Showdown Hold'em table

KJ offsuit is in the published optimal 4x raising range (K5o+), so raising the maximum preflop is the highest-EV play.

7-6 offsuit is well outside the optimal 4x raising range (needs pairs, aces, strong kings/queens/jacks), so checking to see the flop is correct.

7-high with no pair, only a gutshot-ish two-card straight draw and a backdoor flush draw on 8s Qs 3d; well below the 2x flop raise threshold (pair or better / strong flush draw), so check and see the river.

Board 8s Qs 3d 5h 4h with 6h 7s gives me an 8-high straight (4-5-6-7-8), the nut straight on this board; raising 1x is clearly correct and the blind pays 1:1 on a win.

Any ace is a published 4x raise preflop in Ultimate Texas Hold'em strategy; A5o has positive EV for the max raise against the house dealer.

Q7 offsuit is below the published 4x threshold (Q8o+ required for offsuit queens), so checking preflop and waiting for the flop is the higher-EV line.

Top pair (queens) with a 7 kicker on a dry 9-6-Q board is a clear 2x raise on the flop per standard Ultimate Texas Hold'em strategy; we are well ahead of the dealer's random holding.

9-5 offsuit is far below the optimal 4x raising range (no pair, no ace, no qualifying king/queen/jack hand), so checking preserves the option to raise 2x on a favorable flop or 1x on the river.

Holding 5d 9s on a 7d Jc 2s flop gives me nothing but a gutshot-ish backdoor and no pair; standard flop strategy only raises 2x with a pair or strong draw, so I check and wait for the river.

Holding two pair (nines and twos with a jack kicker) on a 7-J-2-2-9 board beats the majority of dealer holdings, so raising 1x is far better than surrendering the ante and blind.

6-2 offsuit is far below the published 4x raising threshold, so checking preflop and waiting to see the flop is correct.

6h2d on 9d-Th-3d gives no pair, no draw worth betting (only a single diamond), so raising 2x is clearly negative EV; check and decide on the river.

My hole cards (6h 2d) play nothing; I'm just the board (3,3,Q,T,9) so I can never beat the dealer, only tie. Tie probability is ~191/990 ≈ 19%, so raising loses ~0.81*30 ≈ 24 chips in expectation versus 20 for folding.

J5 offsuit is below the published 4x threshold (needs J8s+ or JTo), so checking and waiting for the flop is the higher-EV line.

J5 offsuit on 8-7-4 rainbow gives us no pair, no draw beyond a gutshot, and jack-high; this is far below the flop 2x raise threshold (roughly a pair or a strong draw), so checking to see the river for free is correct.

Pair of fives with a jack kicker on 8-7-4-5-K: dealer beats us with roughly 55% of holdings, but many remaining hands don't qualify, so raising 1x has an EV around -6 chips versus -20 for folding.

AQ offsuit is well within the optimal 4x preflop raising range (any ace); raising the maximum preflop has the highest EV.

QTs is in the published 4x raising range (Q6s+), so raising the maximum preflop is the highest-EV play.

J9 offsuit is below the published 4x threshold (J8s+ or JTo), so checking preflop and waiting for the flop is the higher-EV play.

Top pair (jacks) with a flush draw on the flop is a clear 2x raise per standard Ultimate Texas Hold'em flop strategy; checking forfeits value.

7-6 offsuit is well outside the optimal 4x raising range (needs a pair, ace, or strong broadway/suited holding), so checking to see the flop is correct.

Paired the board with a hole card (sevens), which standard flop strategy plays as a 2x raise; waiting to the river only lets the dealer's holding improve against a hand already ahead of most random two-card holdings.

J7 offsuit is below the published 4x threshold (J8s+ or JTo), so checking preflop and waiting for the flop is the higher-EV line.

Jack-high with no pair, only backdoor flush and two-card straight possibilities on Kc 2d Qc; far too weak to raise 2x, so check and see the river for free.

