Showdown Hold'em table

J5 offsuit is not on the optimal 4x raising chart (which requires JTo+ for offsuit jacks), so I check and wait to see the flop.

Two pair (jacks and fives) on the flop is a strong favorite over a random dealer hand, so raising 2x maximizes EV versus checking.

9-5 offsuit is well outside the optimal preflop 4x raising range, so checking to see the flop for free is correct.

Nine-high with no pair and only backdoor straight and flush draws is too weak to raise 2x on the flop. Checking keeps the river option open at no extra cost.

Two pair (jacks and nines) beats most dealer holdings. Calling for one ante clearly beats folding, which forfeits two antes.

Pocket queens are well inside the optimal 4x preflop raising range (33+), so the maximum raise gives the highest expected value.

K8 offsuit falls within the published optimal preflop 4x table (K5o+), so raising the maximum is correct.

J8 offsuit falls outside the optimal preflop 4x range, which includes J8s+ but only JTo for offsuit jacks. Checking keeps a cheap look at the flop.

Top pair of jacks using a hole card is a hidden pair. Standard flop strategy is to bet 2x with any hidden pair, since it is well ahead of the dealer's random range.

86 offsuit is well outside the optimal preflop 4x raising range (33+, any ace, strong kings/queens/jacks), so checking to see the flop is correct.

Eight-high with only a gutshot draw and no pair falls well short of the standard flop 2x raise threshold. Checking keeps the option to raise 1x or fold on the river.

I only have king-high with an 8 kicker, which wins only against unqualified low hands. Exact counting puts calling at about -2.19 antes versus -2.0 for folding, so folding is better.

Pocket threes are listed in the published optimal 4x table (33+), so raising 4x preflop is the reference-optimal play.

Any ace is in the published optimal 4x preflop raising range, so A7o should be raised 4x.

K6 offsuit falls within the published optimal 4x preflop range (K5o+), so raising 4x has higher expected value than checking.

QJ offsuit falls within the optimal 4x preflop raising range (Q8o+), so the maximum raise has positive expected value.

K5 offsuit is in the published optimal 4x raise range (K5o+), so a max preflop raise has the highest expected value.

Q2 offsuit is below the optimal 4x threshold (Q8o+), so checking preflop and deciding later is correct.

Queen-high with no pair and no flush draw on K-T-7 rainbow is well below the flop 2x raise threshold of a hidden pair or a strong draw. Check and decide on the river.

Enumerating all 990 dealer holdings, raising has an EV of about -18.9 chips, slightly better than the certain -20 from folding. The dealer fails to qualify in about 40% of cases, and our K-Q high beats most of those hands.

8-2 suited is well outside the optimal 4x raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking to see the flop is correct.

8-2 offsite with no pair, no flush draw and no real straight draw on Q-5-J is far too weak to raise 2x. Checking keeps the option to fold cheaply on the river.

Queen-high with no pair or draw only beats a tiny fraction of dealer holdings, essentially 7-2 offsuit. Raising would lose about 30 almost every time, while folding caps the loss at 20.

T7 offsuit is not on the optimal preflop 4x table, which requires JTo or better for offsuit non-ace/king/queen hands. Checking keeps the ante and blind live and lets me decide on the flop.

T7 offsite on 8-2-J has no pair and only a gutshot (needs a 9); that's well short of the usual flop raise threshold, so checking to the river is better.

With a pair of tens on a four-diamond board, the dealer beats me in roughly 60% of holdings (601 of 990). Even so, raising costs about 1.46 antes in the worst case, which is better than the 2 antes I lose by folding.

Q5s falls just below the optimal 4x preflop threshold (Q6s+), so I check and wait to see the flop.

Standard flop strategy is to raise 2x with any pair that uses a hole card (except pocket deuces). Our pair of fives with a queen kicker clears that bar against a random dealer hand.

87 offsuit is outside the optimal preflop 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking and seeing the flop is correct.

I hold top pair of eights using a hole card, with a backdoor straight draw. Optimal flop strategy raises 2x with any hidden pair other than pocket deuces.

