Showdown Hold'em table

3c4s offsuit is far below the published 4x/3x raising range (33+, any ace, K2s+, etc.), so checking keeps the flop raise_2x option while limiting risk on a weak hand.

I flopped bottom two pair (4s+3s), which is well ahead of the dealer's pair-or-better qualifying range; the standard optimal flop play is to raise 2x with two pair or better to maximize value.

T6s is outside the optimal 4x preflop range (needs 33+, any ace, K2s+/K5o+, Q6s+/Q8o+, or J8s+/JTo), and a 3x bet is dominated, so checking preserves the flop 2x option with more information.

I play the board (two pair Q-J, K kicker) so I can never win — dealer ties or beats me. Raising 1x pushes everything on the ~55.5% ties and loses 30 only on the ~44.5% dealer wins (EV ≈ -13.4), which beats folding for a certain -20.

J5s falls below the published 4x raise range (needs J8s+), so checking preserves flexibility to raise 2x on a favorable flop instead of committing 40 chips with a marginal suited jack.

84s falls well below the published 4x raising range (33+, any ace, K2s+, Q6s+, J8s+), so raising would be -EV; checking keeps the ante/blind in play and preserves the option to raise 2x on a favorable flop.

8-high with no draw on a K-high board is far too weak to risk 20 chips; keeping the flop option open and deciding with full river information minimizes expected loss.

My best hand is only the board's pair of sevens with an 8 kicker; the dealer always qualifies off the board pair and wins ~85% of holdings (any K/T/7/3, 9+, or an 8-pair/outkicker), so raising 1x has EV about -23 chips vs 0 for folding.

J9o is well below the published 3x/4x raising range and doesn't merit betting 30-40 chips; checking keeps flop options open.

4s6s is well below the optimal preflop raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking preserves the cheap flop decision and avoids committing 30-40 chips on a weak suited connector.

Ace-x hands play well against a dealer who needs pair+ to qualify; any ace is in the published 4x raise range.

QTo offsuit meets the published optimal 4x preflop raise threshold (Q8o+), so betting 4x ante maximizes expected value versus checking.

T4s falls below the published 4x raising range (needs J8s+ among suited hands), so checking keeps the ante/blind in play and defers to a flop decision where suited ten-high can still improve.

Kh-2d offsuit falls below the 4x raise threshold (K5o+ needed offsuit), and a 3x bet is dominated since checking preserves the cheaper flop 2x option with more information.

King-high with no pair, no real draws beyond a backdoor flush, so raising 2x would put 40 more chips at risk as a big underdog; checking keeps the river option open where I can value-bet or fold cheaply.

Ace-King suited is squarely in the published optimal 4x preflop raise range (any ace), so raising 4x maximizes EV versus checking.

KJ suited is a suited king, which meets the published optimal 4x preflop raise threshold (K2s+); raising 4x maximizes EV versus checking.

Pocket queens are far above the published 4x threshold (33+ pairs), so maxing the raise pre-flop maximizes EV against the dealer's qualify-or-fold structure.

KQ offsuit is well above the optimal 4x raise threshold (K5o+), one of the strongest non-ace starting hands, so betting the maximum 4x ante maximizes expected value.

83 offsuit is far below the optimal 4x raising range (33+, aces, strong K/Q/J hands), so checking keeps the flop 2x option and river 1x-or-fold option open and minimizes expected loss.

8-high on a king-high flop has almost no equity against the dealer's qualifying range; checking keeps only ante and blind at risk with a cheap fold option on the river.

My best hand is only pair of fives with an 8 kicker, and the board's pair of fives means the dealer always qualifies; the dealer only loses with two low unpaired hole cards (~7% of combos), making raise_1x EV about -25.5 chips versus -20 for folding.

84o is far below the published 4x/3x preflop raise table (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise 2x on a favorable flop.

My 4s gives me an 8-high straight (4-5-6-7-8). Enumerating all 990 dealer holdings: dealer beats me only with two diamonds (45) or a 9 (161), ties 109, and I win the other 675, so raising 1x has EV ≈ +12 chips versus -20 for folding.