Ace-high with K-Q-J kickers beats roughly a third of dealer holdings (any unpaired non-straight hand without J8+). Enumerating 990 dealer combos gives raise EV about -1.6 ante versus -2 for folding, so raising is the smaller loss.

J9 offsuit is below the published 4x threshold (J8s+ or JTo), so checking preflop and reevaluating on the flop is the higher-EV line.

J9 offsuit on a K-5-2 rainbow flop gives me no pair, no draw beyond a gutshot-ish backdoor, so raising 2x is far below the standard flop raise threshold; checking preserves the option to fold or call 1x on the river.

Pair of nines with a jack kicker on a four-heart board; dealer beats me ~58% of the time (any heart, K, Q, JT, TT+), but a 1x raise still has EV around -11 chips versus -20 for folding, so calling is correct.

4c5c suited connectors are not in the optimal 4x raise range (needs 33+, any ace, K2s+, etc.), so checking preserves the option to raise 2x on a favorable flop.

Hidden pair of fours plus the paired kings gives two pair now; standard flop strategy raises 2x with a hidden pair or two pair or better, and the 2x bet beats waiting for a 1x river decision in EV.

AJ suited is a clear 4x raise under the optimal preflop strategy (any ace raises); maximize the play bet while holding a strong edge.

9-5 offsuit is far below the optimal 4x raising range (needs J8s+/JTo+ or better), so checking and seeing the flop is correct.

Top pair of nines made with a hole card on a 4-9-8 board; standard flop strategy raises 2x with any hidden pair, as it is a clear favorite against random dealer holdings.

K4 offsuit falls below the published 4x threshold (K5o+ or K2s+), so checking and waiting for a favorable flop or river is the higher-EV line.

King-high with no pair and only a gutshot on a Q-T-3 board does not meet the flop raise threshold (hidden pair or strong draw); checking keeps the option to raise 1x or fold on the river with full information.

King-high on Qd Th 3c 9h 8c loses to any pair, any ace, and any J or 7 (straight); only about 84 of 990 dealer holdings lose to us, so raising 1x has worse EV than surrendering the ante and blind.

Ace-ten offsuit is well inside the published optimal 4x raising range (any ace), so raising the maximum preflop maximizes EV.

T4 offsuit is well outside the optimal 4x raising range (needs JTo, Q8o+, K5o+, any ace, or pairs), so checking preserves the option to raise on the flop or river with better information.

4s Td on 5s 6h Jd gives no pair, no flush draw, and only a gutshot (need a 3 or 7 for an open-ended-ish shape); far below the 2x raise threshold, so check and reevaluate on the river.

Ace-high with a J-T kicker on A-J-8-6-5 board: dealer beats us with any 5,6,8,J,A,K,Q (23 outs) plus any pocket pair or straight; enumeration gives raise EV around -21.9 chips vs -20 for folding, so fold.

9-5 offsuit is well outside the optimal preflop 4x raising range, so checking and waiting for the flop is correct.

9d5h on 3h-4d-Ts gives only nine-high with a weak gutshot; this is far below the flop raise threshold (pair or better / strong draws), so check and reassess on the river.

With 9d5h on 3h-4d-Ts-Jd-Td I have only the board pair of tens with a nine kicker; enumerating the 990 dealer holdings, I lose to any A/K/Q/J/T/3/4, any pocket pair, diamond flushes and 9x hands (~835 losers vs ~146 winners), making raise EV about -22.3 chips versus -20 for folding.

J2 offsuit is well below the optimal 4x raising threshold (J8s+ or JTo), so checking preflop and waiting for the flop/river is correct.

J2 offsuit on an A-8-7 board with no pair, no draw and only a jack kicker is far too weak to raise 2x; checking preserves the option to bet 1x or fold on the river.

Ace-high with a jack kicker on an A-9-8-7-4 board: dealer beats us with any board pair, pocket pair, straight, or K/Q kicker. Enumerating the 990 dealer holdings gives raise EV about -22 chips versus -20 for folding, so folding is marginally better.

