Showdown Hold'em table

J6 offsuit is below the published 4x raising range (J8s+ or JTo), so checking preserves option to raise later with more information.

Jack-high with no pair, no four-flush and only gutshot outs is too weak to commit 2x on the flop; checking preserves optimal river decision.

On this paired board my pair of nines with J-6 kickers beats only about 12% of dealer holdings, with about 1% ties; raising 1x has lower expected value than losing the ante and blind by folding.

AK suited is a premium ace hand, which is in the optimal 4x preflop raising range.

J4 suited is below the published 4x raising range (J8s+ or JTo), so checking preserves the option to raise 2x on the flop or 1x on the river with more information.

J-high with only a gutshot to the straight (four Ten outs) and backdoor clubs is too weak to commit 2x now; checking preserves the cheap 1x river option if we improve.

With a pair of 7s and Q-J-9 kickers I win about 19% and tie about 6% against a random dealer, who always qualifies on the paired board; that makes the 1x raise slightly better than forfeiting the ante and blind by folding.

A5 offsuit is any ace, which is in the published optimal 4x preflop range, maximizing value before the board.

6c7s offsuit is below the optimal 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves option to raise 2x on flop or 1x/fold on river.

Top pair of sixes on a low 6-2-3 flop is a made hand likely ahead of a random dealer holding, with additional improvement outs, so committing the 2x flop raise has higher expected value than checking to a smaller river bet.

J2 offsuit is below the optimal 4x raising range (J8s+ or JTo), so checking preserves option to raise later with more information.

Jack-high with no pair and only weak backdoor straight/club potential is not strong enough to commit 2x on the flop. Checking is free and preserves the option to raise 1x or fold on the river with more information.

Ace-high with a Jack kicker wins only 128 of 990 dealer holdings and ties 33, while 613 qualifying losses cost the full ante, blind and play bet; the raise EV is about -2.16 antes versus -2 for folding.

7-3 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 a favorable flop or fold later.

Paired the 7 on a K-7-2 board, giving roughly 55-60% showdown equity against a random dealer hand. With equity above 50%, committing 2x now has higher expected value than checking for a cheaper 1x showdown, despite the weak kicker.

6d7d suited 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 a favorable flop or 1x/fold on the river.

Middle pair of 7s on a K-high, two-club flop has only marginal showdown equity against a random dealer hand. Checking preserves the option to raise 1x on the river with full board information or fold if the runout worsens, which is better than committing 2x now.

Pair of 7s on this board beats a majority of random dealer holdings, including ace-high and smaller pairs, so raising 1x has much higher expected value than folding and forfeiting ante and blind.

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

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

6h5d is 65 offsuit, well below the optimal 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise later with more information.

Open-ended straight draw with eight outs to a blind-paying straight, plus backdoor hearts and pair outs, has enough two-card equity to raise 2x on the flop rather than check.

J8 offsuit is below the optimal 4x threshold, which requires J8 suited or JT offsuit or better, so checking preserves EV by seeing the flop cheaply.

J-high with no pair or draw on a K-3-2 board is too weak to commit a 2x raise against a random dealer hand. Checking is free and preserves the option to raise 1x on the river only if the runout improves the hand.

On the river I have only ace-high J-8 kickers. I beat only 168 of 990 dealer holdings, tie 9, and lose to any pair, a 5 for a wheel, or a better high card, giving a raise EV of about -2.18 antes versus -2 for folding.

K9 suited meets the published optimal 4x preflop table (K2s+), so raising 4x maximizes expected value.

8d7d suited 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 a favorable flop.

With only a gutshot to the straight and no pair, flush draw, or overcards, raising 2x commits too much with low equity. Checking is free and preserves the option to raise 1x on the river only if the draw or a pair improves.

Ace-high with 8-7 kickers beats only about 12% of dealer holdings, mostly low non-qualifying hands, while over 60% of dealer holdings qualify with a pair or better and beat us, making raising worse than folding.

A4 offsuit is any ace, which is in the published optimal 4x preflop raising range, maximizing EV versus checking.

J9 offsuit is below the optimal 4x raising range (J8s+ or JTo+), so checking preserves the option to raise 2x on the flop or 1x on the river with more information.

J-high with no pair, no flush draw and only weak backdoor gutshots on 3-5-7 is too weak to raise 2x; checking preserves option to raise 1x or fold on the river after seeing the full board.