Q8 offsuit meets the published optimal 4x raising threshold (Q8o+), so raising 4x preflop maximizes EV versus checking.

Q2s misses the published 3x/4x raising range (needs Q6s+ suited), so checking and deciding on the flop minimizes risk.

My best hand is A-K-Q-J-9 high; an unqualified dealer can never beat it (only tie with a Q), and any qualifying pair beats me. Raising 1x costs 30 only when the dealer qualifies (~60%) and nets +10 otherwise, EV about -14.9 versus a guaranteed -20 fold, so raising saves chips.

J9s meets the published optimal 4x preflop raise threshold (J8s+ suited), so raising 4x ante is the highest-EV play versus checking.

J2o is well below the published 4x/3x raise range (needs J8s+ or JTo), so checking keeps the ante/blind exposure minimal and preserves the cheap flop raise option if the board improves my hand.

J2o on a paired low flop has little value; 2x is too big a risk, so check and re-evaluate on the river.

Q2 offsuit falls below the optimal 4x/3x raising range (needs Q8o+ or Q6s+), so checking preserves the option to raise 2x on the flop if the board improves my hand.

Queen-high with no draw on a paired board has little chance to beat even a dealer pair; checking keeps the river 1x decision cheap where I can fold junk.

My two pair (Q-Q/9-9) beats ~73% of dealer holdings (255/990 dealer wins, 10 ties), and the paired board guarantees the dealer qualifies, so the 1x play bet has EV ≈ +7 chips versus -20 for folding.

Any ace is in the published optimal 4x preflop raise table, and A2o is well above the check threshold; raising 4x maximizes EV before the board runs out.

J3o is well below the published 4x/3x raising range (needs J8s+ or JTo), so checking minimizes risk and keeps the flop and river decision points open.

We hold the nut flush draw with a jack-high flush already made; raising 2x now puts 20 chips in at the point of maximum fold equity and lets the blind pay 3:2 if the flush comes, while checking would only allow a smaller 1x river bet.

J5o is far below the published 4x/3x raising range (needs J8s+/JTo or better among jacks), so committing 30-40 chips preflop has negative EV; checking keeps the free flop decision and lets me raise 2x only when the board helps.

I hold a wheel straight (5-4-3-2-A) which beats all dealer non-straight holdings; only a dealt 2-3 or 2-6 wheel ties or beats me, so raising 1x is far better than folding.

J3 offsuit falls well below the published 4x/3x raising range (J8s+/JTo+), so checking keeps the ante and blind at minimum risk and preserves the flop decision.

J3o on a K74 board has almost no chance against a qualifying dealer hand; raising 2x would put 30 more chips at risk with a hand that rarely wins, so checking keeps the river fold option open and minimizes losses.

J3-high has no pair, no draw, and no showdown value; the dealer needs only a pair to qualify and beats us almost always. Folding saves the extra 10-chip play bet that raising would risk.

Pair of threes falls below the published 4x threshold (33+), so checking is standard; with only four hands left I take the cheaper 3x play bet to keep showdown equity and blind upside in play rather than checking down.

8s5s falls below the published 4x raise range (needs 33+, any ace, K2s+/K5o+, Q6s+/Q8o+, or J8s+/JTo), so checking keeps the flop decision open instead of committing 40 chips with a marginal suited connector.

Pocket fives fall below the optimal 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise 2x on the flop with a set or strong draw instead of committing 40 chips with a marginal pair.

Q6o falls below the published preflop 4x range (offsuit queens need Q8o+), and a 3x raise is dominated by either 4x or checking, so I keep the ante at risk minimal and retain flop/river decision value.

Q3o offsuit is not in the published preflop raising range (Q8o+ offsuit), so checking keeps the flop 2x option and the cheaper river 1x-or-fold decision, maximizing EV on this final hand.

Top pair (queens) on the flop is well above the 2x-raise threshold; raising builds value while the dealer must make a pair to qualify.