Showdown Hold'em table

8h6d offsuit is well outside the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking and waiting for flop/river information is correct.

Hidden pair of sixes (board 6-T-9) plus a gutshot to a straight and a backdoor flush draw; standard flop strategy raises 2x with any hidden pair, and the draws add equity over waiting for the 1x river bet.

K3 offsuit is below the published 4x threshold (K5o+), so checking preflop and waiting for the flop or river to decide is higher EV than raising now.

Flop is 8s Kd 8c and I hold K3, giving two pair (kings and eights) with top pair on the board; standard flop strategy is to raise 2x with top pair or better, and my hand is well ahead of most dealer holdings.

A7 offsuit is any ace, which is in the published optimal 4x raising range preflop; raising the maximum captures the most value from this edge.

T4 offsuit is well below the published 4x raising threshold (needs JTo or better for ten-high), so checking to see the flop is correct.

Th4s on 3h Qc 6h gives only a one-card flush draw and ten-high with no pair; a 2x raise is far below the threshold, so check and wait for the river decision.

Pair of fours with a ten kicker; dealer beats us roughly 56% of holdings (any 5 straight, Q/7/6 pairs, higher pockets), but raising still costs about 12 chips on average versus a certain 20-chip loss by folding.

Any ace is a 4x raise per the optimal preflop strategy; A3 offsuit is in the raising range.

8-5 offsuit is far below the optimal 4x raising range (no pair, no ace, not a qualifying K/Q/J hand), so checking preserves the option to raise 2x on a favorable flop or 1x on the river.

8s5d on a Th Kh Jd flop gives me nothing: no pair, no draw, and the board is coordinated with high cards that favor the dealer's range. Checking keeps my option to raise 1x or fold on the river.

Pair of 8s on a draw-heavy board: enumeration gives roughly 404 wins, 38 ties, 548 losses among 990 dealer holdings, so raising 1x has EV around -11 chips versus -20 for folding.

T2 suited is below the optimal 4x raising threshold (no pair, no ace, not K/Q/J-high strong enough), so check preflop and wait for the flop.

Ten-deuce on A-K-J gives only a gutshot to a queen with no pair and no flush draw; standard flop strategy says check and wait for the river decision.

Aces and tens with a king kicker wins or ties roughly half the 990 dealer holdings; raising costs -4.6 chips EV versus -20 for folding, so raise.

T9 offsuit is not in the optimal 4x raising range (needs JTo or better for offsuit non-ace/king/queen hands), so checking and waiting for the flop is correct.

Top pair of nines with a hidden hole card and a ten kicker on a dry 7-2-9 board is a standard 2x flop raise; checking to the river only lets the dealer catch up for free.

8-2 suited is far below the optimal 4x raising threshold (not in 33+, any ace, K2s+, Q6s+, J8s+), so checking preflop and waiting for the flop is correct.

8-high with no pair, no draw on Kd 4d 9h; raising 2x with nothing is clearly negative EV, so check and reassess on the river.

Ace-high with no pair on a K-4-9-J-A board; dealer beats me with any A, K, J, 9, 4, Q, T or pocket pair (well over 21 outs), so raising 1x has EV below -20 chips while folding costs exactly 20.

Pocket nines are well inside the published optimal 4x range (33+), so raising the maximum preflop maximizes expected value.

7-4 offsuit is well outside the optimal 4x raising range (no pair, no ace, no strong king/queen/jack), so checking to see the flop is correct.

7-high with only a gutshot (3-6 needed, no, actually 7-4 with T-2-5 gives a gutshot for 3 or 6 to make a straight) and no pair; far too weak for a 2x flop raise, so check and reassess on the river.

Board trips give me 2-2-2-T-7; dealer always qualifies and beats me with any 8+, any 5, any 2, or any pair (~917 of 990 holdings), so raising loses ~27 chips expected vs 20 for folding.

Any ace is in the published optimal 4x range for Ultimate Texas Hold'em-style play; A6o is a standard max raise preflop.

Ace-jack offsuit is a standard 4x raise preflop under the optimal strategy (any ace raises 4x); maximizing the play bet with a strong edge is +EV.

Q4 offsuit is below the published 4x threshold (Q8o+ or Q6s+), so checking preflop and reevaluating on the flop is the higher-EV line.

Hidden pair of queens (second pair) on a dry-ish board; standard flop strategy raises 2x with any hidden pair, which beats checking and only being able to raise 1x at the river.

Pocket sixes fall within the published optimal 4x range (33+), so raising the maximum preflop maximizes expected value against the house dealer.

