Showdown Hold'em table

K9 offsuit meets the published optimal 4x threshold for kings (K5o+), so raising 4x preflop maximizes expected value.

Pocket pair 33 meets the published optimal 4x threshold of 33+, so raising 4x preflop maximizes expected value.

4s2c is well below the optimal 4x raising range (33+, any ace, strong kings/queens/jacks), so checking preserves the option to raise 2x on a favorable flop or fold later.

Bottom pair of 2s on a 5-7-2 board has below-threshold showdown equity against a random dealer hand, with no flush or strong straight draw. Checking preserves the option to raise 1x on the river only if the runout improves the hand.

Pair of twos on a four-diamond, connected board wins only against non-diamond high-card dealer hands (about 210 of 990), while most dealer holdings make a flush, pair or straight for a 30-chip loss; raising EV is below the -20 chip fold.

9-6 offsuit is below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves option to raise 2x on flop or 1x on river.

Weak pair of 9s with a 6 kicker on a J-Q-9 two-spade board is behind many dealer holdings and has few strong draws. Checking preserves the cheaper 1x river option to raise only on favorable runouts or fold, rather than committing 2x now.

Pair of 9s beats all dealer high-card hands and lower pairs; raising 1x has much higher EV than folding and forfeiting ante and blind, despite higher pairs, flushes and straights beating us.

2c3d is far below the optimal 4x raising range of pairs 33+, any ace, and strong kings/queens/jacks, so raising would risk extra chips with a very weak hand. Checking sees the flop for free while preserving flop and river options.

Bottom pair of 2s with only runner-runner flush potential is too weak to commit 2x now. Checking preserves the cheaper 1x river option and lets me fold if the board worsens.

Pair of 2s beats all unpaired dealer hands (404 of 990 combos) and ties 30, giving raise EV about -12.8 chips versus -20 for folding.

9-3 offsuit is well below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves the option to raise 2x on the flop or 1x/fold on the river.

With only 9-high, no pair and just backdoor draws on Q-T-5, raising 2x has negative expectation against a random dealer hand. Checking is free and preserves the option to fold cheaply on the river unless I improve substantially.

On the river I have only queen-high with a 9 kicker, winning against only a small fraction of the 990 dealer holdings and losing to any pair, better high card, flush or straight; the expected value of a 1x raise is below the -20 chip cost of folding.

Q2 offsuit is below the optimal 4x raising range (Q8o+ / Q6s+), so checking preserves the option to raise 2x on a favorable flop or 1x/fold on the river.

Board pair with only a Q kicker and weak 2 is vulnerable to dealer overcards, a 4, a 5, or any pocket pair; equity is too low to commit 2x now, so check to use river information for a cheaper 1x decision.

Pair of fives with A-Q-7 kickers wins against dealer holdings with two distinct low/mid cards below queen and no ace, king, board pair, flush or straight, about 26% wins plus ties, which beats the 20% threshold needed versus folding.

Ah3h is any ace (suited) which is in the published optimal preflop 4x raising range.

K8 offsuit meets the published optimal 4x threshold of K5o or better preflop, so raising the maximum maximizes value with a strong king.

9c6h is offsuit and below the published 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves option to raise 2x on flop or 1x/fold on river.

Bottom pair of 6s with only a gutshot 8 for the nut straight has well under the equity needed for a 2x flop raise. Checking is free and preserves the option to raise 1x on the river only when improved or ahead.

Two pair, sevens and sixes, beats a random dealer hand about 53% of the time with about 5% ties against 43% losses; raising 1x has far higher expected value than folding and forfeiting the ante and blind.

Q3 offsuit is below the optimal 4x raising range (Q8o+ / Q6s+), so checking preserves optionality to raise 2x on a good flop or 1x/fold on the river.

With 2-3-4-5 on board I have an open-ended straight draw to an ace or six, plus a queen overcard and backdoor diamonds, giving strong equity versus a random dealer hand. This draw is strong enough to raise 2x on the flop rather than check and only get 1x on the river.

K2 suited meets the published optimal 4x preflop table (K2s+), so raising the maximum captures value with a strong king suited hand.

Pocket Kings are well above the optimal 4x raising threshold of 33+, giving strong equity against the dealer.

T8 offsuit is below the published 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise 2x on the flop or 1x on the river with more information.

