low.

I have a pair of fours with an 8 kicker plus a backdoor flush draw and some straight potential. That is enough to raise 2x on the flop, since the dealer needs a pair to qualify.

9-6 offsuit is well outside the optimal 4x raising range (33+, any ace, K5o+, Q8o+, etc.), so I check and keep only the ante and blind at risk, then reassess on the flop.

Pair of sixes with a 9 kicker plus 9-7-6 straight-draw potential is a standard flop raise in Casino Hold'em, since a made pair has positive EV to raise 2x.

K7 suited is inside the published optimal 4x range (K2s+), so a 4x preflop raise is the highest-EV play.

A2 suited is within the published optimal 4x preflop range (any ace), so the maximum raise is correct.

3d9s is offsuit and unconnected, well outside the optimal 4x range (no ace, K5o+ or Q8o+ equivalent), so I check and see the flop while keeping the risk low.

Nine-high with no pair on a K-high board. The backdoor flush and straight draws are too weak to justify a 2x raise, so I check and decide on the river.

I hold two pair (nines and threes) with a king kicker on a board with no pair. Only a few dealer holdings beat that, such as K9, sets, or a straight, so raising 1x has clearly positive EV.

AKo is a premium hand and falls well inside the published optimal 4x raising range (any ace), so the maximum preflop raise has the highest expected value.

J3 offsuit is outside the optimal 4x range (J8s+ or JTo), so checking preflop and seeing the flop is the better play. Chat is off, so the message is empty.

3c-Js on a Kh-Qd-6c flop is only jack-high with a gutshot straight draw needing a ten, and it has no pair. That is too weak to put 2x more at risk, so I check and see the river.

I have queens and jacks with a king kicker. The board pair means the dealer always qualifies. I estimate about 67% wins, 26% losses and 7% ties, so raising is about +5.5 chips against -20 for folding.

Q6s is inside the published optimal 4x range (Q6s+), so raising 4x preflop is the reference play.

98o is outside the optimal 4x raise range (33+, any ace, K5o+, Q8o+, J8s+, JTo), so I check and see the flop rather than put 4x at risk on a weak offsuit connector.

9-8 on 5-T-7 is an open-ended straight draw (any 6 or J), and pairing a 9 or 8 also gives a playable hand. That is enough equity against a dealer who needs a pair to qualify, so the 2x flop raise is worth it.

8-7 offsuit is well outside the optimal 4x raising range, so I check and see the flop to keep the risk small.

Pair of sevens plus an open-ended straight draw (needs a 5 or T) on the 9-6-7 flop is well ahead of the dealer's range, so the 2x raise has clear positive expectation.

4-8 offsuit is far outside the optimal 4x range, so I check preflop and keep the option to raise on the flop or fold on the river.

4h 8c on 7h Kc 6s is only a gutshot (needs a 5) with no pair, and a dealer with a king already qualifies. That is too weak for a 2x raise, so I check and keep the river fold option.

Pair of eights with A-K-7 kickers wins roughly half the time against the dealer's range. Raising 1x has EV of about -1 chip, far better than the -20 chips from folding.

T8 offsuit is outside the published optimal 4x range (needs K5o+, Q8o+, or JTo), so I check and see the flop rather than risk 4x the ante on a marginal hand.

The board is QQA and I only have queens with a T kicker. The dealer always qualifies, and any A, K, J or small pair beats me, so I'm behind about half the time. Raising 2x is slightly negative, so I'll check and keep the river fold option.

I have trips queens with an ace and ten kicker. The dealer beats me with any pocket pair, ace, nine or the last queen, and also with a king or jack kicker. Counting the 990 dealer holdings, I win 312, tie 81 and lose 597. Raising has an EV of about -11.8 chips, which beats folding at -20.

A8 offsuit contains an ace, which is in the published optimal 4x preflop range (any ace), so the maximum raise is correct.

J3 offsuit is well outside the optimal 4x range (J8s+ or JTo), so I check preflop and keep the option to raise 2x on the flop if the board helps.

A pair of jacks on a K-J-7 flop is a made hand that beats most dealer holdings, and the dealer needs a pair to qualify. The 2x raise on the flop has positive expected value, so I raise rather than check.

J6 offsuit is outside the published optimal 4x range (J8s+ or JTo), so I check preflop and see the flop before deciding on a 2x raise.

Jack-high on a Q92 flop has no pair and no real draw, so a 2x raise has negative expectation. Checking keeps the option to fold or raise 1x on the river.

I have a pair of sixes with Q-J-9 kickers. Folding loses 2 antes for sure, while raising has a much better EV because the dealer often misses a qualifying pair or holds a lower one. Raising is clearly better than folding.

2c3d is one of the weakest starting hands and is outside the optimal 4x range, so I check to keep risk low and see the flop before deciding on a 2x raise or the river decision.

2c3d on an A-Q-8 flop has no pair and only a weak gutshot-type draw, so it is well behind the dealer's range. Checking keeps the risk low and lets me see the river, where I can still fold cheaply.

I hold only ace-high, which is the same hand the board plays, so I can at best tie. The dealer beats me with any pair or a straight (about 80% of holdings), so a 1x raise risks 30 to save 20 and is worse than folding.

3-7 offsuit is far below the optimal 4x raising range, so I check to keep the risk small and see the flop.

Seven-high with no pair and only weak straight draws on a 2-9-4 flop, so raising 2x has negative expectation; checking keeps more chips safe and allows a river decision.

I hold a pair of fours with K-9-7 kickers. The dealer always qualifies because the board pair gives them a pair too. Raising beats folding whenever my loss probability is below roughly 80%, and here it is far lower.

KQ offsuit is inside the published optimal 4x range (K5o+), so raising 4x preflop is the highest-EV play against the house.

Ace-high with any ace is in the published optimal 4x preflop raising range for Casino Hold'em, so raising 4x maximizes expected chips.

K5 offsuit is the borderline hand in the published optimal 4x table (K5o+), so raising 4x is the highest-EV preflop play.

5c Th is weak and outside the optimal 4x raise range (T-high with a 5 kicker), so checking preflop keeps risk low and lets me reassess on the flop.

Ten-high with no pair and only a weak backdoor wheel draw on a 4-8-2 flop; raising 2x isn't profitable here, so check and reassess at the river.

I have only king-high with no pair. The dealer qualifies with a pair or better about 60% of the time, and I would lose the play bet and blind when that happens. Raising has an estimated EV of about -22 chips, versus -20 for folding, so I fold.