Showdown Hold'em table

8-6 offsuit is below the optimal 4x raising range (33+, any Ace, strong K/Q/J hands), so checking preserves option to raise later or fold cheaply.

Bottom pair of sixes with an eight kicker and only backdoor draws is too weak to commit 2x now; checking preserves the cheaper 1x river decision after seeing the turn and river.

On the river I have two pair, tens and sixes with a nine kicker, which beats dealer ace-high and lower two-pair holdings in a clear majority of the 990 dealer combinations, well above the roughly 20% win rate needed to raise 1x rather than fold.

K3 offsuit is below the optimal 4x threshold of K5o+ (and not suited), so checking preserves option to raise 2x on flop or 1x on river.

Flopped top two pair Kings and eights on a dry rainbow board, well ahead of most dealer holdings and unlikely to fold on the river, so raising 2x now gets maximum value.

A7 offsuit is any ace, which is in the published optimal 4x preflop range, so raising 4x maximizes expected value.

T4 offsuit is below the optimal 4x raising range (33+, any ace, strong K/Q/J hands), so checking preserves EV and lets me evaluate the flop cheaply.

Ten-high with only backdoor flush and straight draws on a Q-6-3 flop has low equity versus a random dealer hand, well below the threshold for a 2x flop raise. Checking preserves the cheaper 1x river decision after seeing the full board.

Pair of 4s wins against about 423 of 990 dealer holdings, mostly non-qualifying high cards. Raising 1x has EV about -1.16 antes versus -2 antes for folding, so raising is better.

A3o is any ace, which is in the published optimal 4x preflop range, maximizing EV versus checking.

8s5d offsuit is below the published 4x raising range (33+, any ace, K5o+, Q8o+, JTo or better suited equivalents), so checking preserves optionality to raise 2x on a favorable flop or 1x/fold on the river.

With 8-5 and no pair, flush draw, or meaningful straight draw on a K-J-T flop, raising 2x has negative expectation; checking preserves the option to raise 1x or fold on the river.

With a pair of 8s, raising loses less on average than folding the ante and blind for certain; many dealer hands are unqualified high cards or lower pairs that we beat.

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 on a good flop or fold cheaply.

Only a gutshot to Broadway with Ten-high on an A-K-J board; raising 2x has negative equity versus a random dealer, while checking is free and preserves the river 1x/fold option.

With Aces and Tens on a paired-Ace board I win against all dealer holdings without an Ace, King, Jack, Queen or Ten, roughly tying the dealer's win rate; raising 1x loses far less on average than folding and forfeiting the ante and blind.

T9 offsuit is below the published 4x raising range (JTo or better for offsuit broadway), so checking preserves option to raise 2x on flop or 1x on river.

Top pair of nines with a ten kicker on a 9-7-2 board is ahead of a random dealer hand often enough to commit the 2x raise, with added value protecting against diamond and overcard draws.

2s8s is below the optimal 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.

With 8-high, no pair and no meaningful draw on Kd-4d-9h, raising 2x has negative expected value. Checking is free and preserves the option to raise or fold on the river after seeing the full board.

On the river I have only ace-high A-K-J-9-8. Any dealer pair or Q/T kicker beats me (789 of 990 holdings), I win only 144 and tie 57, giving a raise EV of about -20.7 chips versus -20 for folding.

Pocket nines are 33+ in the published optimal 4x preflop table, so raising 4x maximizes expected value.

7-4 offsuit is below the published 4x raising range of 33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo, so checking preserves optionality to evaluate the flop.

7s4d on Ts2c5c has no pair and no strong draw, only weak pair outs, so raising 2x is negative EV versus checking to realize cheap river equity.

Board trips give me only T-7 kickers; dealer beats me with any full house, quad, or J+ / 8+ kicker, winning only about 40 of 990 holdings, so raising 1x has worse EV than folding and losing ante+blind.

A6 offsuit is any ace, which is in the published optimal 4x preflop range, maximizing EV by raising the maximum early.

AJ offsuit with any ace meets the published optimal 4x preflop table, maximizing value with a strong ace-high hand.

Q4 offsuit is below the optimal 4x raising range (Q8o+), so checking preserves the option to raise 2x on the flop or 1x/fold on the river with more information.

Pair of queens with the ace on board as kicker is ahead of most dealer holdings and has positive showdown equity, so raising the larger 2x now is worth more than waiting for only a 1x river bet.

Pocket sixes are 33+ in the published optimal 4x preflop table, so raising 4x maximizes expected value.