5-2 suited is far below the optimal 4x raising threshold (no pair, no ace, no qualifying king/queen/jack hand), so checking preflop and waiting for the flop is correct.

Flush draw with low spades (2s 5s) and no pair; standard flop strategy only raises a four-flush when a hole card is Ten or higher, so checking and deciding on the river is better.

We hold a jack-high spade flush (2s 5s with 7s Js 4s on board), which beats the vast majority of dealer holdings; only a full house, quads, or higher flush beats us. Raising is clearly +EV and the blind pays 3:2 on a winning flush.

J2 offsuit is well below the 4x raise threshold (J8s+ or JTo), so checking preflop and waiting for the flop is optimal.

Jack-high with no pair and only backdoor draws on A-6-3 board; standard flop strategy says check and wait for the river to decide.

Pair of jacks with ace kicker on a board with no possible straights; the dealer only beats me with an ace, a jack with a better kicker, two clubs, or a two-pair/trips holding, roughly a quarter of holdings, so raising is far better than folding.

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

8-4 offsuit is far below the published 4x raising range (no pair, no ace, weak kickers), so checking preflop to see the flop is the correct play.

Holding 4s8d on a Td7h Ts board gives me nothing but the board pair and a weak kicker with only a gutshot (5-6 or 6-9 runouts); the standard flop strategy only raises 2x with a hidden pair or better, so checking and deciding on the river is correct.

Two pair tens and fours with an 8 kicker wins against roughly two-thirds of the 990 dealer holdings (only tens, sevens, better 4-kickers, pocket pairs 55+/22/44 and diamond flushes beat us), so raising has positive EV versus the certain -20 of folding.

A7 offsuit is any-ace, which the published optimal strategy raises 4x preflop; maximizing the bet while we have the edge is correct.

9-8 offsuit is not in the optimal 4x raise range (needs 33+, any ace, K5o+, Q8o+, JTo), so checking preflop and waiting for the flop/river decision is correct.

9-8 offsuit on a 6-A-6 board gives me no pair, no draw, and only a weak kicker; the flop 2x raise rule needs a pair or strong draw, so I check and see the river.

Board pair of sixes with A-K-9 kickers; dealer always qualifies. Enumerating 990 dealer holdings gives ~144 wins, ~57 ties, ~789 losses, so raising 1x costs about 19.5 chips versus 20 for folding—marginally better to call.

T2 suited is not in the optimal 4x raising range (needs J8s+ or similar), so checking and deferring to the flop/river decision is the higher-EV play.

Only an open-ended straight draw with ten-high and no pair; standard flop strategy raises 2x only with hidden pairs, two pair+, or strong flush draws, so checking and deciding on the river is higher EV.

Jack-high board with T2 gives us nothing; dealer beats us with any A/K/Q, any board pair, or several straights, far above the ~21-out threshold, so raising 1x has EV around -24 vs -20 for folding.

J5 offsuit is below the published optimal 4x threshold (J8s+ or JTo), so checking preflop and deciding on the flop or river is the higher-EV line.

J5 offsuit on a paired board of Td 4s 4h gives us only the board pair with a jack kicker and no draws; standard flop strategy requires a pair using a hole card or a strong draw to raise 2x, so checking and deciding on the river is correct.

Board pair of 4s with A-J-T kickers; dealer always qualifies, and I win against ~220 of 990 holdings and tie 69, so EV of raising (~-16.8) beats folding (-20).

K3 offsuit falls below the K5o+ threshold in the published optimal 4x table, so checking preflop and reevaluating on the flop is correct.

King-high with no pair, no flush draw on a monotone spade board, and only backdoor straight outs; checking to see the river is clearly better than committing 2x with nothing.

Pair of kings with ace kicker on a four-spade board; roughly half the 990 dealer holdings beat us (any spade, ace, king, or set/wheel), but raising 1x still costs far less than folding's guaranteed -20.