Showdown Hold'em table

K2 offsuit falls outside the optimal preflop 4x range, which requires K5o or better for offsuit kings. Checking keeps the option to raise 2x on the flop or 1x on the river more cheaply.

I've paired the board deuce with a hole card, giving a hidden pair with a king kicker. Standard optimal flop strategy raises 2x with any hidden pair except pocket deuces, and I also have a backdoor spade flush draw.

The reference optimal 4x table raises K5o or better, and K6o is in that range. Raising 4x preflop has a higher EV than checking.

K2 offsuit is below the optimal 4x threshold (K5o+ for offsuit kings), so checking and reassessing on the flop is better than raising.

A pair made with a hole card (2s on the board, plus a king kicker) meets the standard flop raise threshold. Only pocket deuces are excluded, so raising 2x beats checking.

The published optimal 4x preflop table includes any ace, so A8 offsuit should be raised the maximum 4x.

A2 suited contains an ace, and the published optimal strategy says to raise 4x preflop with any ace. The suited cards add flush value for the blind payout.

ATo contains an ace, and the optimal preflop strategy raises 4x with any ace. Raising the maximum here has higher expected value than checking.

T3 offsuit is not on the optimal preflop 4x raising table, so checking is correct. It keeps the option to raise 2x on the flop or 1x on the river, or to fold.

The only pair is the board's sixes, which the dealer shares, and my ten kicker is weak with no real draw. Standard flop strategy says check here and decide on the river.

The board pair means the dealer always qualifies. With 6s and a T kicker, we beat only about 56 of 990 dealer hands and tie 33, so raising has an EV of about -26 chips versus -20 for folding.

74 offsuit is well outside the optimal 4x preflop raising range. Checking is free and lets me see the flop before committing more.

I hold a hidden pair of fours on the flop, and standard optimal flop strategy raises 2x with any hidden pair except pocket deuces. My 7 also adds some straight potential.

98o is not in the optimal preflop 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking to see the flop is correct.

Nine-high with only backdoor straight and flush draws is well below the standard flop 2x raise threshold (two pair, a hidden pair, or a strong four-flush). Checking keeps the option of a river decision.

I hold a 9-high straight (5-9), which beats every dealer hand except a two-spade flush or a tying 98. Raising wins the ante, the play bet and the 1:1 straight blind payout far more often than not.

9-6 offsuit is well outside the optimal 4x preflop raising range (33+, any ace, strong kings/queens/jacks), so checking to see the flop for free is correct.

96 offsuit on a Q-8-A board has no pair and no real draw, only a gutshot to a 7 and weak backdoors, so a 2x raise has negative EV. Checking keeps the river decision open for free.

The board does not give me a flush or a straight, so I have only ace-high (A-Q-9-8-7). By my count that beats about 67 of the 990 possible dealer hands, so a 1x raise is worth roughly -25 chips versus -20 for folding.

74 offsuit is well outside the optimal preflop 4x raising range, so checking to see the flop for free is correct.

A pair of sevens using a hole card is a hidden pair, and the standard flop strategy is to raise 2x with any hidden pair except pocket deuces. The raise should beat checking, even with the king on board and a weak kicker.

T7 suited is not in the optimal preflop raising range (J8s+ is needed for Jx suited, and T-high hands only raise when paired), so checking and reassessing on the flop is correct.

Ten-high with only the board's pair of fives and no strong draw is well below the standard flop 2x raise threshold, so check and decide on the river.

Our hand plays the board (66-55-Q), so we can only tie or lose. By enumeration the dealer beats us about 58.5% of the time, which puts raising at about -17.5 chips versus -20 for folding.

8-3 suited is well outside the optimal preflop 4x raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking and seeing the flop for free is correct.

8-high with no pair, no flush draw on a three-heart board, and only runner-runner straight possibilities. Raising 2x has negative EV here, so I'll check and decide on the river.

I only have jack-high with no pair. Counting the dealer's possible hands, raising loses about 25 chips on average, versus 20 chips for folding.

T8 offsuit is outside the optimal 4x raising range (which needs JTo+ for offsuit jacks/tens), so checking to see the flop for free is correct.

