Showdown Hold'em table

T8 offsuit 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.

With ten-high and only a weak gutshot draw on an ace-high flop, raising 2x is negative EV; check to see turn/river cheaply and decide on the river.

On the paired board I only have pair of fives with A-T-8 kickers; exact enumeration gives about 136 wins and 9 ties in 990 dealer holdings, so raising 1x has lower EV than folding and losing the ante and blind.

Pocket pair 55 meets the 33+ threshold in the published optimal preflop table, so raising 4x maximizes expected value.

8-5 offsuit is well below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves option to raise later only if the flop improves it.

With only an open-ended straight draw and no pair or flush draw on a king-high flop, raising 2x commits too much while behind. Checking preserves the cheaper 1x river option if the draw completes.

Pair of 5s beats all 380 non-qualifying dealer high-card hands, plus low pocket pairs and low-kicker pair of 5s, for 422 wins and 6 ties vs 562 losses. Raising EV is about -12.3 chips, better than folding for -20 chips.

K9 offsuit falls within the optimal preflop 4x range (K5o+), so raising 4x maximizes expected value.

9-3 offsuit is well below the optimal 4x/3x 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 meaningful draw on an A-J-7 board, raising 2x has negative equity against a random dealer hand. Checking is free and lets me fold or raise 1x on the river only if I improve.

Pair of 3s beats all dealer high-card holdings; exact enumeration gives about 410 wins and 62 ties versus 518 losses, for an expected loss of about 11.5 chips versus 20 chips when folding.

Pocket jacks are well above the 33+ threshold in the optimal preflop 4x table, so raising the maximum maximizes value.

9h6h 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 1x/fold on the river.

Top pair of 6s with a 9 kicker is marginal on a wet 3c-6c-4c board where flushes and straights are already possible and a club turn is dangerous. Checking preserves the option to raise 1x on the river only when the runout improves or remains favorable, rather than committing 2x now.

Pair of sixes beats dealer's unpaired holdings and lower pairs; although a club or higher pair often wins, the expected loss from calling 1x is less than the 2 ante lost by folding.

Q4o is below the optimal 4x raising range (Q6s+ or Q8o+), so checking preserves the option to raise 2x on a favorable flop or 1x/fold on the river.

Top pair of queens made with a hole card is a strong hidden pair with positive showdown equity against a random dealer hand, justifying the larger flop raise despite the three-diamond board.

T3o is 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 on the river with more information.

T-3 has only ten-high on a Q-6-4 board with no meaningful pair, straight, or flush draw, so raising 2x has negative equity versus a random dealer hand. Checking preserves the cheaper 1x river option if the turn or river improves the hand.

On a paired queen board my pair of queens with ten kicker only beats unimproved dealer hands with kickers below ten, which is well under the roughly 20% win equity needed to justify the 1x raise versus folding.

J4 offsuit is below the published 4x threshold of J8s+/JTo and has no ace or king, so checking preserves the option to raise 2x on the flop or 1x/fold on the river.

J-high on Q-T-7 with no flush draw and only runner-runner straight possibilities is too weak to commit 2x; check to see turn/river cheaply and decide on river.

Board pair of Queens gives dealer automatic qualification. With J kicker I win about 210 of 990 dealer holdings and tie 42, so 5W+3T>1 and raising 1x has higher EV than folding.

5-3 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 with more information.

With 3-5 unpaired on a K-7-8 board and only weak runner-runner straight possibilities, equity is far too low to commit a 2x raise against a dealer who never folds. Checking preserves the option to raise 1x on the river only if the hand improves.

I only play the board pair of 8s with K-7-6 kickers, so I can never beat the dealer and can only tie when the dealer holds two unpaired low non-diamond cards that do not make a straight; that tie probability is far below the threshold needed to call.

AQ offsuit is an ace hand, which is in the optimal preflop 4x raising range, maximizing value before the board.

T2 offsuit is 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 on the river with more information.

Board pair of 9s with only a ten kicker and no draw is too weak to commit 2x now; checking preserves the cheaper 1x river decision with more information.

On a paired 9 board I have only pair of 9s with J-T-8 kickers; dealer always qualifies and beats me with any 9, board pair, pocket pair, straight, or A/K/Q kicker. Exact enumeration gives about 144 wins and 45 ties in 990 holdings, making a 1x raise slightly worse than folding.

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

4d6c is a weak offsuit hand outside the optimal 4x range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves optionality to evaluate the flop.

Weak 6-high with only backdoor flush and backdoor straight draws on a Q-J-3 board; raising 2x has negative expectation versus checking to see the turn and river for free and deciding then.