Second pair of tens with a weak 8 kicker on a Q-high board is only medium strength against a random dealer hand. Checking preserves the option to raise 1x on the river with more information rather than committing 2x now.

On the river I have a pair of tens with ace-queen kickers. Exact enumeration gives 655 winning, 6 tying and only 329 losing dealer holdings out of 990, for about -0.8 chips versus -20 chips folding, so raising 1x is far better.

A4o is any ace, which is in the published optimal 4x preflop range, so raising 4x maximizes expected value.

Pocket 9s are in the published optimal 4x range (33+), so raising the maximum preflop maximizes expected value.

K7 offsuit meets the published optimal 4x threshold of K5o+, so raising the maximum preflop maximizes expected value.

T6 offsuit is below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves EV and lets me evaluate the flop.

With Tc6h on Td6s6d I have a full house, sixes over tens, which will beat the dealer the vast majority of runouts. Raising 2x now maximizes the 1:1 play bet and preserves the 3:1 blind payout for a full house versus checking for only 1x later.

K2 offsuit is below the optimal 4x raising range, which requires K5o+ or K2s+, so checking preserves the option to raise later with more information.

King-high with no pair and only weak backdoor draws on T-8-3 is not strong enough to commit 2x now. Checking preserves the cheaper 1x river decision after seeing the full board.

King-high loses to any dealer pair, straight, or ace/king-better-kicker hand; exact river enumeration gives fewer wins and ties than qualifying dealer losses, so raising 1x has lower EV than folding.

4s2h is well below the optimal 4x raising range (33+, any ace, strong kings/queens/jacks), so checking preserves the option to raise 2x on a good flop or 1x/fold on the river.

Bottom pair with a low four-flush draw has only moderate showdown equity; checking preserves the option to raise 1x or fold on the river rather than committing 2x now.

On the river I have two pair, nines and twos, which beats any dealer holding that only plays the board pair of nines. That is over half of the 990 dealer combinations, so raising 1x has a much higher expected value than folding and losing the ante and blind.

2d4c is well below the optimal 4x raising range (33+, any ace, strong kings/queens/jacks), so checking preserves the option to raise 2x on the flop or 1x/fold on the river.

Bottom pair of 2s on a K-J board has low showdown equity and no strong draw; checking preserves the option to fold on the river or raise 1x only if the runout improves the hand, rather than committing 2x now.

With a pair of 2s I beat all unpaired dealer high-card hands (about 404 of 990 holdings) and tie about 30, giving a raise EV around -12.8 chips versus -20 for folding.

Pocket 2s are below the published 4x raising range of 33+, so raising preflop is negative EV; check to see the flop cheaply.

Pocket deuces are only a low underpair on the J-8-4 flop, likely below 50% equity against a random dealer hand. Checking preserves the option to raise 1x on the river or fold, rather than committing 2x while behind most made hands and vulnerable to overcards.

Pair of 2s beats all 288 non-qualifying dealer high-card holdings out of 990, giving a raise EV of about -18.3 chips versus -20 chips for folding.

QJo is above the Q8o+ threshold in the published optimal 4x preflop table, so raising 4x maximizes expected value.

A7 offsuit is any ace, which is in the published optimal 4x preflop range, maximizing EV versus checking.

K5 suited meets the published optimal 4x preflop threshold (K2s+), so raising 4x maximizes expected value.

K9 offsuit meets the published optimal 4x preflop table (K5o+), so raising 4x maximizes expected value.

J9 suited meets the published optimal 4x threshold of J8s+, so raising 4x preflop maximizes expected value.

Any ace is in the published optimal 4x preflop range, so raising 4x maximizes expected value over checking.

8-6 offsuit is well below the published 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves optionality to raise 2x on a favorable flop or 1x/fold on the river.

Trip eights on the flop is a very strong made hand, beating two-pair and overpair hands and losing only to rare full houses or a better-kicker eight, so raising 2x maximizes value.

K2 offsuit is below the optimal 4x range (K5o+ or K2s+), so checking preserves the option to raise 2x on the flop or 1x on the river with more information.

King-high with no pair, flush draw, or strong straight draw is too weak to commit 2x on the flop. Checking preserves the cheaper 1x river decision if we improve.

With a pair of 2s I beat all dealer high-card hands and low-kicker pair-of-2s hands; exact enumeration gives a raise EV of about -1.17 antes versus -2 antes for folding, so raising 1x loses less.