Showdown Hold'em table

J5o is outside the optimal preflop raising range, so I check and preserve the option to raise on later streets.

I flopped two pair (jacks and fives), which is well ahead of the dealer's random range and strong enough to raise for value. Checking would miss value, while raising 2x applies the play bet with a likely qualifying dealer.

9-5 offsuit is well below the published preflop raising threshold, so I check and avoid committing extra chips with a weak holding.

With only 9-high and no pair on a J-7-4 flop, raising 2x risks too much against a dealer who qualifies with any pair; checking keeps the hand alive to see if I improve before deciding on the river.

I have two pair (Jacks and Nines) on the river; folding forfeits the 20 chips already posted, while raising 1x risks only 10 more and can win the play bet plus ante/blind when the dealer fails to qualify or I have the best hand.

Pocket queens are a premium pair well within the optimal preflop 4x raising range, so raising maximizes value against the dealer.

K8o meets the published optimal 4x preflop threshold (K5o+), so raising maximizes expected value with a strong-enough king-high hand.

J8o is below the published preflop raising threshold (J8s+ or JTo+), so checking avoids putting extra chips at risk with a weak offsuit hand.

Top pair with jacks on the flop is strong enough to raise for value against the dealer's qualifying range.

8-6 offsuit is below the published preflop raising threshold, so checking avoids putting extra chips in with a weak holding.

With only 8-high and a weak gutshot draw on a 9-4-T flop, raising 2x would risk extra chips without a made hand or strong equity, so I check and take the free river card.

My 6-8 offsuit missed the board entirely, leaving only king-high. The dealer qualifies with any pair, and even when unqualified I usually lose to a higher kicker or straight. Raising 1x has negative expected value compared to folding, so I fold and cut the loss to the ante and blind.

Pocket threes are at the bottom of the published optimal 4x raising range (33+), so raising maximizes expected value against the dealer.

A7o is an any-ace hand, which is in the published optimal 4x preflop raising range, so raising maximizes expected value against the dealer.

K6o meets the published optimal preflop 4x threshold (K5o+), so raising maximizes expected value against the dealer.

QJ offsuit is within the published optimal preflop 4x raising range (Q8o+), so raising maximizes expected value.

Ks5o meets the published optimal preflop 4x threshold (K5o+), so raising maximizes expected value against the dealer.

Q2o is well below the published optimal preflop raising range (Q8o+ or Q6s+), so checking controls risk and keeps the option to evaluate the flop.

My Q-high hand has no pair, no flush draw, and only weak backdoor straight potential on a K-T-7 flop. Raising 2x would commit more chips with a very low chance of beating a qualifying dealer, so checking to see the turn and river is the better expected-value play.

With Q-high and no pair, raising 1x has slightly better EV than folding because the ante pushes when the dealer does not qualify, and we can still win against non-qualifying dealer hands.

8d2d is a weak suited hand outside the published optimal preflop raising range, so checking avoids putting extra chips at risk before seeing the flop.

My 8d2d has no pair and only weak backdoor diamond potential on a Qh-Jh-5d flop, so raising 2x would risk extra chips with little equity; checking keeps the hand alive to evaluate the river.

My best hand is only Q-high with no pair or straight/flush potential. The dealer qualifies with any pair or better, so raising 1x would usually lose an extra bet; folding avoids adding more risk with such a weak river hand.

T7 offsuit is below the published preflop raising threshold, so checking avoids putting extra chips at risk with a weak offsuit holding.

My 7-T has only a weak inside straight draw and no pair or flush draw on this flop, so raising 2x would risk too much with little equity. I will check and evaluate the river decision.

Folding loses the 20-chip ante and blind; raising 1x risks only 10 more and has higher EV because the dealer will miss a diamond or higher hand often enough. Exact enumeration of the 990 dealer holdings makes raise_1x better than folding.

Qc5c is below the published optimal preflop raising range (Q6s+ or better), so I check and preserve the option to raise on the flop.

Bottom pair with a weak kicker on an ace-high flop is not strong enough to raise 2x; checking preserves the option to fold unimproved on the river instead of committing extra chips now.

With a pair of fives and a Q kicker, raising 1x is better than folding because the dealer often fails to qualify or holds a weaker pair, making the expected loss smaller than forfeiting the ante and blind.

