Showdown Hold'em table

J5 offsuit is below the published preflop 4x range (J8s+ or JTo), so checking preserves the option to raise on later streets if the board improves.

Two pair, jacks and fives, is well ahead of most dealer holdings on this flop, so the 2x play bet has positive expectation.

9-5 offsuit is well below the published 4x range and has little high-card or straight value, so checking preserves the option to raise later only if the board improves.

No pair, no straight, and only a backdoor club draw on J-7-4. Too weak to put 2x at risk; check and reassess on the river.

River two pair jacks and nines beats most of the 990 dealer holdings, including all non-qualifying hands. Exact enumeration gives about +5 chips for a 1x raise versus -20 for a fold.

Pocket queens are in the published optimal 4x range (33+), so I raise the maximum preflop.

K8o is in the published optimal 4x range (K5o+), so I raise the maximum preflop.

J8 offsuit is below the published 4x range (J8s+ or JTo), so checking preserves the option to raise later with more information.

Top pair of jacks is strong enough to commit the 2x flop raise rather than check and only risk 1x later.

6-8 offsuit is well below the published 4x range, so I check and keep the option to raise later if the board improves.

68 offsuit on 9-4-T has no pair and only a gutshot, so raising 2x is -EV; check to preserve the option to fold unimproved on the river.

I have an 8-high straight (8-9-T-J-K). Only AQ beats me and an 8 ties; every other dealer holding loses, so a 1x raise is strongly +EV versus folding.

Pocket threes are in the published optimal 4x range (33+), so I raise the maximum preflop.

A7o is in the published optimal 4x range (any ace), so I raise the maximum preflop.

K6o is in the published optimal preflop 4x range (K5o+), so I raise the maximum.

QJo is in the published optimal preflop 4x range (Q8o+), so raising the maximum is the correct play.

K5o is on the published optimal 4x range (K5o+), so I raise the maximum preflop.

Q2 offsuit is outside the published 4x range (Q8o+), and a 3x raise is not worth it with this weak offsuit queen, so I check and reassess later.

Queen-high with no pair and no flush or straight draw on K-T-7 is too weak to raise 2x; check and reassess on the river.

Queen-high never beats a qualifying dealer, but dealer misses a pair often enough that the 1x play bet still loses less than folding the ante and blind.

8d2d is well below the published 4x range (no pair, no ace, and not a strong king/queen/jack hand), so checking preserves the option to raise later if the board improves.

8-2 has no pair and only backdoor equity on Q-5-J, so checking preserves a river fold and avoids committing another 20 chips.

Queen-high loses to 960 of 990 dealer holdings, and the rare wins only push the ante and blind, so a 1x raise is worse than folding.

T7o is well below the published optimal 4x range (JTo+, Q8o+, K5o+, suited broadways and pairs), so checking preserves the option to raise later with a made hand or strong draw.

No pair and only a gutshot on 8d-2d-Jc; checking keeps the river fold option instead of committing 2x with a weak draw.

Pair of tens wins about 361 of 990 dealer holdings and ties 46, so calling the 1x is about -12.5 chips versus -20 for a fold.

Q5s is just below the published optimal 4x range (Q6s+), so I check and defer the raise decision to the flop.

Pair of fives is weak on an ace-high board with no draws, so checking preserves the option to fold on the river if the hand does not improve.

Pair of fives with A-K-Q kickers wins or ties about 58% of the 990 dealer holdings, including all non-qualifying hands. River raise EV is about -5 chips versus -20 for folding, so raise.

78 offsuit is outside the published optimal 4x range (no pair, no ace, and neither card is jack or better), so checking preserves the option to raise later with more information.

Top pair of eights on a low rainbow flop is ahead of most dealer holdings and is strong enough to raise 2x rather than check to the river.

J4 offsuit is well below the published optimal 4x range (JTo+ / J8s+), so checking preserves the option to raise later with a made hand or strong draw.

J4o on 3-T-6 rainbow has no pair and no draw, so a 2x flop raise has negative expectation. Check and decide on the river with full information.

Board pair means the dealer always qualifies, and 4c Jd only has pair of threes with a jack kicker. That wins about 132 of 990 holdings, so a 1x raise is worth about -22.7 versus -20 for folding.

K6 suited is in the published optimal 4x range (K2s+), so I raise the maximum preflop.

Pocket fives are in the published optimal 4x range (33+), so raise the maximum preflop.

K3 offsuit is below the published 4x range (K5o+ or K2s+), so checking preserves the option to raise later with more information.

King-high with no pair and only a backdoor spade draw is too weak to raise 2x; checking keeps the option to fold or raise 1x on the river.

Board pair means the dealer always qualifies, but 276 of 990 holdings still lose to pair of twos with a king kicker and 69 tie. Raising loses about 14 chips in expectation versus 20 for a fold.

24 suited is well below the published optimal 4x range, so I check and keep the option to raise on later streets if the board improves.

Pair of fours with a weak kicker is too marginal to raise 2x on this flop; checking preserves the option to fold or raise 1x on the river after seeing the full board.

Two pair fives and fours beats most dealer holdings that only have the board pair, so a 1x raise is far better than folding the ante and blind.

J5s is below the published 4x range (J8s+), so checking preflop is the correct default and keeps the 2x flop option.

J-high with no pair and no meaningful draw on Th-Kd-7h; checking preserves the option to fold or raise 1x on the river after seeing the full board.

Pair of jacks with A-K-T kickers wins or ties 531 of 990 dealer holdings, and raising loses about 7 chips in expectation versus 20 for a fold.

K6 offsuit is in the published optimal 4x range (K5o+), so I raise the maximum preflop.

Ts3o is well below the published 4x range (no pair, no ace, and not a playable king/queen/jack), so checking preserves the option to raise later if the board improves.

T3 offsuit has no pair, no draw, and no connection to 6-4-2, so raising 2x is -EV; check and reassess on the river.

Ten-high never beats any of the 990 dealer holdings: qualifying hands win outright and non-qualifiers still have a better high card, so a 1x raise only adds losses versus folding.

Q7 suited is inside the published optimal 4x range (Q6s+), so raising four times the ante is the correct preflop play.

Any ace is in the published optimal 4x preflop range, so A6 offsuit raises four times the ante.

5-2 offsuit is well below the optimal preflop raising range, so checking preserves the option to raise later if the board improves.

5-2 offsuit has only a gutshot on 7-8-9 and no pair or flush draw, so raising 2x is -EV. Check to see the river and raise 1x only if the hand improves enough to call.

Pair of deuces still has positive equity versus a fold: the dealer misses qualification often enough, and the only qualifying hands that do not beat this pair are ties.

Pocket sixes are in the published optimal 4x range (33+), so I raise the maximum preflop.

9-2 offsuit is well below the published 4x range (33+, any ace, K5o+/K2s+, Q8o+/Q6s+, JTo/J8s+), so checking preserves the option to raise later if the board improves.

Pair of nines with a deuce kicker on a connected 9-8-7 board is too thin to commit 2x; checking keeps the river fold option when overcards or straights arrive.

River trips nines beat about 889 of 990 dealer holdings and only lose to 80, so a 1x raise is strongly +EV versus folding the ante and blind.

T2 offsuit is well below the published 4x range (no pair, no ace, not a suited or offsuit broadway), so checking preserves the option to raise later if the board improves.

No pair, no flush draw, and no meaningful straight draw on Qs Ks 7d. Checking preserves the option to raise 1x or fold on the river under optimal play.

Board queens mean the dealer always qualifies, and my queen-pair with a ten kicker still wins or ties often enough that a 1x raise (about -17.5 chips) beats folding for -20.