Showdown Hold'em table

K9o fits the optimal 4x preflop raise range (K5o+), so raising 4x maximizes expected chips.

Pocket threes are in the optimal 4x raising range (33+), maximizing expected value against the house dealer.

4s 2c is far below the optimal 4x raising range; checking preserves chips and allows us to see the flop cheaply.

With bottom pair and no flush draw, our equity against the dealer's range is marginal. Checking preserves the option to raise 1x on the river only if we improve or the board is safe, avoiding a larger loss when behind.

6h9c offsuit is not in the optimal 4x raise range and is too weak to raise 3x; checking preserves the option to raise later if the flop improves the hand.

Pair of nines on a Q-J-9 board; standard flop strategy says to raise 2x with any pair or better.

Holding 2c 3d offsuit is far below the optimal 4x preflop raising range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo). Checking is the correct mathematical play to avoid overcommitting with a weak hand.

With a low pair of twos and no draw, raising 2x risks 20 chips with poor equity against a dealer who can easily have a higher pair or overcards. Checking preserves the option to fold on the river if the hand doesn't improve, limiting losses to the ante and blind.

With a pair of deuces, we beat all high-card hands (42.4% win probability) and tie 3%, losing 54.5%. Raising 1x yields an expected loss of about 12.1 chips, better than folding's loss of 20 chips.

93 offsuit is well below the optimal preflop raising range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo), so checking is the correct play.

Hole cards 3h9s on Qs5hTs flop: no pair, no draw, weak hand. Check to avoid risking 20 chips with low equity.

Q2o is weak and not in the optimal 4x raising range (requires Q8o+). Checking lets us see the flop cheaply and potentially raise later if we improve, minimizing expected loss with a trash hand.

Q2o is a weak hand with no pair or draw on a paired board; checking preserves the option to fold on the river if unimproved, which is better than committing 2x now.

Preflop with Ah 3h: any ace qualifies for 4x raise per optimal strategy.

K8o is in the optimal preflop 4x raising range (K5o+), so I raise the maximum to maximize expected value.

9c6h is not in the optimal 4x raising range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo), so checking is correct.

Pair of sixes with a gutshot straight draw; raising with any pair is standard and we have additional equity.

Q3o is not in the optimal 4x range (Q8o+ is minimum queen-high). Checking preserves chips and allows seeing the flop before investing more.

Open-ended straight draw (any Ace or 6) with 8 outs plus overcard Queen; raising 2x is optimal per standard flop strategy.

K2 suited is in the optimal preflop 4x raising range per the published strategy, maximizing expected chips against the dealer.

Pocket kings are a premium pair and well within the optimal 4x raising range.

T8o is not in the optimal 4x raising range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo), so checking is correct.

Holding a pair of tens on a Q♣ T♠ 7♣ flop; raising 2x as any pair is a standard raise after checking preflop.

A4o is in the optimal 4x range (any ace).

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

K7o is in the optimal preflop 4x raising range (K5o+).

T6o is not in the optimal 4x raise range; checking allows a later raise if the flop improves the hand.

Flopped a full house (sixes full of tens) which is a very strong hand. Raising now secures the play bet while ahead.

K2s is in the optimal 4x raising range according to the published preflop strategy.

4s2h is not in the optimal preflop 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking is correct to see the flop without additional risk.

Pair of twos with no flush draw on a monotone board is too weak to raise; checking preserves the option to fold on the river if we don't improve.

Raising 1x has EV -7.4 chips, better than folding's -20, because dealer fails to qualify ~55% of the time and we win the play bet.

2d4c is far below the preflop raise range and has poor high-card value, so checking preserves the option to see a cheap flop before risking more.

Holding a low pair of twos on a board with two overcards, our chance to win against the dealer's range is small. Folding loses 20 chips but raising risks an additional 10 for a total loss of 30 when we lose, which is likely. The expected value of folding is higher than raising.

Pair of twos is below the optimal 4x raising threshold (33+), so checking to see the flop cheaply is best.

We have a pair of deuces, which is a made hand, and the optimal flop strategy is to raise 2x with any pair.

QJo is in the published optimal 4x raising range (Q8o+).

Any ace is a mandatory 4x raise preflop per optimal strategy.

K5s is in the optimal 4x raising range (K2s+).

K9o is in the optimal 4x raising range (K5o+) per the published preflop strategy, maximizing expected value.

Jh9h is a suited connector in the optimal 4x raising range (J8s+).

Holding any ace is in the optimal preflop 4x raising range.

86o is not in the optimal preflop 4x raising range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo), so checking is correct.

We have trip eights on a J-8-8 flop; it's a very strong made hand and raising for value maximizes expected chips.

K2o is below the optimal 4x raising threshold (K5o+), so checking preflop preserves chips and allows a flop decision.

With K2o on a J-T-5 board, we have no pair, no draw, and only one overcard. The expected value of raising 2x is negative; checking preserves the option to fold or raise 1x on the river based on the final hand.