J3 offsuit is below the optimal 4x threshold of J8s+ or JTo and is not a pair, ace, or qualifying king/queen hand. Checking preserves the option to raise 2x on a favorable flop or 1x/fold on the river.

Board pair of tens with only a jack kicker is below 50% equity against a random dealer hand, so raising 2x is worse than seeing the runout cheaply and deciding for 1x on the river.

With two pair tens and sevens and a jack kicker, I win about 310 of 990 dealer holdings and tie 78, giving a raise EV of about -12 chips versus -20 for folding. Raising 1x therefore loses less than folding.

9c6c suited is below the published 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves option to raise 2x on a favorable flop or 1x/fold on the river.

Middle pair of sixes with a nine kicker is ahead of most random dealer holdings on this T-6-2 flop, with chances to improve to trips, two pair, a flush, or a straight, making a 2x raise positive expectation over checking.

2-3 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 only if the flop improves it.

Bottom pair plus an open-ended straight draw (any ace or six makes a straight) gives strong equity and many improving outs, meeting the flop 2x raising threshold versus a random dealer hand.

K8 suited falls in the published optimal 4x range (K2s+), so raising 4x preflop maximizes expected value.

Q4o is below the optimal 4x range (Q6s+ or Q8o+), so checking preserves the option to raise 2x on the flop or 1x on the river with more information.

Queen-high with only a backdoor diamond draw has low showdown equity against a random dealer hand, so raising 2x is not value. Checking preserves the option to raise 1x on the river if I improve or fold cheaply if I miss.

With only queen-high on the river, I beat only non-paired, non-flush dealer high cards below a queen; most dealer holdings make a pair or better, so raising 1x has lower expected value than folding.

J9 offsuit is below the JTo threshold for a preflop raise in the optimal 4x table, so checking preserves value by seeing the flop cheaply.

Top pair of Jacks on a T-J-3 flop is a made hand ahead of most dealer holdings, meeting the standard flop 2x raise threshold for a pair or better despite the modest kicker.

J7 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.

Jack-high with no pair and no strong draw on an ace-high flop has low equity against a random dealer hand; checking preserves the cheaper 1x/fold river decision instead of committing 2x now.

Ace-high with J kicker beats dealer's unpaired non-King hands often enough; exact enumeration gives about -18.9 chips EV for calling versus -20 chips for folding.

Q7 offsuit is just below the published Q8o+ threshold for a 4x preflop raise, so checking to see the flop cheaply has higher expected value than committing 3x or 4x.

Middle pair of 7s with a queen kicker on a K-8-7 board is marginal against a random dealer hand; checking preserves the option to raise 1x or fold on the river after seeing both remaining cards rather than committing 2x now.

Pair of 7s with Q kicker beats about half of random dealer holdings, including all non-qualifying high cards and lower pairs, making the 1x raise EV well above folding and losing ante plus blind.

2-4 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 a favorable flop or fold later.

2h4s on 8s3hJh is only jack-high with weak runner-runner straight and backdoor heart draws, far too weak to commit 2x. Checking is free and preserves the option to fold or raise 1x on the river if we improve.

Our best hand is just the board pair of 3s with J-8-5 kickers, which the dealer can always at least play. The dealer never loses and only ties with an unpaired 2-4 holding, so raising 1x has far worse EV than folding.

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

AKo with any ace is in the published optimal 4x preflop range, maximizing value with a premium hand.

Q3 offsuit is below the optimal 4x range (Q8o+ or Q6s+), so checking preserves option to raise 2x on flop or 1x on river.

Flopped two pair, queens over eights, giving strong equity against a random dealer hand. Raising 2x now puts the larger play bet in while ahead rather than settling for a 1x river bet.

J5 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.

Top pair with a weak kicker on a very coordinated J-T-9 two-heart board has only marginal equity and many bad turn/river cards; checking preserves the option to fold later rather than committing 2x now.

On the river I have two pair, Jacks and Tens, which beats about 76% of the 990 dealer holdings, ties about 6%, and loses about 18%; with the board paired the dealer always qualifies, so raising 1x has strongly positive EV versus folding.

A2 suited is any ace, which is in the published optimal 4x preflop range, so raising 4x maximizes expected value.

2d5h 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 cheaply later.

Only a gutshot wheel draw with four outs and no pair or flush draw; checking sees the turn and river free and preserves the cheaper 1x river decision if we improve.

We only play the board pair of 3s with A-K-6 kickers, so the dealer can never lose and only ties with unpaired 2/4/5 hole cards (33 of 990 combos); raising expects about -29 chips versus -20 folding.