Showdown Hold'em table

KJo is K5o+ in the published optimal 4x preflop table, so raising 4x maximizes expected value.

6-7 offsuit is below the optimal 4x/3x raising range (33+, any ace, strong K/Q/J hands), so checking preserves the option to raise 2x on a favorable flop or 1x/fold on the river.

Weak 7-high with only backdoor flush and straight draws, not a 4-flush or open-ended draw worth a 2x raise; checking keeps the free card and optimal river option.

We have an 8-high straight; dealer can only beat it with two spades or two hearts for a flush (90 of 990 holdings), ties with 6-7, and loses otherwise, so raising has far higher EV than folding.

A5 offsuit is any ace, which is in the published optimal 4x preflop raising range.

Q7 offsuit is below the published 4x raising threshold of Q8o+, so checking to see the flop preserves EV over committing 3x or 4x preflop.

Flopped top pair of queens on a dry 9-6-Q rainbow board, which is well ahead of a random dealer hand and strong enough that the extra 2x play bet has positive expectation over checking to a 1x river bet.

9-5 offsuit is below the optimal 4x/3x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves option to raise later with more information.

With 9-high, no pair and only weak runner-runner straight possibilities on 7d-Jc-2s, raising 2x has poor equity. Checking keeps the cheaper 1x river option if the hand improves.

We have two pair, nines and twos with a jack kicker on a paired board. Dealer only beats us with a two, jack, high-kicker nine, big pocket pair, or 8-T for a straight, roughly 28% of holdings, so raising 1x is far better than folding.

6-2 offsuit is well below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo+ etc.), so checking preserves the option to raise later with more information.

Weak 6-2 with only a backdoor diamond draw on 9d-Th-3d; raising 2x has negative expectation versus checking free and re-evaluating on the river.

Board pair of 3s with Q-T-9 kickers means my 6-2 can never win, only tie when dealer has two unpaired low non-diamond cards below 9; that is about 191/990, below the 1/3 tie rate needed to justify the 1x raise.

J5 offsuit is below the optimal 4x raising range (J8s+ or JTo), so checking preserves the option to raise later with more information.

J-high with only a gutshot to a straight has well under 50% showdown equity, so a 2x raise has negative expected value. Checking keeps the option to raise 1x on the river if I improve and fold if I miss.

Pair of 5s wins against 437 of 990 dealer holdings and ties 6, giving a raise EV of about -10.9 chips versus -20 chips for folding.

AQ offsuit is an ace hand in the published optimal 4x preflop table, so raising 4x maximizes expected value.

Qd Td is queen-ten suited, which falls within the published optimal 4x range of Q6s or better preflop. Raising 4x maximizes expected value with this strong suited broadway hand.

J9 offsuit is below the published 4x threshold of JTo or J8 suited, so raising preflop is negative EV. Check to see the flop for free.

Top pair of Jacks with a 9 kicker plus backdoor flush and straight draws has strong equity against a random dealer hand, so raising 2x now puts more money in while ahead than checking to a 1x river decision.

6-7 offsuit is outside the optimal preflop 4x raising range (33+, any ace, strong K/Q/J hands), so checking preserves option to raise 2x on flop or 1x/fold on river.

With only a low pair of 7s on a K-T-7 board, no flush or open-ended straight draw, and many dealer holdings ahead, equity is too low to commit 2x now; checking preserves the option to raise 1x on a favorable river or fold.

Pair of 7s wins against many high-card and lower-pair dealer hands; raising 1x loses only 10 extra when beaten but can win 10-20, giving about -8 chips EV versus -20 for folding.

J7 offsuit is below the optimal 4x threshold of JTo or J8s+ and is not a pair, ace, or qualifying king/queen hand, so checking preserves EV to evaluate the flop.

Weak jack-high with only backdoor flush and two-card straight draws on a K-Q board; checking preserves the cheaper 1x river option if the runout improves.

Ace-high J-7 beats 332 of 990 dealer holdings, ties 9, and loses to 649; raising nets about -16.1 chips versus -20 for folding, since wins against non-qualifying dealer hands pay the play bet while the ante and blind push.

J9 offsuit is below the optimal 4x raising range (J8s+ or JTo+), so checking to see the flop preserves EV over committing 3x/4x.

J-high with no pair and no meaningful draw on a king-high flop has low equity against a random dealer hand, so raising 2x is negative EV. Checking keeps the hand alive cheaply for optimal 1x river play if it improves.

Pair of 9s on a four-heart board wins against non-heart high-card and lower-pair dealer hands often enough that the 1x raise EV, about -1.24 antes, is better than folding for -2 antes.

4c5c suited is below the published 4x range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking to see the flop cheaply maximizes EV over raising.

Flopped two pair, kings and fours, ahead of most dealer holdings without a king, a four, or a higher pocket pair, and the paired board means the dealer always qualifies, so raising 2x maximizes value from this made hand.

Ad Jd is suited ace-high, which falls in the published optimal 4x range of any ace preflop. Raising 4x maximizes value with this strong holding.

9s5h 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/fold on river.

Top pair on the flop has strong equity against a random dealer hand, enough to justify committing the 2x raise now rather than risking only 1x on the river.

K4 offsuit is just below the published 4x threshold of K5o+, so raising preflop is not profitable; checking preserves flop 2x and river 1x options at lower risk.

King-high with only backdoor flush and backdoor Broadway draws on Q-T-3 is too weak to commit 2x on the flop; checking preserves the option to raise 1x or fold on the river.

