Showdown Hold'em table

3-4 offsuit is well outside the optimal 4x raising range, so I check preflop and keep the risk small to see the flop.

Two pair (fours and threes) on the flop is well ahead of the dealer's likely holdings, so the 2x raise has clear positive expected value.

T6s is not in the published 4x raise range (only T-high hands like JTo or J8s+ qualify), so I check preflop and keep the option to raise 2x on the flop if it helps.

I hold only king-high with an open-ended straight draw (need a 9 or ace), and any dealer pair from K, Q or J beats me. A 2x raise is likely negative EV, so I check to keep the river option and raise 1x only if the straight or a pair improves me.

The board already gives queens and jacks with a king kicker, so my hand plays the board and can only tie or lose. The dealer beats me only with an ace, king, queen, jack or a 9-10 straight, about 44% of holdings, and the rest tie. Raising risks 30 to lose in the losing cases versus a guaranteed 20 loss by folding, so it is better whenever the loss chance is under 2/3.

J5s is outside the published optimal 4x raise range (J8s+ or JTo), so I check preflop and will re-evaluate on the flop.

The board pair means the dealer always qualifies, and my J-high with a pair of 3s loses to any dealer pair, 3, 7, or A/K/Q. A 2x raise is clearly negative EV, so I check and keep the option to fold on the river.

The board is two pair and my Q kicker plays. The dealer always qualifies, and I win about 40% of the time, lose about 60%, and tie a little. Raising has an EV of roughly -10 chips versus -20 for folding, so I raise.

8s4s is outside the optimal 4x raising range (8-high suited is weak), so I check preflop and keep the option to raise on the flop or river based on how the board develops.

8s4s on a 3c Ks 7c flop has no pair and only weak backdoor potential (8-high with a 4-card gap to nothing), so a 2x raise has negative EV against a dealer who qualifies with any pair; checking keeps the option to fold on the river.

The board pair of sevens means the dealer always qualifies. My pair of sevens with a K-T-8 kicker loses to nearly any dealer hand with a card of A, Q, J, 9, K, T or a pocket pair, so I win only about 8-9% of the time. Raising is worth about -24 chips against -20 for folding, so I fold.

J9 offsuit falls outside the published optimal 4x range (J8s+ or JTo), so I check preflop and keep the option to raise 2x on the flop.

I have a pair of nines with a jack kicker, a second pair on a T-9-2 flop, plus straight potential with J-T-9. That is well above the flop raise threshold, so I raise 2x.

4s6s is outside the published optimal 4x range (33+, any ace, K2s+, etc.) and is a weak suited connector, so I check preflop and keep the option to raise 2x on the flop if it improves.

I have a pair of sixes plus a straight draw (any 5 completes 3-4-5-6-7) on the flop. That is a clear 2x raise against a dealer who needs a pair to qualify.

Any ace is in the published optimal 4x raise range for Casino Hold'em, so A4 offsuit is a 4x raise preflop.

Queen-ten offsuit is inside the published optimal 4x range (Q8o+), so the 4x raise is the highest-EV preflop play.

T4 suited is outside the published optimal 4x range (only Q6s+, J8s+ and K2s+ are included), so I check preflop and keep the option to raise 2x on the flop if it improves.

Top pair of tens on a 3-T-7 board is well ahead of the dealer's range on average, so the 2x flop raise has positive expected value.

K2 offsuit is outside the published optimal 4x range (K2s+ or K5o+), so I check preflop and keep the option to raise on the flop or river.

King-high with only a backdoor flush draw and weak straight outs is not strong enough to put 2x more on the flop, so I check and decide again on the river.

The board pair of 3s means the dealer always qualifies, so raising needs only about a 20% win chance. My pair of 3s with K-J-T kickers beats roughly half of dealer holdings, so raising clearly beats folding.

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

KJ suited is inside the published optimal 4x range (K2s+ and K5o+ both cover it), so a 4x raise is correct preflop.

Pocket queens are well inside the optimal 4x preflop range (33+), so the maximum preflop raise has the best expected value against the house dealer.

K-Q offsuit is in the published optimal 4x range (K5o+), so the maximum preflop raise has the best expected value against the house dealer.

8-3 offsug is well outside the optimal 4x raising range (K5o+, Q8o+, etc.), so checking preflop keeps risk low and lets me reassess on the flop.

8h3c on a Kh As 6d flop has no pair, no real draw, and is well behind a dealer who will often hold a pair or better, so a 2x raise would be negative EV. Checking keeps the exposure small and leaves the river fold option open.

My best hand is a pair of fives with A-K-8 kickers, and the board pair means the dealer always qualifies. The dealer beats me with any ace, king, six, five, pocket pair, or Q/J/T/9 kicker, so I win or tie only about 12% of the time. Raising has an EV of roughly -22.8 chips against -20 for folding, so I fold.

