Showdown Hold'em table

J5 offsuit is below the published 4x threshold (J8s+ or JTo), so checking preserves option to raise later.

Two pair jacks and fives on a rainbow flop is a strong made hand ahead of most dealer holdings, so raising 2x maximizes value before draws complete.

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

With 9-high on a J-7-4 board, only backdoor straight and flush draws and weak pair outs, equity is far below the threshold for a 2x raise. Checking is free and preserves the option to raise 1x on the river if improved.

On the river I have two pair, jacks and nines, which beats most dealer holdings; exact enumeration gives a large positive expectation versus folding and losing the ante and blind.

Pocket queens are well above the published 4x threshold of 33+, giving strong equity against a random dealer hand and qualifying hands.

K8 offsuit meets the published optimal 4x threshold of K5o+, so raising the maximum preflop maximizes expected value.

J8 offsuit is below the optimal 4x preflop range (J8s+ or JTo), so checking preserves the option to raise later with more information.

Top pair of Jacks on a J-9-3 flop is well ahead of a random dealer hand with positive showdown equity, so committing the larger 2x raise now has higher expected value than checking to raise only 1x later.

8-6 offsuit is below the optimal 4x 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.

Only a gutshot to a ten-high straight with no pair or flush draw; raising 2x risks extra chips with low equity, while checking preserves the cheap 1x river decision if I improve.

King-high 8-kicker wins only against unpaired non-Ace/non-Queen dealer hands and ties with an 8; exact enumeration gives about -21.9 chips versus -20 for folding.

Pocket 3s meet the published optimal 4x threshold of 33+, so raising 4x preflop maximizes expected value.

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

K6 offsuit meets the published optimal 4x threshold of K5o+, so raising 4x preflop maximizes expected value.

QJ offsuit meets the published optimal 4x preflop range (Q8o+), so raising 4x maximizes expected value.

K5 offsuit meets the published optimal 4x threshold of K5o+, so raising 4x preflop maximizes expected value.

Q2 offsuit is below the Q8o+ threshold for a preflop 4x raise, so checking preserves option to raise 2x on a good flop or fold cheaply later.

With only queen-high, no pair and no strong draw on a K-T-7 board, raising 2x has negative value since the dealer never folds. Checking is free and preserves the option to raise 1x on the river only if I improve.

Exact river enumeration gives about 204 wins, 21 ties and 765 losses out of 990 dealer holdings; raising loses about 1.96 antes on average versus 2 antes for folding, so a 1x raise is marginally better.

8d2d is below the optimal 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves option to raise later or fold cheaply.

Weak high-card hand with only backdoor diamond and straight draws on a Q-J board; against a dealer who never folds, raising 2x has negative value, so check to realize equity cheaply and decide on the river.

River Queen-high with 8 kicker wins only about 24 of 990 dealer holdings and ties 21, so raising 1x has far worse expected value than folding and losing the ante and blind.

T7 offsuit is below the optimal 4x raising range (JTo+ for jack-high), so checking preserves option to raise 2x on flop or 1x/fold on river.

Ten-high with only a gutshot to a jack-high straight and no pair or flush draw is too weak to commit 2x on the flop. Checking preserves equity cheaply for an optimal river decision.

On the river I have a pair of tens. Exact enumeration gives about 361 winning, 28 tying and 601 losing dealer holdings, for an expected value near -13 chips versus -20 chips for folding, so raising 1x is better than folding.

Q5 suited is below the published 4x raising range (Q6s+ or Q8o+), so checking preserves the option to raise 2x on a favorable flop or 1x/fold on the river.

I have a pair of fives using a hole card with a queen kicker on an ace-ten-five board, which is ahead of most random dealer holdings and has outs to two pair or trips. Its showdown equity is high enough that getting 2x paid on wins outweighs waiting for only a 1x river raise.

7-8 offsuit is below the optimal 4x/3x 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 of 8s on a low unpaired flop beats all unpaired dealer hands and most pocket pairs, giving equity well above the threshold to commit the larger 2x raise rather than check.