A pair of tens that uses a hole card, plus backdoor straight chances, meets the standard flop guideline to raise 2x with any hidden pair. Betting now should beat checking and deciding on the river.

98 offsuit is not in the optimal preflop 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking to see the flop is correct.

Nine-high with no pair and only a backdoor diamond draw on an A-K-Q board falls well short of the flop 2x raise threshold of two pair, a hidden pair or a strong flush draw. Checking keeps the river fold option open at no extra cost.

Exact count: against 701 qualifying dealer hands a raise loses 30, against 280 non-qualifying hands it wins 10, and 9 hands tie. That puts the raise at about -18.4 chips versus -20 for folding, so raising 1x loses less.

7-3 offsuit is well outside the optimal preflop 4x raising range, so the best play is to check and see the flop for free.

The 3-7 offsuit on a K-4-8 rainbow board has no pair and only a weak gutshot to a 5-6, so it is well below the flop raising threshold. Checking is free and keeps the river decision open.

King-high with no pair or draw rarely beats the dealer: the dealer qualifies about 60% of the time, and even an unqualified dealer usually holds a higher kicker. Raising 1x has clearly worse EV than surrendering the 20 chips of ante and blind.

86 offsuit is well outside the optimal preflop 4x raising range, so I check and will reassess on the flop for free.

With 8-high, no pair and no real draw, standard flop strategy says check (raise only with a hidden pair or better, or a strong flush draw). Checking keeps the river option open.

On this board our hand is only queens with a 9-8-6 kicker. The paired queens mean the dealer always qualifies, and we beat only about 108 of 990 dealer holdings, so raising is worth about -2.32 antes against -2 for folding.

Q9 offsuit meets the published optimal 4x preflop threshold (Q8o+), so a 4x raise beats checking here.

The reference optimal preflop table says to raise 4x with any ace, so A7o qualifies. A 4x raise has higher EV than checking.

A2 offsuit falls within the published optimal 4x preflop range, which includes any ace, so raising the maximum is the reference-optimal play.

Any ace is in the published optimal 4x preflop raising table, so A8 offsuit should be raised the maximum.

Any ace is in the published optimal 4x preflop raising range, so A8 offsuit gets the maximum raise.

J5 suited falls outside the optimal preflop raising range, which needs J8s or better. Checking lets me see the flop without adding risk.

J-high with only a gutshot to a 7 and no pair or flush draw falls well short of the standard flop 2x raise threshold. Checking keeps the river decision open at lower risk.

With the board I hold two pair, jacks and fours, which beats most dealer holdings. Calling the 1x play bet is far better than folding away the ante and blind.

The reference 4x table includes J8s+, so J9 suited is a preflop 4x raise under optimal Ultimate Texas Hold'em-style strategy.

Q7 offsuit falls below the optimal 4x threshold (Q8o+), so checking preflop keeps the option to raise 2x on the flop or 1x on the river.

Top pair of queens made with a hole card is a strong hidden pair, and standard optimal flop strategy raises 2x with any hidden pair better than pocket deuces.

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

Eight-high with no pair and only a weak backdoor straight draw falls well short of the flop 2x raise threshold (two pair, a hidden pair, or a strong flush draw). Checking keeps the river fold option open.

We have a pair of eights on the board, and only about 7 single cards (tens and sixes) beat us outright. That is far below the usual threshold of about 21 dealer outs, so calling beats folding and giving up 2 antes.

A4 suited is inside the published optimal 4x preflop range, which includes any ace, so the maximum raise has the highest expected value.

AJ suited is well inside the optimal 4x preflop raising range, since any ace qualifies, so the maximum raise gives the highest expected value.

Q9 offsuit is in the published optimal preflop 4x range (Q8o+), so a 4x raise maximizes expected value.

T8 offsuit is not in the optimal preflop 4x range (J8s+/JTo needed for offsuit jacks, and ten-high offsuit never qualifies), so checking and deciding on later streets maximizes EV.

T8 on Q-6-9 is only an open-ended straight draw with no pair. Standard flop strategy raises with a hidden pair or better, or with a strong flush draw, so checking and deciding on the river is the better play.

A pair of tens with a queen kicker is strong here. Folding costs 2 antes for sure, while raising wins often against dealer hands that don't qualify or hold weaker pairs, so its EV is well above -2.