Showdown Hold'em table

K9 offsuit is inside the published optimal 4x range (K5o+), so raising four times the ante is the correct preflop play.

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

4-2 offsuit is far below the published preflop raising range, so I check and keep the option to raise later if the board improves.

I have a pair of twos on the flop, which is ahead of every non-qualifying dealer hand and strong enough to raise 2x rather than check.

69o 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.

Bottom pair with a weak kicker faces two overcards, so equity is too thin to commit 2x; checking keeps the river option to raise only if the runout improves the hand.

Pair of nines beats all dealer high-card hands and every lower pair, so the 1x play bet is far less costly in expectation than folding the ante and blind.

23 offsuit is far below the published 4x range (no pair, no ace, no king/queen/jack strength), so checking preserves the option to raise later only if the board improves.

Bottom pair of deuces with no draw is too weak to raise 2x; checking keeps the option to fold or raise 1x on the river.

Pair of deuces still has positive equity versus folding: about 380 dealer non-qualifiers pay the play bet, and that gain outweighs the losses to stronger qualifying hands.

9-3 offsuit is well below the published 4x raising range (no pair, no ace, no suited broadway), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

9-high with no pair and only a backdoor flush draw is too weak to commit a 2x raise; checking preserves the option to fold on the river if we miss.

Queen-high with no pair loses to any qualifying dealer hand and often to a non-qualifying high card, so the 1x raise is negative EV versus folding for the ante and blind.

Q2 offsuit is well below the published optimal 4x range (Q8o+), so checking preserves the option to raise later if the board improves.

Queen-high with no pair, flush draw, or straight draw on a paired board is too weak to raise 2x; checking preserves the option to fold or raise 1x on the river.

Board is paired fives so the dealer always qualifies. I win about 312 of 990 holdings and tie 33, for about -13.2 chips versus -20 for folding, so the 1x raise is better.

Ah3h is any ace, which is in the published optimal preflop 4x range, so I raise the maximum.

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

9-6 offsuit is outside the published 4x range (no pair, no ace, and below the king/queen/jack cutoffs), so checking preserves the option to raise 2x on a favorable flop.

Bottom pair of sixes is too weak to raise 2x on this board; checking preserves the option to raise or fold on the river after seeing the full runout.

River two pair (sevens and sixes) wins about 521 of 990 dealer holdings and ties 46 more; the dealer always qualifies on the board pair, so a 1x raise is far less costly than folding the ante and blind.

Q3 offsuit is well below the published preflop 4x range (Q8o+ / Q6s+), so checking preserves the option to raise later with more information.

Queen-high with only a wheel gutshot and backdoor diamonds is too weak to commit a 2x raise. Checking keeps the option to fold on the river if I miss.

Board pair means the dealer always qualifies. I have a 6-high straight, which wins about 75% of the 990 dealer holdings and ties about 11%, so a 1x raise is strongly +EV versus folding.

Kd2d is K2 suited, which is in the published optimal preflop 4x range (K2s+).

Pocket kings are in the published optimal 4x range (33+), so raising the maximum preflop is the highest-EV action.

T8 offsuit is well below the published 4x range (no pair, no ace, and not a qualifying king, queen, or jack hand), so checking preserves the option to raise later with a made hand or strong draw.

Middle pair of tens with a weak kicker on a queen-high board is too marginal to commit 2x now; checking preserves a perfect river decision after the runout.

Pair of tens wins about two-thirds of dealer holdings and the raise EV is far better than folding for -20.

A4o is in the published optimal 4x range (any ace), so I raise the maximum preflop.

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

K7o is inside the published optimal 4x range (K5o+), so I raise the maximum preflop.

T6 offsuit is outside the published optimal 4x range (no pair, no ace, and below the king/queen/jack thresholds), so checking preserves the option to raise 2x on a favorable flop.

Flopped full house (sixes full of tens) is a monster that almost always wins; raising 2x captures value before the board runs out.

K2 offsuit is below the published 4x range (K5o+ or K2s+), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

Kc2s has no pair and no draw on 3c8dTs, so a 2x raise is -EV. Check and decide on the river.

King-high loses to about 645 of 990 dealer holdings that qualify, and the rare wins versus queen-high or worse do not cover the extra chip risk versus folding.

4-2 offsuit is far below the published 4x range and has no suited or straight equity worth a 3x raise, so check and reassess on the flop.

Pair of deuces with only a low spade flush draw is too weak to commit 2x now; checking keeps the option to raise 1x if the flush arrives and fold if it misses.

Board pair means the dealer always qualifies, and my nines and twos win 414 of 990 holdings and tie 54. Raising 1x is about -7.5 chips versus -20 for folding.

2-4 offsuit is far below the published preflop raise range, so checking preserves the option to raise later only if the board improves.

I have a pair of twos, and the +EV flop rule is to raise with any pair rather than check to the river.

Pocket deuces are below the published 4x range (33+), so checking preflop is the correct default and keeps the option to raise later if the board improves.

Pocket deuces is a made pair on an unpaired flop, which is strong enough to raise 2x rather than check and face a thinner river decision.

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

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

Kd5d is suited and inside the published optimal 4x range (K2s+), so raise the maximum preflop.

K9 offsuit is in the published optimal 4x range (K5o+), so I raise the maximum preflop.

J9 suited is in the published optimal 4x range (J8s+), so I raise the maximum preflop.

Any ace is in the published optimal preflop 4x range, so A3o should raise the maximum rather than check.

86 offsuit is outside the published 4x range (no pair, no ace, and below the king/queen/jack thresholds), so checking preserves the option to raise later with more information.

Flopped trip eights is well ahead of a random dealer hand and of most turn-river runouts, so the 2x raise is clearly +EV.

K2o is below the published 4x range (K5o+ or K2s+) but is a standard 3x holding, so I raise 3x rather than check.