Showdown Hold'em table

6-5 offsuit is not on the optimal preflop 4x raising chart, so I check and see the flop before committing more chips.

Six-high with no pair and no real draw on a K-J-3 flop is far too weak to raise 2x. Checking is free and keeps the option to raise or fold on the river.

I have a 3-to-7 straight, which the dealer cannot beat on this board; the best the dealer can do is tie with 6-5. Raising wins the ante, the play bet and a 1:1 blind payout.

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

J9s falls within the published optimal preflop 4x range (J8s+), so a max raise is the higher-EV play than checking.

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

The board pair gives the dealer at least the same pair, so my 9-3 kickers lose to most dealer hands, and the wheel draw is only a backdoor. Checking to decide on the river is better than putting 2x at risk.

The board already shows aces and deuces, so my 9 kicker plays and the dealer always qualifies. By my count the dealer beats me in about 789 of 990 holdings and I win only 144, so raising is worth about -21 chips versus -20 for folding.

84 offsuit is well outside the optimal 4x preflop range, so checking is correct and keeps the flop and river decisions open.

The 4 in my hand pairs the board, giving me two pair (nines and fours with an eight kicker). The dealer is always playing a pair of nines, and by my rough count they are ahead only about 18% of the time now and I still win roughly 65% after the turn and river, so the 2x raise should earn more than checking.

KJo falls within the published optimal 4x preflop range (K5o+), so a maximum raise has the highest expected value.

4-3 offsuit falls outside the optimal preflop 4x raising range (which starts at 33+, any ace, and K/Q/J high combos), so I check and keep the option to raise later for free.

A hole card pairs the board, giving a hidden pair of threes. Standard optimal flop strategy raises 2x with any hidden pair, since it beats many dealer holdings, while checking forfeits too much when the dealer fails to improve.

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

K6 suited falls within the published optimal 4x preflop range (K2s+), so raising 4x maximizes expected value.

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

A hidden pair of fours on the flop beats many dealer holdings and falls under the standard 2x flop-raise rule (hidden pair except pocket deuces). That makes raising better than checking to the river.

J5 offsuit is well below the optimal preflop 4x threshold (JTo+ for jack-high offsuit), so checking to see the flop for free is correct.

Jack-high with no pair and only a remote runner-runner straight draw is far too weak to put 2x at risk. Checking lets me see the river for free and fold there if I haven't improved.

Raising with ace-king-queen-jack high loses about 15.8 chips on average, versus a certain 20-chip loss from folding. The dealer fails to qualify about 38% of the time, and I win most of those hands.

Q6 offsuit falls below the optimal 4x table, which requires Q8o+ for offsuit queens. Checking preserves the option to raise on the flop or river.

Queen-high with only backdoor flush and straight draws is well short of the usual 2x flop raise threshold (a pair or a strong four-flush). Checking keeps the option to reassess on the river.

Queen-high is behind most dealer hands, but if the dealer does not qualify we still win the play bet. A rough count gives the raise an EV of about -19.9 chips versus -20 for folding, so raising is marginally better.

K7 offsuit falls within the published optimal 4x preflop table (K5o+), so raising 4x maximizes expected value.

3-4 offsuit is well outside the optimal preflop 4x raising range (33+, any ace, strong kings/queens/jacks), so checking to see the flop for free is correct.

3-4 offsite on an 8-7-8 flop leaves me with only a gutshot straight draw and the board pair, which the dealer shares, so raising 2x has negative EV. Checking keeps the option to raise 1x or fold on the river.

Two pair (eights and fours, nine kicker) wins about 48% and ties about 3% against the 990 possible dealer hands. Calling risks 10 more chips for an EV of about -5 chips, versus a sure -20 from folding.

Q2 offsuit is below the optimal 4x preflop threshold (Q8o+ for offsuit queens), so checking is correct.

A hole card makes a pair with the board (2s with a Q kicker). Standard optimal flop strategy for this format bets 2x with any hidden pair except pocket deuces, so raising beats checking.

The optimal 4x table raises pairs only from 33 up, so pocket 2s is a check preflop. Checking keeps the option to raise 2x on the flop or 1x on the river.

Our pocket 2s give two pair (8s and 2s) on a paired board, so the dealer almost always qualifies. We should still beat most dealer holdings, roughly 65-70% equity by a rough count, which makes the 2x raise worth more than checking.

J4 offsuit is outside the optimal 4x raising range (J8s+ or JTo), so checking preflop has the higher expected value.

