Showdown Hold'em table

7-4 offsuit is well outside the optimal preflop 4x raising range, so checking to see the flop for free is correct.

Seven-high with only a gutshot on the flop is far below the flop 2x raising threshold of two pair, a hidden pair, or a strong flush draw. Checking keeps the option to fold on the river.

Seven-high with no pair only beats a dealer who has no pair and low cards. That is about 40 of 990 dealer holdings, with about 33 ties, while the dealer qualifies in about 597, so calling costs more than folding's 20-chip loss.

Pocket sevens fall inside the published optimal 4x preflop range (33+), so a maximum raise has the highest expected value.

76 offsuit is well outside the optimal preflop 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking to see the flop is correct.

A pair of sevens made with a hole card, plus straight potential, meets the standard optimal flop threshold for a 2x raise (a hidden pair other than pocket deuces). Raising should beat checking.

T5 suited falls outside the optimal preflop 4x table (which requires J8s+ or better for jack-high-or-lower suited hands), so checking and re-evaluating on the flop is correct.

T-high with no pair and no four-card flush draw on the A-7-4 flop falls well below the standard flop raise threshold (a hidden pair or strong draw). Checking keeps the river decision open at no extra risk.

With only ace-high (A-J-T-7-6) using the board, the dealer qualifies about 65% of the time and we lose to nearly all of those hands. Raising works out to roughly -22.5 chips versus -20 for folding, so folding loses less.

K9 offsuit falls inside the optimal 4x preflop range (K5o+), so raising the maximum is the highest-EV play.

Q9 suited is within the published optimal 4x preflop range (Q6s+), so raising 4x maximizes expected value.

Q7 offsuit is below the optimal 4x threshold (Q8o+ for offsuit queens), so checking preflop and reassessing on the flop is correct.

Top two pair (sevens and sixes) with a queen kicker is well ahead of most dealer holdings, so the 2x raise is clearly better than checking. Standard flop strategy is to raise with any hidden pair or better.

T3 suited is not on the optimal 4x preflop list (which needs J8s+ for jack-high suited hands), so checking and seeing the flop for free is the higher-EV play.

A pair of tens using one of my hole cards counts as a hidden pair, and optimal flop strategy raises 2x with any hidden pair. That makes raising better than checking.

Q4 offsuit is outside the optimal 4x raising range (Q8o+ required), so checking and seeing the flop is correct.

Queen-high with only a gutshot to a 5 falls well short of the usual flop-raise threshold (a pair or better, or a strong flush draw). Checking is free and keeps the river decision open.

The paired board means the dealer always qualifies, and my 66-Q-J-8 wins about 17.8% and ties about 4.5%. By my count that makes raising slightly less costly than folding: about -19.75 chips versus -20.

T3 offsuit is well outside the optimal 4x raising range (which needs at least JTo for unpaired non-ace, non-king offsuit hands), so checking is correct and we'll see the flop for free.

With 3-T on a J-7-7 flop, the only pair is the board's pair of sevens, which the dealer shares. There is no draw or hidden pair, so checking and deciding on the river beats putting in a 2x raise.

Folding loses 20 chips. The dealer always qualifies on this paired board, and with 77QJT I win about 22% and tie about 6%, so calling works out to roughly -17 chips, which beats folding.

This game plays like Ultimate Texas Hold'em, and the optimal 4x preflop strategy includes any ace. A2 suited clearly qualifies for the maximum raise.

9-4 offsuit falls well outside the optimal 4x raising table, so checking is correct. It lets me see the flop for free.

Top pair of nines using a hole card, plus straight draws. Basic flop strategy bets 2x with any hidden pair, so raising is the higher-EV play here.

The reference optimal preflop strategy says to raise 4x with any ace, so A2 offsuit is a 4x raise.

94 suited is not in the optimal preflop 4x raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking preserves the option to raise on the flop or river.

Nine-high with only a backdoor flush draw and no pair is far below the flop raising threshold, so checking keeps the option to decide on the river.

I have only queen-high (Q-J-T-9-7), so any dealer pair beats me. Exact counting puts the expected value of raising at about -20.8 chips, slightly worse than the -20 lost by folding.

Pocket nines are well inside the optimal preflop 4x range (33+), so the maximum raise gives the highest expected value.