Pair of sixes beats all non-qualifying dealer hands and some qualifying low pairs, with ties against a lone six; exact enumeration gives about -8.8 chips expected versus -20 for folding.

J5 offsuit is below the optimal 4x raising range (J8s+ or JTo), so checking preserves the option to raise 2x on a favorable flop or 1x/fold on the river.

Top pair Jacks with a weak 5 kicker is vulnerable to ace, king or queen runouts and dealer two-pair or better kickers. Checking preserves the option to raise 1x on favorable rivers or fold bad ones, which has higher expected value than committing 2x now.

Pair of Jacks beats about 70% of random dealer holdings on this river, with only about 29% losses and few ties, so raising 1x has far higher expected value than folding and losing the ante and blind.

Any ace is in the published optimal 4x preflop range, so raising 4x maximizes expected value with Ah3d.

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

Q6 offsuit is below the published 4x threshold of Q6s+ / Q8o+, so checking to see the flop preserves EV over raising.

With queen-high, no pair and no strong draw on a king-high flop, raising 2x has negative expectation; checking preserves the cheaper 1x river decision.

With a pair of 8s and K-Q-J kickers, I win against low unpaired non-flush dealer hands and tie with a queen, giving enough win/tie equity that raising 1x loses less than folding the ante and blind.

T2 offsuit is below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves option to raise later with more information.

Weak king-high with a low four-flush draw: the 2c flush loses to any dealer club and overall equity is well below the threshold needed to commit 2x on the flop, so checking preserves the option to raise 1x or fold on the river.

Player has an Ace-high flush; dealer only wins with at least one of the 8 remaining clubs (324 of 990 holdings), while 666 holdings lose, giving a positive raise EV versus folding for -20 chips.

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

With only board pair of 4s and Q kicker, no flush draw and only a remote wheel draw, raising 2x has negative equity against a dealer who always qualifies here; checking preserves the option to raise 1x or fold on the river with full information.

With Aces and fours and a queen kicker, I win against about 401 of 990 dealer holdings and tie 85, well above the ~20% win equity needed for a 1x river raise versus folding.

Ad6h is an ace hand, which is in the published optimal 4x preflop range (any ace), so raising 4x maximizes expected value.

7c-4c 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.

Low four-flush with 7-4 kickers has well under the roughly 46% showdown equity needed to commit 2x now; checking preserves the option to raise 1x only if the flush or another strong hand completes.

We have an ace-high flush on an unpaired board; only dealer two-club holdings with a club above 7 (25 of 990 combos) beat us, so raising 1x has strongly positive EV versus folding and losing ante and blind.

9-8 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.

Flopped a J-high straight with 8-9 on J-T-7, beating all pairs, sets and two-pair hands and only losing to a flopped flush. Equity is high enough to commit 2x now rather than check for a smaller river raise.

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

Q7 offsuit is just below the published 4x threshold of Q8o+ (Q6s+ suited), so raising 4x or 3x is not profitable. Check to see the flop for free and decide later.

Q-high with only backdoor straight potential and no flush draw is too weak to raise 2x on this flop; checking preserves the option to raise 1x or fold on the river.

On the river I have only queen-high against an unpaired board. Most dealer holdings make a pair, ace/king-high, a straight or a flush, and winning only pays the 1x play bet when the dealer does not qualify, so raising has lower expected value than folding.

KQo is well above the published 4x threshold (K5o+), so raising the maximum preflop maximizes expected value.

5s6s 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.

Only a gutshot 8 for a straight plus runner-runner spades and weak pair outs; current six-high has low showdown equity, so committing 2x now is worse than checking to realize the draw cheaply and raise 1x on the river only if improved.

We have a Q-high flush using both spades; only a higher dealer flush (both hole cards spades with an 8 or higher spade, 25 of 990 holdings) beats it, so raising 1x has strongly positive EV versus folding, including the 3:2 blind payout.

T9o is below the published 4x raising threshold of JTo/J8s and has no ace or high pair, so checking to see the flop preserves EV over committing 3x/4x now.

Top two pair on the flop is well ahead of most dealer holdings, with positive expected value from a larger play bet despite the heart draw on board.

9-5 offsuit is well below the optimal 4x raising range, so checking preserves the option to raise 2x on a favorable flop or fold cheaply on the river.

With 9-high and no pair or meaningful draw on an A-Q-6 board, raising 2x is negative EV; checking is free and preserves the cheaper 1x river option if I improve.

On the river I have only ace-high A-K-Q-9-7, which beats only about 134 of 990 dealer holdings and ties 45, with most losses costing the extra play bet; the raise EV is about -2.14 antes versus -2 antes for folding.