Jack-high with only backdoor straight and flush draws is too weak for a 2x flop raise under standard strategy, so I check and decide on the river.

The dealer always qualifies on this paired board. Of the 990 dealer holdings, 220 lose to my Q-J-T kickers, 69 tie and 701 win. That makes calling worth about -16.8 chips versus -20 for folding, so raising 1x loses slightly less.

J8s is on the published optimal 4x preflop list (J8s+), so raising 4x maximizes EV.

7-4 offsuit is well outside the optimal preflop 4x raising range, so I check and decide on the flop with more information.

The only pair is the board's 5s, and 7-high kickers are weak, so there is no hidden pair or strong draw worth a 2x raise. Standard flop strategy is to check and decide on the river.

I hold 5s and 4s with a king kicker. The dealer loses to this unless they pair a K, T or 5, hold a pocket pair or A4, or make a spade flush, so my win chance is well above the roughly 20% needed to beat folding.

9-6 suited is not in the optimal preflop 4x raising range (33+, any ace, strong kings/queens/jacks), so checking and seeing the flop for free has the higher expected value.

The 6 in my hand pairs the board for Queens and sixes, a hidden pair that is well ahead of most dealer holdings. Standard flop strategy is to raise with a hidden pair or better.

J6 offsuit is not in the optimal preflop 4x raising range (J8s+ or JTo), so checking to see the flop is correct.

Jack-high with only backdoor flush and straight draws is well short of the usual flop 2x threshold (a hidden pair or better, or a strong flush draw), so checking to the river is best.

I hold a 6-high straight (2-3-4-5-6), which beats almost every dealer holding except a flush from two hearts or a higher straight. Raising has strongly positive EV, and a win also pays the blind 1:1, while folding would forfeit 20 chips.

A7 offsuit contains an ace, and the published optimal strategy raises 4x with any ace preflop.

A8 suited contains an ace, and any ace is a 4x raise under the published optimal preflop strategy. The suitedness also adds flush equity for the blind payout.

Q9 offsuit meets the optimal 4x threshold of Q8o+, so raising 4x preflop has higher EV than checking.

Pocket tens are well inside the optimal 4x preflop raising range (33+), so raising the maximum preflop maximizes expected value.

Q6 offsuit falls below the optimal 4x threshold, which starts at Q8o for offsuit queens. Checking and deciding on the flop or river is better.

Queen-high with no pair and only backdoor draws is well short of a flop 2x raise, so checking keeps the river decision available at no extra risk.

A pair of queens with an ace kicker loses to only about a quarter of dealer holdings, so calling 10 more is well above the break-even point against a sure 20-chip loss from folding.

J7 offsuit is outside the optimal preflop 4x raising range (J8s+ or JTo), so checking to see the flop is better.

The only pair is the board's 4s, so the dealer always qualifies, and my J-7 kicker is weak. With no hidden pair or strong draw, a 2x flop raise loses value, so I'll check and decide on the river.

I hold two pair, sevens and fours with an ace kicker. The paired board means the dealer always qualifies, and I beat roughly 620 of 990 dealer holdings, so raising has positive EV compared with the certain -20 from folding.

76 offsuit is not on the optimal 4x raising chart (it needs 33+, any ace, K5o+, Q8o+ or JTo), so checking to see the flop is better.

7-6 on a 9-T-3 flop is only a gutshot to an 8 with no pair, which is far too weak for a 2x raise. Checking keeps the option to see the river for free and then raise 1x or fold.

Seven-high with no pair. Enumerating dealer hands puts raising at about -20.7 chips versus -20 for folding, since the dealer pairs or holds an overcard too often.

7-5 offsuit is well outside the optimal preflop 4x raising range, so checking to see the flop for free is correct.

A pair of sevens that uses my hole card, plus a gutshot to the 6, is ahead of much of the dealer's range. Standard flop strategy is to bet 2x with any hidden pair better than deuces.

75 offsuit is not in the optimal preflop 4x raising range, so the best play is to check and see the flop for free.

7-5 offsite on a T-J-3 flop has no pair and no draw beyond weak backdoors, so raising 2x would be clearly -EV. Checking keeps the option to fold on the river for only the ante and blind.

With only king-high, we lose to any dealer pair or straight (about 80% of dealer hands), so raising is worth roughly -24.5 chips. Folding costs a fixed 20 chips, which is the smaller loss.