Showdown Hold'em table

K2s is within the optimal preflop raise range (K2s+), so betting 4x ante maximizes EV.

K6 offsuit clears the published optimal 4x preflop threshold (K5o+), so raising 4x is the highest-EV play against the house dealer.

K2s offsuit misses the published 4x/3x raise table (needs K2s+ suited or K5o+ offsuit), so checking keeps the pot small and defers to flop/river decisions.

Ace-eight offsuit falls under 'any ace' in the published optimal preflop table, so raising 4x the ante maximizes EV versus checking.

A2s meets the published optimal preflop 4x raise table (any ace), so raising 4x before the flop maximizes expected value versus checking.

Ace-ten offsuit falls squarely in the published optimal 4x preflop range (any ace), so raising 4x has positive EV versus checking and lets the strong ace run out with maximum stake.

T3 offsuit falls well below the published 4x/3x raise range (weakest offsuit raise is JTo), so checking preserves equity and keeps the flop decision cheap.

74 offsuit is far below the 4x/3x raising ranges (33+, any ace, K/Q/J thresholds), so checking keeps the ante-blind at risk only through the free flop decision; folding would forfeit 20 chips with no upside.

9-8 offsuit is below the published 3x/4x raise range, so checking is optimal and preserves the flop option.

9-6 offsuit is far below the 4x/3x raising range (33+, any ace, K/Q/J standards), so checking costs nothing now and preserves the option to raise 2x on the flop or fold later, which strictly dominates folding preflop.

6-high with no pair and no draw on Q-8-A; raising 2x has very negative EV against a dealer likely holding an ace or pair, so check and re-evaluate on the river.

My best hand is ace-high A-Q-9-8-7, which only wins when the dealer whiffs completely (about 96/990 wins plus 64 ties), but raising adds just 10 at risk while folding surrenders the full 20 already posted; raising's EV (~-15) beats folding's fixed -20.

72o is well below the published 4x/3x raising range, so checking and deciding on the flop minimizes risk.

I hold only a pair of sevens with a weak kicker; dealer pairs or better beat me, and dealer no-pair leaves the ante pushing with only play and blind at risk, but 74-low with a T-high board wins too rarely to justify 10 more chips.

T7s is below the published 4x/3x raise range (needs K-high+ or better), so checking keeps the pot small and preserves flop/river options.

T-high with only a backdoor flush draw has poor equity against a board that gives the dealer trips; raising 2x here is clearly -EV, so check and re-evaluate on the river.

My best five is just the board's two pair (66 55 Q-kicker), so I can only tie or lose, but only 489 of the 990 dealer holdings beat me (any A, K, 5, 6, or pocket pair 7+; the other 501 push). Raising costs 30 only on those losses (EV ≈ -14.8), which beats folding for a certain -20.

8s3s is well below the published 4x/3x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves flexibility to raise 2x on a favorable flop.

8s3s on 9h2h4h gives only 9-high with no pair, no draw, and no heart outs; raising 2x would risk 20 more chips against a dealer that usually pairs, so checking to re-evaluate on the river is clearly best.

T8o falls below the published 4x range (needs JTo+ offsuit or J8s+ suited), so checking keeps the flop decision open, where a 2x raise can be made with better information.

Th8s is only an open-ended straight draw with no pair; raising 2x here is -EV, so I check and decide on the river with full information.

8-9 offsuit falls well below the optimal 4x/3x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the cheaper 2x flop decision instead of risking 30-40 chips with a marginal connector.

7-3 offsuit is far below the published 4x/3x raise threshold (33+, any ace, K/Q/J-class hands), so raising would be strongly -EV. Checking preserves the cheap flop raise option and keeps river decisions flexible.

King-high with no pair and no draw (backdoor straight needs running 5-6, no flush possibilities) has very little equity against a dealer who qualifies ~72% of the time on this board; putting 20 more chips at risk with raise_2x is clearly -EV, so I check and decide raise_1x vs fold on the river.

6-8 offsuit is far too weak for a 3x/4x raise; checking keeps the option open to see a cheap flop before committing more money.

With 6-8 on a 9-2-3 board I have at best 8-high and no viable draw (no flush possibility, only a runner-runner 5-7 straight), so a 2x raise would be a huge underdog investment; checking keeps the river decision cheap.

My best five is just the board's pair of queens (QQ986), and the dealer always qualifies off the board pair. I only win ~11% of dealer holdings (two low unpainted cards) and push ~1%, so the 1x raise EV (about -4 chips vs folding) is negative; folding forfeits only the already-posted ante and blind.

Q9o meets the published optimal 4x preflop raise threshold (Q8o+ offsuit), so raising 4x maximizes expected value versus checking.

Ace-seven offsuit falls inside the published optimal preflop 4x raise range (any ace), which yields higher EV than checking and preserving later streets.

A2o falls under 'any ace' in the published optimal preflop table, so raising 4x has higher EV than checking and leaving the flop decision.

A8o contains an ace, which is a standard 4x raise in the optimal preflop table for this game; raising 4x with any ace has higher EV than checking and letting the dealer see cheap streets.

Ace-high with a suited 8 is comfortably in the published optimal 4x preflop range (any ace), so raising 4x maximizes expected value versus checking.

J5s falls below the published 4x raise range (needs J8s+), so checking is optimal; it keeps the cheap flop raise_2x option for favorable boards instead of committing 30-40 chips with a weak suited jack.

J5s is just jack-high here: no pair, no flush possible (board has two diamonds against my two spades), and a straight needs runner-runner 7 and 9. Raising 2x with essentially no equity is clearly -EV, so I check and reassess at the river.

J9s falls inside the published optimal 4x preflop range (J8s+ suited), and the blind bonuses for flushes/straights add extra value to suited connectors, so raising 4x (40 chips) is the max-EV play.

Q7s falls just below the published 3x/4x raising range (Q6s+), so checking keeps the flop option open with a marginal hand.

Top pair with a strong queen on a coordinated board; raising 2x gets more money in with the best hand most of the time versus dealer's random range.

83o is far too weak to raise preflop; checking preserves the option to raise 2x on the flop if it helps, minimizing losses otherwise.

8-high with no real draw on a rainbow T-high board has almost no equity to justify risking 20 more chips; checking preserves the cheaper river raise-or-fold decision.

Any ace is in the published optimal preflop 4x raise range, and A4d has solid equity against the dealer's pair-or-better qualifying range, so betting the maximum 4x ante maximizes expected value.

AJs is a premium suited ace that clears the optimal 4x raise threshold (any ace), giving strong equity against the dealer's pair-or-better qualification requirement.

Q9o misses the published 4x range (needs Q8o+ or Q6s+), and checking keeps the river fold option alive, minimizing expected loss on a weak hand.

T8o is well below the 4x/3x raising range (33+, any ace, K2s+, K5o+, Q6s+, Q8o+, J8s+, JTo), so checking to see a free flop is correct; I can still raise 2x on the flop if it improves.