J4 offsuit is not on the optimal 4x preflop table (only JTo among offsuit jacks), so checking and reassessing on the flop is the higher-EV play.

J-high with only a gutshot (needs a 5) and no pair on a 3-T-6 rainbow board is far too weak to raise 2x, so checking keeps the river decision open.

Only the board's pair of 3s with a J kicker; by rough enumeration the dealer, who always qualifies here, beats this about 85% of the time. Raising is worth about -22.7 chips, so folding for a sure -20 is slightly better.

K6 suited is within the published optimal 4x preflop range (K2s+), so raising the maximum gives the highest expected value.

Pocket fives are inside the published optimal 4x raising range (33+), so the maximum preflop raise has the highest expected value.

K3 offsuit falls below the optimal 4x threshold (K5o+ for offsuit kings), so checking preflop and deciding later is higher EV.

King-high with no pair and only a backdoor flush draw falls below the flop 2x raise threshold. Checking keeps the option to bet or fold on the river.

The dealer always qualifies because of the board pair of deuces, and our K-high kicker beats or ties roughly 28% of dealer holdings. Raising costs about -17 chips in expectation versus -20 for folding, so calling the 1x is better.

4-2 suited is well outside the optimal preflop 4x raise range (it needs 33+, any ace, or strong kings, queens and jacks), so checking to see the flop is correct.

A hidden pair of fours, made with a hole card, plus some straight potential fits standard optimal flop strategy, which says to raise 2x with any hidden pair except pocket deuces.

J5 suited is outside the published 4x preflop range, which needs J8s+ for suited jacks. Checking keeps the flop and river decisions open.

J5 offsuit on a K-T-7 flop makes no pair and has no real draw, only weak backdoor straight chances. Standard flop strategy only raises with a hidden pair or better or a strong flush draw, so I check and decide on the river.

Pair of jacks with A-K-T kickers loses to roughly 46% of dealer holdings. Calling risks 10 more chips to avoid a certain 20-chip fold loss, so raising has clearly higher EV.

K6 offsuit falls within the published optimal 4x preflop table (K5o+), so raising 4x maximizes expected value.

T3 offsuit is well outside the optimal preflop 4x raising range, so checking to see the flop for free is correct.

Ten-high with only a gutshot to a five and no pair or flush draw falls short of the flop 2x raising standard. Checking keeps the river fold option open.

I hold a 2-6 straight. Only a dealer 7-3 or 7-8 for a higher straight beats it, so raising is clearly profitable, and a win also pays the blind 1:1.

Q7 suited falls within the optimal preflop 4x range (Q6s+), so raising the maximum gives the best expected value.

Any ace is in the published optimal 4x preflop raising table, so A6o warrants the maximum raise.

5-2 offsuit is far outside the optimal preflop 4x range (33+, any ace, strong kings/queens), so checking to see the flop for free is correct.

With 5-2 offsuit on 7-9-8 there is no pair and only a gutshot to a 6, which is well short of the flop 2x raise threshold. Checking keeps the option of a cheap river decision.

A pair of twos beats every unpaired dealer hand, and those hands do not qualify. By my rough count, raising costs about 12 to 13 chips on average, compared with a certain 20-chip loss from folding.

Pocket sixes fall within the optimal 4x preflop table (33+), so the maximum raise has the highest expected value.

9-2 offsuit is far outside the optimal 4x raising range (33+, any ace, strong kings/queens/jacks), so checking to see the flop for free is correct.

Top pair of nines using a hole card is a hidden pair, which standard flop strategy plays at 2x. It is ahead of most dealer holdings even with a weak kicker on a connected board.

T2 offsuit is well outside the optimal 4x raising range, so checking is correct. That keeps the option to raise on the flop or fold on the river.

Ten-high with no pair and only a backdoor straight draw is far too weak to raise 2x on the flop. Checking keeps the option to see the river for free and then fold or bet 1x.

The board pairs queens, so the dealer always qualifies. Against the 990 possible dealer hands I win about 25%, tie about 5% and lose about 71%, so raising has an EV of roughly -16 chips versus -20 for folding.