J-high on a 3-5-7-4-T board beats only unpaired, non-flush dealer high cards with no A/K/Q, pair, or 6 for a straight; most dealer holdings win and usually qualify, making a 1x raise worse than folding.

6-3 offsuit is well below the optimal 4x raising range (33+, any ace, strong K/Q/J), so checking preserves the option to raise later or fold cheaply.

Bottom pair of 3s on a 9-high two-heart board has low showdown equity against a random dealer hand and no strong draw. With no fold equity, committing 2x now is worse than checking to use river information and only raise 1x when improved or favorably situated.

I have trip 3s on a paired board; dealer always qualifies, and only about 74 of 990 dealer holdings (a remaining 3 with a better kicker/full house, matching pocket pairs, or a 4-6/A-4 straight) beat me, so raising 1x has strongly positive EV versus folding.

9-4 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 9-high, no pair and no strong draw on a J-5-3 flop, raising 2x is negative EV; checking is free and lets us improve or fold cheaply on the river.

Board pair of 3s with J-9-5 kickers wins only about 109 of 990 dealer holdings and ties 9, giving a raise EV below the -2 ante fold cost.

J6 offsuit is below the optimal 4x range (J8s+ or JTo), so raising preflop is negative EV. Check to see the flop cheaply and decide later.

Jack-high with no pair and only weak backdoor draws is too weak to commit 2x on the flop; checking sees the turn and river for free and preserves optimal river play.

Board is two pair with my Jack kicker; I win against low non-pairing dealer holdings and tie with a Jack, giving about 226 wins and 69 ties in 990 holdings. Raising 1x loses only 10 extra when beaten but gains 40 when winning and 20 when tying versus folding, so it has higher EV than folding.

Pocket aces are in the published optimal 4x preflop range (33+), so maximizing the play bet now has the highest expected value.

T8 suited 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 a good flop or 1x on the river.

Pair of 8s plus a four-card spade flush draw on the flop has strong showdown and improvement equity, favoring committing the 2x raise now over waiting for only a 1x river raise.

3d4h offsuit is well below the optimal 4x raising range of pairs 33+, any ace, and strong kings/queens/jacks, so checking preserves the option to raise later with more information.

With only the board pair of queens, low kickers, and a runner-runner heart draw, equity is too weak to commit 2x now. Checking preserves the cheaper 1x river decision after seeing the full board.

My hole cards do not play; my best hand is the board pair of Queens with A-J-7 kickers, so I can never beat the dealer, only tie when the dealer also plays the board. Raising expects about -26 chips versus -20 for folding.

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

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

JTo meets the published optimal 4x preflop threshold (J8s+ or JTo), so raising 4x maximizes expected value.

KQo is well above the K5o+ threshold in the optimal preflop 4x table, so raising 4x maximizes expected value.

T6 offsuit is below the published 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves the flop 2x and river 1x options at lower risk.

With T-6 on an A-Q-7 board I have only ace-high, no pair, no flush draw and only runner-runner straight possibilities. Raising 2x would risk extra chips with very low equity, so checking to see the turn and river for free is best.

I play the board pair of 7s with A-K-Q kickers and can only tie or lose. Dealer ties with 501 of 990 holdings that do not pair the board, form a pocket pair, or make Broadway, so raising costs about 1.48 antes on average versus 2 antes for folding.

4c5s is a weak offsuit low hand outside the optimal 4x raising range (33+, any ace, strong K/Q/J), so checking preserves optionality to raise 2x on a good flop or fold later.

With only a gutshot to a 6 and no pair or four-flush on Ac7c8s, raising 2x has negative expectation versus a random dealer. Checking preserves the free runout and the option to raise 1x on the river only if improved.

On the river I only have the board pair of 7s with A-8-5 kickers. Almost any dealer holding pairs the board, makes two pair, a higher kicker, or better, leaving only about 12 winning and 20 tying combos out of 990, far below the equity needed to raise.

Ad4s is an ace hand, which is in the published optimal preflop 4x raising range (any ace). Raising 4x maximizes expected value versus checking.

J5 suited is below the J8s+ threshold for an optimal 4x preflop raise, so checking preserves the option to raise 2x on a favorable flop or 1x/fold on the river.

J-high with no pair, flush draw, or straight draw on a Q-2-7 rainbow flop has low equity versus a random dealer hand; checking preserves the option to raise 1x on the river only if I improve.

Board is paired Q-Q-7-7 and I have a J kicker. I win against lower kickers and lower pocket pairs, tie with a Jack, and raising loses about 6.4 chips on average versus 20 chips for folding.