King-high on Q-T-9-8 board only beats unpaired low dealer holdings and ties some K-low hands, while any pair, straight with a Jack, or Ace-high beats it; the raise EV is below the -2 ante fold cost.

ATo is an ace hand, which is in the published optimal 4x preflop range, so raising 4x maximizes expected value.

T4 offsuit is below the published 4x raising range (33+, any ace, strong K/Q/J hands), so checking to see the flop for free is optimal.

With ten-high, no pair, no flush draw and only weak runner-runner straight possibilities on the 5-6-J flop, raising 2x has negative expected value. Checking is free and preserves the option to raise 1x or fold on the river with full information.

Ace-high with a ten kicker wins only against lower unpaired dealer hands and ties with ten plus low card; most dealer holdings make a qualifying pair or better, giving raising a worse expected value than folding.

9-5 offsuit is below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo+), so checking preserves option to raise 2x on a favorable flop or fold later.

9d5h on 3h4dTs is only nine-high with a weak gutshot and no flush draw, well below a profitable 2x flop raise. Checking preserves the cheaper 1x river decision after seeing both remaining cards.

With only a pair of tens and J-9-5 kickers, exact enumeration gives about 146 wins and 9 ties in 990 dealer holdings, below the threshold needed for a 1x raise versus folding.

J2 offsuit is well below the optimal 4x raising range (J8s+ or JTo), so checking preserves the option to raise 2x on a favorable flop or fold later.

J-high with no pair and only a backdoor straight draw on an ace-high flop is too weak to commit 2x; checking preserves the cheaper 1x river decision if we improve.

With only ace-high J-9-8-7, most dealer holdings make a pair or a better high card; exact enumeration gives about -22.2 chips for raising versus -20 for folding.

2s5s is below the optimal 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves option to raise 2x on a favorable flop or fold later.

Four spades give a flush draw, but with only Jack-high and low hole cards showdown equity is well below half. Checking sees the turn and river free and preserves the cheaper 1x river raise when the draw completes, rather than committing 2x while behind.

I have a Jack-high flush on a paired board. Only 56 of 990 dealer holdings beat it (two spades for a higher flush, or a 4/board-rank combination for a full house or quads), so raising 1x has far higher EV than folding.

J2 offsuit is below the optimal 4x raising range (J8s+ or JTo, any ace, etc.), so checking preserves optionality to raise on the flop or river.

With only ace-high jack kicker on an ace board and weak runner-runner club/straight draws, equity is far too low to commit 2x with no fold equity. Checking preserves the option to fold cheaply or raise 1x on the river only if improved.

Pair of Jacks on this board beats most random dealer holdings, including Ace-high and smaller pairs, and the exact river equity makes raising 1x far better than folding the ante and blind.

QJo meets the published optimal 4x preflop table (Q8o+), so raising 4x maximizes expected value over checking or a smaller raise.

8-4 offsuit is well below the optimal 4x raising range of pairs 33+, any ace, and strong king/queen/jack hands. Checking preserves the option to raise 2x on the flop or 1x/fold on the river with more information.

With only the board pair of tens and an 8 kicker on Td7hTs, my equity against a random dealer hand is far too low to commit a 2x raise. Checking is free and preserves the option to raise 1x or fold on the river after seeing the full board.

On the river I have two pair, tens and fours, which beats a dealer holding only the board pair of tens. Exact enumeration gives about a 66% win rate, well above the ~20% needed to justify a 1x raise over folding.

A7o is an ace hand, which is in the published optimal preflop 4x raising range (any ace). Raising 4x maximizes expected value versus checking.

98o is below the published 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves the option to raise 2x on the flop or 1x on the river with more information.

Only the board pair of sixes with 9-8 kickers and no flush or open-ended draw; raising 2x risks extra chips with a weak, easily out-kicked hand, while checking lets me improve to two pair or a straight and fold on the river if unimproved.

On the river I have only a pair of sixes with A-K-9 kickers. Exact equity is slightly below the threshold for a 1x raise, with an expected loss worse than folding and surrendering the ante and blind.

T2 suited is below the optimal 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves option to raise 2x or 1x with more information.

With only an open-ended straight draw and backdoor flush draw on the flop, checking preserves the option to raise 1x on the river when the draw completes and fold for just the ante and blind when it misses, which is better than committing 2x now with modest equity.

Jack-high with a ten kicker wins only against a small range of dealer high-card hands, ties few, and loses to any pair or higher kicker; raising 1x has much worse expected value than folding and losing the ante and blind.

J5 offsuit is below the optimal 4x raising range (J8s+ or JTo), so checking preserves EV by seeing the flop without committing extra chips.

J5 on a T44 board is only the board pair with a jack kicker, losing to most high kickers, tens, and pocket pairs, with no flush or straight draw. Checking preserves the option to raise 1x only if the runout improves the hand, rather than committing 2x now.

Board pair means dealer always qualifies. I win with low unpaired dealer cards (~220/990), tie ~69/990, giving raise EV about -16.8 chips versus -20 for folding, so raising 1x is better.

K3 offsuit is below the K5o+ threshold for an optimal preflop 4x raise, so checking preserves the option to raise later at lower cost.

King-high with no spade and only runner-runner straight potential on a monotone 4-5-9 flop is too weak to raise 2x; checking preserves the option to raise 1x or fold on the river.

Pair of Kings with Ace kicker wins against about 454 of 990 dealer holdings, ties 10, and raising expects about -9 chips versus -20 for folding, so raising 1x is better.