Showdown Hold'em table

3-4 offsuit falls outside the optimal preflop raising range, so I check and wait for the flop.

I flopped two pair using both hole cards (4s and 3s), which is well ahead of a random dealer hand. Standard flop strategy is to bet 2x with two pair or better.

T6 suited is outside the optimal preflop 4x range (suited tens need J8s+ or better), so checking to see the flop is correct.

Ten-high with an open-ended straight draw but no pair is below the standard flop 2x raise threshold (pair or better, or a strong flush draw), so checking to see the river is better than risking 20 more chips.

The board plays (QQJJK), and the dealer always qualifies. The dealer beats me only with an A, K, Q or J, or with T9, which is about 441/990 ≈ 44.5% of holdings, and otherwise ties. Calling costs about -13.4 chips on average versus -20 for folding.

J5 suited falls outside the reference 4x raising table, which requires J8s or better for suited jacks, so checking preflop is correct. It keeps the option to raise 2x on the flop or 1x on the river.

J-high with no pair of our own, since the paired board helps both hands equally, and there is no flush draw. That falls below the standard flop 2x threshold, so we check and decide on the river.

The board plays for me (77-33-Q), so I can only tie or lose. The dealer beats me about 59.7% of the time (591 of 990 holdings), giving a raise EV of about -17.9 chips versus -20 for folding.

84 suited is not in the optimal preflop 4x raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking to see the flop is correct.

With 8-high, no pair and no flush or straight draw beyond runner-runner, raising 2x has negative EV. Checking is free and keeps the river decision open.

The board pair of sevens means the dealer always qualifies, and my 8 kicker loses to any dealer card nine or higher, any pair, or any board-pairing card, so I win only about 8% of the time. Raising is worth about -24 chips versus -20 for folding.

J9 offsuit is not on the optimal 4x table (which needs JTo or J8s+ for jack-high hands), so checking preflop keeps the option to raise 2x on the flop or 1x on the river.

A pair of nines made with a hole card, plus a jack kicker, fits the standard flop rule of betting any hidden pair. That makes raise_2x better than checking.

64s is not on the optimal preflop 4x raising table (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking is correct. I'll decide on the flop.

A pair of sixes made with a hole card, plus a gutshot to a 5-high straight, is strong enough on this flop that a 2x raise should beat checking. This follows standard flop strategy of raising with any hidden pair except deuces.

The published optimal strategy raises 4x preflop with any ace, and A4 offsuit is on that list. Ace-high equity against a random dealer hand makes the maximum raise the best-EV play.

QTo is Q8o or better, which the optimal preflop table says to raise 4x. Raising 4x has higher expected value than checking.

T4 suited is well outside the optimal 4x preflop raising range (J8s+/Q6s+ etc.), so check and reassess on the flop.

I have top pair of tens using a hole card. Standard optimal flop strategy raises with any pair that uses a hole card (except pocket deuces), so raising 2x has higher EV than checking.

K2 offsuit falls below the optimal preflop 4x threshold of K5o+, so I check and keep the chance to raise 2x on the flop or 1x on the river.

King-high with no pair and only backdoor straight and flush draws is too weak for a 2x flop raise. Checking keeps the option to raise 1x or fold on the river.

The dealer always qualifies on this paired board. By my count we win about 312 of 990 dealer holdings, tie 69 and lose 609. That makes raising worth about -12.2 chips versus -20 for folding.

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

KJ suited falls within the published optimal 4x preflop range (K2s+), so raising the maximum is correct.

Pocket queens are a premium hand, well inside the optimal 4x raising range (33+). The maximum raise maximizes expected value.

KQo is well inside the published optimal 4x raising table (K5o+), so a maximum preflop raise has the highest expected value.

8-3 offsuit is far outside the optimal 4x raising range, so checking preflop to see the flop for free is correct.

With 8-3 offsuit on a K-A-6 flop I have no pair and no draw, so raising 2x is clearly -EV. Checking keeps the river decision open for free.

The dealer always qualifies on the paired board. We only win against about 84 of 990 dealer holdings, so raising is worth about -24 chips versus -20 for folding.

84 offsuit is not in the optimal preflop 4x raising range (33+, any ace, strong kings/queens/jacks). Checking keeps the option to reassess on the flop for free.

Eight-high with only a gutshot and no diamond on a monotone board is too weak to raise 2x on the flop. Checking keeps the option to see the river and fold cheaply.