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

Jack-high with no pair and no meaningful draw on the 3-T-6 board has low equity against a random dealer hand, so raising 2x would commit extra chips negatively. Checking preserves the option to raise 1x on the river only if the runout improves the hand.

Board is paired so dealer always qualifies. My pair of 3s with J-T-6 kickers beats only about 132 of 990 dealer holdings and ties 21, with 5*W+3*T<1, so raising 1x has lower EV than folding.

K6 suited meets the published optimal 4x preflop threshold of K2s+, so raising 4x maximizes expected value.

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

K3 offsuit is below the K5o+ threshold for a 4x raise, and a 3x raise would overcommit with a weak kicker. Checking preserves the option to raise 2x on a favorable flop or fold later.

King-high with only backdoor flush and straight draws is too weak to commit 2x on the flop; checking preserves the option to raise 1x on the river if I improve and to fold cheaply otherwise.

Board pair gives K-Q-T kickers; exact count gives 276 wins, 69 ties, 645 losses in 990 dealer holdings, so raising 1x (about -14 chips) beats folding for -20.

2c4c 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.

Weak bottom pair of 4s with a 2 kicker on a T-5-4 board has only modest equity against a random dealer hand and many turn/river cards can overtake it. Checking is free and preserves the option to raise 1x or fold on the river with full information, which is better than committing 2x now.

Two pair 5s and 4s with Ace kicker beats random dealer about 541/990 with 70 ties; raising loses only ~0.06 ante in expectation versus losing 2 antes by folding, and dealer always qualifies on the paired board.

J5 suited is below the optimal 4x threshold of J8s+ or JTo, so checking preserves the option to raise 2x on a favorable flop or 1x on the river.

Jack-high with no pair and no flush or open-ended straight draw on a K-T-7 board has low showdown equity; checking preserves the free turn/river and optimal 1x river option instead of committing 2x now.

Pair of Jacks beats many dealer high-card and lower-pair holdings; exact river equity gives a raise expected loss well under the 2-unit cost of folding.

K6 offsuit meets the published optimal 4x preflop threshold of K5o+, so raising 4x maximizes expected value.

T3 offsuit is below the published 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves the option to raise 2x on a favorable flop or 1x/fold on the river.

With only ten-high, a gutshot to a five and overcard outs, raising 2x has lower expected value than checking for free and deciding on the river with optimal fold/raise play.

I have a 2-6 straight on a board where the dealer can only beat me with 3-7 or 7-8 for a higher straight (28 of 990 holdings), ties with any 3, and otherwise loses, so raising 1x has far higher EV than folding.

Q7 suited meets the published optimal 4x threshold of Q6s+, so raising 4x preflop maximizes expected value.

A6 offsuit is any ace, which is in the published optimal 4x preflop raising range, maximizing EV versus checking.

5c2h is far 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.

Weak 5-high with only a gutshot to a straight on the 7-9-8 flop; equity is far too low to commit a 2x raise, so check and re-evaluate on the river.

Pair of 2s beats all 376 dealer high-card holdings out of 990 and ties 22, for a raise EV of about -1.41 antes versus -2 antes for folding.

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

9-2 offsuit is well below the optimal 4x raising range (33+, any ace, strong kings/queens/jacks), so raising would be negative EV. Checking preserves the option to raise 2x on a favorable flop or fold later.

Top pair of 9s on the 7-8-9 flop has sufficient showdown equity against a random dealer hand to make the 2x raise profitable, consistent with raising a pair or better on the flop rather than checking for a smaller river bet.

T2 offsuit is below the published 4x raising range (33+, any ace, K5o+, Q8o+, JTo or better suited equivalents), so checking preserves the option to raise 2x on a favorable flop or 1x/fold on the river.

Weak king-high with only backdoor straight and flush possibilities and no pair or strong draw; checking preserves the cheaper 1x river decision instead of committing 2x now.

With a board pair of queens and K-T kickers, I win against unpaired low dealer holdings and tie with some T-x hands; risking 10 more to win 20 or save 20 on a tie has higher EV than folding for -20.