Showdown Hold'em table

86o is below the optimal preflop 4x raising range; checking allows evaluating the flop before committing chips.

Bottom pair with a gutshot on a coordinated board is too weak to raise; checking preserves the option to raise on the river if we improve or fold if we miss, maximizing expected value.

K3 offsuit is not in the optimal 4x range (needs K5o+), so checking to see the flop preserves equity and allows a 2x raise if the board is favorable.

With two pairs (Kings and Eights) on a board with no flush or straight possible, our hand is strong against the dealer's random range. The dealer qualifies with a pair or better, and we beat most qualifying hands. Folding would forfeit the ante and blind, while raising gives positive expected value.

Holding an ace meets the optimal preflop 4x raise criteria (any ace). Raising 4x maximizes expected value.

T4o is not in the optimal preflop raising range, so checking preserves chips for later opportunities.

No pair or draw on the flop; checking to see the turn and river before committing more chips.

A3o is any ace, which is in the optimal 4x raise range.

85o does not meet the 4x preflop raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves equity.

Holding 8s5d on a ThKhJd board with no pair and no draw, raising 2x would be -EV; checking preserves the option to fold on the river.

T2o is far below the optimal 4x raising range; checking preserves the option to raise later if the flop improves the hand.

With two pairs (Aces and Tens) on a board where the dealer always qualifies, raising 1x loses about 4.6 chips on average, while folding loses 20 chips, so raising is the better choice.

T9o is below the optimal 4x threshold; checking preserves chips for later decisions.

Middle pair with a ten kicker on a relatively dry board; raising 2x is optimal per standard strategy to capture value from weaker hands and avoid being bluffed out on the river.

8s2s is not in the optimal 4x raising range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo); checking preserves the option to raise 2x on a favorable flop.

With 2s8s on Kd4d9h I have no pair and no meaningful draw, so raising 2x would commit chips with a very weak hand; checking preserves the option to fold or raise only if the board improves.

Pocket nines are in the optimal 4x raising range according to the published strategy.

Hand is weak (7-4 offsuit) and not in the 4x raising range; checking to see flop cheaply.

7s4d on Ts2c5c has no pair and no draw; checking preserves the option to raise later if the hand improves.

With trip deuces kickers T-7, we lose to any dealer full house (any T, 5, or pocket pair), four of a kind (case 2), or better kickers (two cards J+). Folding loses 20 chips; raising risks 30 to win 20 and is -EV.

Any ace is in the optimal preflop raise_4x range per the reference strategy.

AcJs is an Ace and a suited Jack, both within the optimal 4x range (any ace and J8s+).

Q4o is not in the optimal 4x raise range (requires Q6s+ or Q8o+) and lacks the strength for a 3x raise, so checking preserves chips and allows a raise on the flop if the board improves the hand.

We have a pair of Queens on a board with no flush or straight possible. Enumerating the 990 dealer hands, we win 73% of the time (318 qualify wins + 404 non-qualify wins), tie 3%, lose 24%. The expected value of raising is +3.3 chips while folding loses 20 chips, so raising is optimal.

Pocket sixes qualify for the optimal preflop 4x raise range (33+), maximizing expected value against the dealer.

J3o is below the optimal 4x threshold; checking avoids overcommitting with a weak hand.

J3o misses the board completely; checking is correct to see the river and only invest if we improve.

With J3o on a double-paired board (TT775), our two pair with Jack kicker is beaten by any dealer ten (trips), seven (full house), pocket pair JJ+ (better two pair), or a Queen or higher kicker on the board. Folding loses 20 chips, while raising loses 20 when dealer misses and 30 when they qualify; our weak hand does not justify risking an extra 10 chips.

9c6c is not in the optimal preflop 4x raising range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo). Checking preserves the option to raise on the flop or river if the board improves our hand.

I have a pair of sixes on the flop, which is a made hand. According to optimal flop strategy, I should raise 2x with any pair to maximize expected value.

2h3d offsuit is far below the 4x and 3x preflop raising ranges, so checking is best to see a cheap flop and hope to connect.

Pair of threes with an open-ended straight draw (8 outs) provides strong equity against the dealer's range, making a 2x raise the optimal play.

K8s is in the published optimal 4x preflop raising range (K2s+).

Q4o is well below the 4x raising threshold (Q8o+) and has no value to raise 3x; checking to see the flop for a possible 2x opportunity.

Qh4d on 9d5d7h is a weak Q-high with no pair, no flush draw, and only backdoor straight possibilities. Raising 2x would risk 20 chips with poor equity against the dealer's range, while checking preserves the option to raise 1x or fold on the river after seeing two more cards, minimizing expected loss.

J9o is below the preflop raise-4x threshold (needs JTo or better), so checking preserves chips and lets us see the flop before investing further.

With a pair of jacks and an open-ended straight draw (any 8 or Q), our hand has strong equity against the dealer's random range. Raising 2x is the optimal flop decision.

J7o is not in the optimal 4x raising range, so check.

J7o on A53 flop has no pair and no draw, with only ~24% chance to pair by river. Raising 2x risks 20 chips with negative EV, while checking allows a cheaper river decision only if the hand improves.

Player's best hand is Ace-high with A,Q,J,T,7. Dealer qualifies with pair or better. Probability of dealer having worse than Ace-high is extremely low, as any pair, King, or high card 7+ beats us. Folding loses only the ante and blind (20 chips), which is better than risking an additional 10 chips with a negligible chance of winning.

Q7o is below the optimal 4x range (Q8o+), and raising 3x with this offsuit marginal hand would risk chips; checking allows seeing the flop cheaply and possibly raising 2x if we connect well.

Pair of sevens with Queen kicker is a weak hand on this coordinated board (potential straights, higher pairs common). Raising risks an additional 10 chips for a likely loss against a random dealer hand; folding limits loss to 20 chips, which has higher expected value.

2h4s is far below the optimal 4x raising range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo), so checking to see the flop cheaply is correct.

Hand is a weak 2-4 offsuit with no pair and no draw on a J-8-3 board; raising 2x would risk 20 chips with very low equity.

With a pair of threes, we beat dealer's no-pair hands about 51.8% of the time, yielding +10; otherwise lose 30. EV ≈ -9.3 chips, better than folding's -20.

KJo is in the optimal preflop 4x raising range (K5o+).

AK offsuit is in the optimal preflop 4x raising range (any ace), so raise 4x to maximize expected value.

Q3o is not in the optimal 4x range (requires Q8o+), so checking to see the flop is correct.

We have two pair (Queens and Eights) on the flop, which is a strong hand against a random dealer holding. Raising 2x is likely +EV compared to checking, as we are ahead of most dealer hands and have outs to a full house.

J5o is not in the optimal preflop raise range (requires J8s+ or JTo+), so checking is correct.

I have top pair on a coordinated board; raising 2x is standard with any pair to get value before scare cards come.

Any ace is a mandatory 4x raise preflop per optimal strategy, and A2s has positive expectation.

25o is far below the optimal 4x range and too weak to invest additional chips preflop; checking preserves the option to raise on later streets if the board improves.

With 2d5h on Ah-6s-3c, we have only a gutshot straight draw and no pair. Raising 2x would be negative EV, so we check to preserve chips and decide later.

Our hand is only high card A, which loses to any dealer hand with a pair or a card higher than 6, and ties otherwise. Raising risks an additional 10 chips with an expected value of about -24.15 chips, worse than folding's -20.