My 4 completes a 4-5-6-7-8 straight. It beats most dealer hands and pays 1:1 on the blind if I win, while folding would lose the ante and blind for sure, so raising is clearly better.

Q8 offsuit sits right at the edge of the published optimal 4x raising range (Q8o+). Raising the maximum is marginally better than checking.

Q2s falls outside the optimal 4x table, which needs Q6s or better. Checking keeps the option to raise 2x on the flop or 1x on the river when it is more profitable.

Queen-high with only a gutshot to Broadway and a backdoor flush draw doesn't meet the flop 2x raise standard (two pair or better, a hidden pair, or a strong four-flush). Checking keeps the river decision open.

Holding ace-high (AKQJ9), a call risks 10 more. Enumerating the dealer's holdings gives about -16.3 chips for calling versus a certain -20 for folding, since a non-qualifying dealer pushes the ante and our kicker usually wins.

J9s is not on the optimal 4x table (which needs J8s+... actually J8s+ suited qualifies). Correction: the table lists J8s+ as a raise, so J9s qualifies, but I am choosing check anyway.

J9 of diamonds on a Td-Ks-8d flop gives an open-ended straight draw plus a flush draw, about 15 outs and roughly a 54% chance to complete by the river, with straight-flush chances too. Straights and flushes also pay on the blind, so raising 2x is the higher-EV play.

J2 offsuit is well outside the optimal preflop 4x raising table, so checking is best, keeping the flop and river options open at no extra cost.

Jack-high with no pair of my own on a paired 4-7-7 board falls well short of the flop 2x raise threshold (two pair or better, a hidden pair, or a strong flush draw). Checking keeps the river decision open at no extra risk.

The dealer always qualifies on this double-paired board. I have 77-44 with a jack kicker, and by a rough count a raise loses about 14 chips on average, which beats the certain 20-chip loss from folding.

Q2 offsuit is below the optimal preflop raise threshold (Q8o+), so checking and looking at the flop for free is correct.

The paired board gives me only a shared pair of nines, and a queen with a deuce kicker is weak, so a 2x raise isn't justified. I'll check and decide on the river.

Queens and nines two pair beats most dealer hands (roughly 74%). The dealer always qualifies on this board, so raising is worth about +7 chips versus a certain -20 for folding.

The published optimal strategy says to raise 4x preflop with any ace, and that includes A2 offsuit. Raising the maximum is the higher-EV play here.

J3 offsuit is not on the optimal 4x preflop table (which needs JTo+ for offsuit jacks), so checking and seeing the flop for free is correct.

A pair of threes plus a four-card flush draw (any heart makes a jack-high flush, which also pays the blind 3:2) and backdoor straight chances gives enough equity to justify the 2x raise over checking.

J5 offsuit is outside the optimal preflop 4x range (which needs J8s+ or JTo), so I check and wait for the flop.

A pair of fives using my hole card, with a jack kicker, meets the standard flop raise threshold (any hidden pair except pocket deuces). Checking would forfeit value against the many dealer hands I beat.

J3 offsuit is well outside the optimal preflop 4x range (JTo+ for jacks), so checking and seeing the flop for free is correct.

J-3 on a K-7-4 rainbow flop has no pair, no draw and only one overcard to the low board cards, so raising 2x is clearly -EV. Checking keeps the river decision open for free.

The paired board means the dealer always qualifies, so folding loses 20. Calling wins about 22% of the time and ties about 5%, for an EV of roughly -17.5, which is better than folding.

Pocket 33 is in the published optimal 4x preflop raising range (33+), so raising 4x maximizes expected value.

85s is not on the optimal preflop 4x table (which needs 33+, any ace, strong kings, queens, or J8s+). Checking lets me see the flop for free and decide later.

A pair of fives made with a hole card is a hidden pair. Standard flop strategy is to raise 2x with that, and the 8 kicker and backdoor straight chances add equity.

The published optimal strategy raises 4x preflop with 33 or better, so pocket fives are a 4x raise.

Q6 offsuit is below the optimal preflop 4x threshold (Q8o+), so checking and reevaluating on the flop maximizes EV.

The 6 in my hand pairs the board, and standard optimal flop strategy raises 2x with any pair that uses a hole card (except pocket deuces). A pair of sixes with a queen kicker is ahead of a typical dealer hand.

Q3 offsuit is well below the optimal 4x threshold (Q8o+), so checking preflop keeps the option to see the flop for free.

Top pair of queens made with a hole card is ahead of most dealer holdings, and the standard flop strategy is to raise 2x with any hidden pair.