8-4 offsuit is well outside the optimal 4x raise range, so I check preflop to keep the risk small and see the flop before deciding on a 2x raise.

8c4s on a Jd 5d 7d flop is only 8-high with no pair, no flush draw and a weak straight draw (gutshot-ish 4-5-7-8 needs a 6). That is far below the flop raise threshold, so I check and keep the option to fold on the river.

My 4s and 8c make a 4-8 straight on the board. It only loses to a dealer 9 or a diamond flush, so the raise is far better than folding and forfeiting 20 chips.

Q8 offsuit is inside the published optimal 4x preflop range (Q8o+), so the 4x raise maximizes expected value.

Q2 suited is outside the published optimal 4x raise range (Q6s+), so I check and keep the option to raise on the flop.

Only ace-high with a gutshot straight draw needing a ten on a board of A-K-J that the dealer likely pairs, so adding a 2x raise is negative EV. Checking keeps the river fold-or-raise option.

I have ace-high with no pair, so any dealer pair, straight or flush beats me. The dealer misses a qualifying hand about 28% of the time, and then I win the play bet. That puts raising at about -18.8 chips against -20 for folding, so raising is slightly better.

J9 suited falls within the published optimal 4x range (J8s+), so a 4x preflop raise maximizes expected value.

J2 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.

The board pair of sevens means the dealer always qualifies, and my sevens with a jack kicker lose to any dealer ace, king or queen, any pocket pair, and any 4 or 7. I'm likely behind, so I won't add a 2x raise on the flop and will decide again at the river.

The board is 7-7-4-4-3 and I have two pair with a jack kicker, so the dealer always qualifies. I win only if the dealer lacks a Q/K/A kicker, a pair of 8s or higher, a 7 or 4, or a flush, which is roughly 40% of holdings. Raising 1x needs only about 20% to beat folding, so it is clearly better.

Q2 offsuit is outside the optimal 4x range (Q8o+ needed), so I check and see the flop for a cheaper decision.

The board pair of 9s means the dealer always qualifies, and my Q-kicker pair of 9s loses to any dealer A, K, Q, 3 or 9, roughly 55% of the time. Raising 2x is negative EV, so I check and keep the river decision.

I hold queens and nines with a 3 kicker. The board is paired, so the dealer always qualifies, and only about 26% of dealer hands beat me: any 9 or 3 (full house), a Q with a kicker above 3, or KK/AA. I win roughly 72%, so the raise is clearly positive EV, and folding would lose 20 chips for certain.

Ace-high hands like A2o are in the published optimal 4x preflop range (any ace), so raising 4x maximizes expected value.

J3 offsuit is outside the optimal 4x raising range (needs J8s+ or JTo), so checking preflop keeps risk low and lets me reassess on the flop.

I hold a pair of threes plus a four-card heart flush draw with Jh, Th and Qh, so the hand has showdown value and strong improvement outs. That makes the 2x flop raise positive in expectation.

J5 offsuit is outside the published optimal 4x range (J8s+ or JTo), so I check preflop and keep the option to raise 2x on the flop if the board helps.

Pair of fives with a jack kicker plus an open-ended straight draw (3 or 7) on the 4-5-6 flop is well above the flop raise threshold, so raising 2x has positive expected value.

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

Jack-high with no pair and no real draw on a 7-K-4 flop is too weak to put 2x in; checking keeps the option to fold on the river.

I have a pair of fours with K-J-8 kickers. The board is paired, so the dealer always qualifies. By my estimate I win about 27% of the time and tie about 4%. Raising only needs roughly a 20% win rate to beat folding, so I raise.

Threes and fours (two pair) on the flop is well ahead of most dealer holdings, so raising 2x has clearly positive expected value. Only a ten, a higher pocket pair or a four beats it.

8s5s is outside the published 4x raise range (no ace, and not K2s+, Q6s+ or J8s+), so the standard play is to check preflop and see the flop with only the ante and blind at risk.

I have a pair of fives with an eight kicker on a 5-7-3 flop. Casino Hold'em strategy raises the flop with any pair, so I take the 2x raise.

Pocket fives fall inside the published optimal 4x range (33+), so a 4x preflop raise maximizes expected value against the house dealer.

Q6 offsuit is outside the published optimal 4x range (Q8o+ or Q6s+), so I check preflop and keep the option to raise 2x on the flop.

Pair of sixes with a queen kicker is a made hand that beats most dealer holdings, so the 2x flop raise is standard and worth more than waiting for the river.

Q3 offsuit is outside the published optimal 4x range (Q8o+ needed for queens), so checking preflop and seeing the flop keeps risk low and preserves the option to raise on the flop or fold at the river.

Top pair of queens on the flop is well ahead of a random dealer hand, so the 2x raise has positive expected value even with a weak 3 kicker.