J3 offsuit is below the optimal 4x raise threshold (J8s+ or JTo), so check and see the flop for free.

J3 offsuit on a 7-T-T board gives me nothing but jack high with no draw; the paired board doesn't help me specifically, so raising 2x is far worse than checking and deciding on the river.

I hold board two pair TT77 with a jack kicker; dealer beats me with any T, 7, A, K or Q (16 of 45 unknowns, ~59%), but raising EV is about -11 chips versus -20 for folding, so calling 1x is correct.

9c6c is not in the optimal 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preflop and waiting for the flop or river is the higher-EV line.

Flop 6d 2c Ts with 9c 6c gives middle pair of sixes with a nine kicker; standard flop strategy is to raise 2x with any pair (even a weak one) since we beat most dealer holdings, and the 9c6c also has backdoor flush/straight equity.

2h3d offsuit is far below the 4x raising threshold (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise later only if the flop improves the hand.

Pair of threes plus an open-ended straight draw (any ace or six) on a 5-4-3 board; the combined pair and 8-out draw equity makes the 2x raise better than checking and facing a 1x-or-fold river decision.

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

Q4 offsuit is below the published 4x threshold (Q6s+ or Q8o+), so checking and waiting for flop/river information is the optimal play.

Qh 4d on 9d 5d 7h gives me no pair, no draw of note (one diamond for a backdoor flush, gutshot needs a 6 with 4-5-7 for 3-4-5-6-7). Queen high with weak backdoors is well below the flop 2x raise threshold, so I check and see the river for free.

Queen high with no pair on a 9-5-7-T-2 board with three diamonds; dealer has far more than 21 outs (any board pair, K, A, flush, straight, better Q kicker), so folding loses less than calling.

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

Top pair (jacks) with a gutshot straight draw on a Ts Js 3c flop; standard flop strategy raises 2x with top pair or better, and this hand is well ahead of a random dealer holding.

J7 offsuit is below the optimal 4x raising threshold (J8s+ or JTo), so checking preflop to see the flop is the correct play.

Jd7s on As-5d-3s gives no pair, no draw beyond a backdoor flush; flop 2x raise requires roughly a pair or strong draw, so checking and deciding on the river is correct.

Ace-high with J kicker vs 990 dealer holdings: ~625 qualify and beat us (-30), ~116 non-qualifying ace-high beats us (-20), ~240 we win (+10); EV of raising ≈ -18.9 chips vs -20 for folding, so raise is marginally better.

Q7 offsuit is below the published 4x threshold (Q8o+ or Q6s+), so checking preflop and reevaluating on the flop is the higher-EV line.

Flop gives a hidden pair of sevens (7c with the board 7d) plus a queen kicker; standard flop strategy raises 2x with any hidden pair, so betting now beats checking to the river.

2-4 offsuit is far below the optimal 4x raising range; check and wait to see the flop before committing chips.

Holding 2h 4s on an 8s 3h Jh board gives us no pair, no draw of note (just a backdoor heart flush/gutshot), so the 2x flop raise is far below the standard pair-or-strong-draw threshold; checking keeps the river 1x option open.

Our 2h4s doesn't play; we hold only the board (3,3,J,8,5) with no straight. Dealer always qualifies via the board pair and beats us with 39 of 45 unseen cards, with the rest only tying, so folding loses less than raising.

KJ offsuit is within the published optimal 4x raising range (K5o+), so raising the maximum preflop maximizes EV.

AK offsuit is a premium holding well within the optimal 4x raising range (any ace), so raising the maximum preflop maximizes expected value.

Q3 offsuit is below the 4x raise threshold (Q8o+ or Q6s+), so checking preflop and waiting for the flop is optimal.

Top pair queens on a paired board gives queens and eights, well ahead of the dealer's range; standard strategy raises 2x with two pair or better on the flop.

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

Top pair of jacks using a hole card is a standard 2x flop raise; the board is coordinated but a hidden top pair is still well ahead of the dealer's random holding on average, and we also hold a backdoor heart.

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

2d5h offsuit is far below the optimal 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking to see the flop is correct.

Only a gutshot to the 4 (4 outs) with no pair and 5-high; the flop raise reference says check with no made hand or strong flush draw, so I check and decide on the river.

My hole cards don't play (board pair of 3s with A-K-6 kickers), so I can only tie or lose, but the dealer beats me only with an A, K, 6, 3, or a pocket pair (~48% of 990 holdings). Raising costs 30 when losing with ~48% chance (EV about -14.5) versus a sure -20 from folding.