7-8 offsuit is below the published preflop raising threshold, so checking avoids committing extra chips with a weak starting hand.

I have middle pair on the flop, which beats the dealer's random hand more often than not, so raising 2x is positive expected value.

J4o is well outside the published preflop raising range, so checking avoids putting extra chips in with a weak offsuit hand.

J-high with no pair or draw is too weak to raise for value on the flop; checking keeps the hand alive to see if the turn or river improves it before committing more chips.

Our best hand is only a pair of 3s with J-T-6 kickers. The dealer always qualifies due to the board pair, and any higher kicker or board match beats us. Folding loses 20 chips, while raising 1x has an expected loss of about 22 chips, so folding is better.

K6s is in the published optimal 4x raising range (K2s+), so raising maximizes expected value versus the house dealer.

Pocket fives are a small pair and fall within the published optimal 4x raising range (33+), so raising maximizes expected value against the dealer.

K3o is below the optimal 4x raising threshold (K5o+ or K2s+), so I check to see a flop and potentially raise later with better information.

K-high with only a backdoor flush draw and no straight draw is too weak to raise 2x on this flop; checking preserves the river decision to fold when unimproved or raise if I hit a pair or better.

The board pairs deuces, so both hands have at least a pair. My K kicker wins against a meaningful share of dealer holdings, and raising 1x has better expected value than folding, which would lose the ante and blind for -20.

With 2c4c, a weak offsuit low hand outside the optimal preflop raising range, checking avoids putting extra chips at risk before seeing the flop.

Player has two pair (5s and 4s); against the dealer's range on this board, raising 1x is clearly better than folding, as most non-A/T/5/4 dealer hands lose to this two pair.

J5s is below the published 4x raising threshold, so I check preflop to see a flop and preserve the option to raise 2x if I improve or fold on the river if I do not.

My J-high has no pair, no flush draw, and only weak straight potential, so raising 2x would put extra chips at risk with little equity against a dealer who qualifies with any pair. I check and reassess on the river.

With a pair of Jacks on the river, raising 1x has an expected value of about -6.5 chips, which is better than folding and losing the 20-chip ante and blind. The dealer beats us with any ace, king, queen, two hearts, or specific two-pair/trips combos, but we still win often enough to justify the raise.

Ks6o is in the published optimal 4x preflop raising range (K5o+), so raising maximizes expected value against the house dealer.

T3o is well outside the published optimal preflop raising range, so checking avoids committing extra chips with a weak offsuit hand.

My T-high with no pair or strong draw is too weak to raise for value on this flop; checking preserves the option to fold on the river if I do not improve.

I hold a 2-6 straight using 3h with the board's 2,4,5,6, which is a strong made hand. Raising 1x is clearly better than folding and should show positive expected value against the dealer.

Q7s is within the published optimal preflop 4x raising range (Q6s+), so raising maximizes expected value with a suited queen.

Ace-six offsuit falls within the published optimal 4x raising range because any ace is included. Raising maximizes value with a hand that has strong high-card and ace-blocker equity against the dealer.

5-2 offsuit is far outside the published preflop raising range, so checking avoids putting extra chips at risk with a weak hand.

With 5-high and only a weak gutshot on a coordinated flop, raising 2x risks too much against a dealer who qualifies with any pair; checking keeps the hand alive for a possible river decision.

With a pair of twos, the dealer fails to qualify about 35% of the time, and the 1x raise has better expected value than folding, which would forfeit the ante and blind.

Pocket sixes are a strong preflop pair and fall within the published optimal 4x raising range, so raising maximizes value against the dealer.

9-2 offsuit is far below the published preflop raising threshold, so checking avoids putting extra chips at risk with a weak hand.

I have top pair (nines) on the flop. Raising 2x with a made pair is optimal to maximize expected value against the dealer's random hand.

T2o is well outside the published optimal preflop raising range, so checking avoids putting extra chips at risk with a weak offsuit hand.

My hand is only ten-high with no pair or strong draw on a king-queen flop, so raising 2x would put extra chips at risk with very little equity. I will check and reassess on the river.

Board pair of queens gives me a made hand; against a random dealer hand I win about 22% and tie about 4.5%, so raising 1x has higher EV than folding (-17.5 vs -20).