J5 offsuit is not in the optimal preflop 4x raising range (J8s+ or JTo), so checking and deciding on the flop or river is better.

Jack-high with only backdoor flush and straight draws is far too weak to raise 2x on the flop. Checking keeps the option to fold or raise 1x on the river.

The paired queens on the board mean the dealer always qualifies. Counting the dealer's possible hands, raising has an expected value of about -18 chips, compared with a certain -20 for folding, so the raise is the smaller loss.

Q2 offsuit falls outside the optimal preflop 4x raising range, which needs Q8o+ for offsuit queens. Checking keeps the option to raise 2x on the flop or 1x on the river.

I hold four to a diamond flush with my own Qd, a hidden card of ten or higher, so the flush draw alone gives about 35% to hit. That matches the standard flop raise_2x guideline and should beat checking on EV.

KTs falls within the optimal preflop 4x raising range (K2s+), so a max raise is the highest-EV play.

Q8 suited falls within the published optimal preflop 4x raising range (Q6s+), so raising the maximum is the highest-EV play.

The published optimal 4x preflop table includes JTo, so offsuit jack-ten is a 4x raise. Raising the maximum here beats checking in expectation.

7-3 offsuit is well outside the optimal 4x raising range, so checking to see the flop for free is correct.

No pair and only a gutshot straight draw (a 6 completes 3-4-5-6-7). Standard flop strategy raises 2x only with a pair using a hole card or better, or strong flush draws, so checking is correct.

The board plays for me, so I can't win, but I tie about 41% of dealer holdings. Raising costs about 17.8 chips on average, which beats the certain 20-chip loss from folding.

J6 suited is below the optimal 4x raising threshold (J8s+), so checking preflop and re-evaluating on the flop is correct.

With jack high, no pair, and only backdoor straight and flush draws, this hand falls well short of the standard 2x flop raise threshold. Checking keeps the river decision open.

I hold two pair, jacks and sevens with a king kicker, which beats most dealer holdings; I lose only to a king, a seven, a higher pocket pair or a straight. Raising 1x is clearly better than folding and giving up 20 chips.

K6 offsuit is inside the published optimal 4x preflop table (K5o+), so raising 4x maximizes expected value.

The published optimal preflop strategy raises 4x with any ace, so A4 offsite qualifies. Raising 4x has higher expected value than checking.

Q3 offsuit falls outside the optimal 4x table, which requires Q8o+ for offsuit queens. Checking is free and keeps the flop and river decisions open.

Q-high with no pair and no draw on a K-6-2 board is far below the flop 2x raising threshold, so I check and keep the river decision open.

The 3 in my hand completes a 6-high straight (2-3-4-5-6) with the board. It beats almost every dealer holding and pays 1:1 on the blind when I win, so raising is far better than folding.

9-3 offsuit is well outside the optimal preflop 4x raising range, so checking to see the flop for free is correct.

With 9-3 on an 8-5-J board I have no pair and only a weak gutshot (needing a 10 for 8-9-10-J and a 7 for 5-7-8-9 isn't a straight). Raising 2x has negative EV here, so I check and keep the river decision open.

My jack-high hand with no pair almost never beats a dealer who qualifies. Enumerating the dealer's possible hands puts raising at about -25.6 chips, versus -20 for folding, so folding loses less.

3-6 offsuit falls well outside the optimal 4x raising range (33+, any ace, strong kings, queens and jacks). Checking lets me see the flop for free.

A hidden pair (3s paired using my hole card) meets the standard optimal flop raise threshold. Betting 2x here beats checking to the river.

K2 offsuit falls outside the optimal 4x raising range, which only includes K5o and better, so checking preflop is the higher-EV play. Checking keeps the option to raise on the flop or river.

Top pair of kings using a hole card is well ahead of a random dealer hand, and basic strategy raises 2x on the flop with any hidden pair except pocket deuces.

T9 offsuit is not in the optimal preflop 4x raising table (it needs JTo or better among unpaired non-ace/king hands), so checking and deciding on the flop or river is best.

Top pair of nines with a ten kicker on a low 2-3-9 board is well ahead of most dealer hands. Basic strategy is to raise 2x on the flop with any pair that uses a hole card.

K7 suited falls within the optimal 4x preflop range (K2s+), so raising 4x maximizes expected value.