Showdown Hold'em table

J6 offsuit is below the published 4x threshold (J8s+ or JTo), so checking preflop and waiting for the flop is correct.

J6 with no pair on 3-9-5 is far too weak for a 2x flop raise; checking keeps the cheaper 1x river option in case we improve.

Board pair of nines with J-6 gives the dealer roughly 85% of 990 holdings that beat us (any 9, 3, 4, 5, Q, K, A, pocket pairs, straights); raising 1x loses about 23 chips in expectation versus 20 for folding.

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

J4 suited is below the published 4x threshold (J8s+), so checking preflop and waiting for the flop is the higher-EV line.

J4 offsuit on a 9-7-8 board gives us no pair, no draw beyond a gutshot-ish nothing (J-10 needed), and the board is coordinated; raising 2x here is clearly negative EV, so check and decide on the river.

Board pair of sevens with Q-J-9 kickers; dealer always qualifies here. Enumerating dealer holdings I win ~19% and tie ~6%, lose ~75%: EV of raising ≈ -17 chips versus -20 for folding, so the 1x call is slightly better.

A5 offsuit is any ace, which is in the published optimal 4x preflop raising range; raising the maximum preflop is +EV versus waiting.

7-6 offsuit is well outside the optimal 4x raising range (no pair, no ace, not a strong king/queen/jack hand), so checking and waiting for the flop preserves EV.

Top pair of sixes using a hole card plus a gutshot straight draw on a low rainbow-ish board; standard flop strategy raises 2x with any hidden pair above deuces.

J2 offsuit is well below the optimal 4x raising threshold (J8s+ or JTo), so I check and wait to see the flop before committing chips.

Jack-high with no pair, no flush draw, and only a gutshot (Q-8 for a straight) on a 4-9-T board; standard flop strategy is to raise 2x only with a pair or better or a strong draw, so checking to see the river is correct.

Jack-high with no pair on a dry A-T-9-6-4 board; exact count shows 613/990 dealer holdings qualify and beat me, 192 more beat me without qualifying, only 128 win, giving raise EV about -21 vs -20 for fold, so folding is marginally better.

7-3 offsuit is far below the optimal 4x raising range (no pair, no ace, not a qualifying king/queen/jack hand), so I check and wait to see the flop before committing chips.

Hidden middle pair of sevens on a dry K-7-2 board is a standard 2x raise on the flop; equity against a random dealer hand is well above the break-even point for raising now versus checking to the river.

7-6 suited is not in the optimal preflop 4x raising range (no pair, no ace, below the K/Q/J thresholds), so checking to see the flop is correct.

Hidden pair of sevens (hole 7 pairs the board) is a standard 2x flop raise in this variant; checking to the river only costs equity against a dealer who often misses.

Any ace is in the published optimal 4x preflop raising range for Ultimate Texas Hold'em-style play; A5o has enough equity against a random dealer hand to maximize the bet now.

K7 offsuit is K5o+ which is in the published optimal 4x raising range for Ultimate Texas Hold'em-style play, so raising 4x preflop maximizes EV.

6-5 offsuit is well below the optimal 4x raising range (no pair, no ace, no strong king/queen/jack), so checking and waiting for the flop is the EV-maximizing play.

Only an open-ended straight draw with no pair; standard flop strategy checks here and keeps the cheaper 1x river option if the straight comes in.

I hold a queen-high flush (Ah Qh 7h 6h 5h) with the 6h as my playing card; only a dealer holding Kh, Jh, Th, 9h or 8h beats me, so raising 1x is clearly better than folding.

J8 offsuit is below the 4x raise threshold (J8s+ or JTo required), so checking preflop to see the flop is optimal.

J8 offsuit on a K-3-2 rainbow flop with no pair, no draw, and only two overcards to the low cards is far too weak to raise 2x; check and see the river for a cheaper 1x decision.

Ace-king high with no pair on a board where any A, K, 4, 3, 2, 5 (straight) or Q beats me; enumeration gives roughly 18% win equity, so raising 1x costs more than the -20 from folding.

K9 suited is in the published optimal 4x raising range (K2s+), so raising the maximum preflop maximizes expected value.

8d7d suited connectors fall outside the published optimal 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preflop and waiting for the flop is higher EV.

Only a gutshot with no pair or flush draw on a two-club board; standard flop strategy says check and reevaluate on the river.

Ace-high with no pair on a Tc Jc 2s Ad 6s board; the dealer beats me with any pair card (15 outs) plus any 9, Q, or K (12 more), so 27 outs is well over the 21-out threshold and raising loses more than the 20 chips folded.

Ace-four offsuit is in the published optimal 4x range (any ace), so raising the maximum preflop has the highest expected value.

J9 offsuit is below the published 4x threshold (J8s+ or JTo), so checking preserves the option to raise 2x on a favorable flop or 1x on the river.

J9 offsuit on a 3-5-7 rainbow flop with no pair, no flush draw, and no straight draw is far too weak for a 2x raise; check and wait for the river where I can raise 1x if I improve or fold otherwise.

J-high with no pair on a board that gives the dealer many straight (any 6), flush (two diamonds) and pair outs; dealer beats me far more than 50% of the time and usually qualifies, so raising costs more than folding.

3c6d offsuit is well outside the optimal 4x raising range, so checking preserves the option to raise 2x on a favorable flop or 1x on the river.

We hold a hidden pair of threes (3c pairs the board); standard flop strategy raises 2x with any hidden pair except pocket deuces, as it beats most dealer holdings often enough to justify the bet now rather than waiting for the smaller river bet.

9-4 offsuit is far below the optimal 4x raising range (no pair, no ace, not a qualifying king/queen/jack hand), so checking and waiting for a flop or river decision is correct.

4d 9c on Jh 5c 3d is just a gutshot draw with no pair; standard flop strategy only raises 2x with a pair or better or strong draws, so checking preserves the option to fold or raise 1x on the river.

Board pair of 3s with 9-high kickers and no hand of my own; dealer always qualifies and beats me with any A/K/Q/J/T, any 3/5/2, any pocket pair, or a straight — roughly 90% of holdings, so folding (-20) beats raising (~-25).

J6 offsuit is below the published 4x raising threshold (J8s+ or JTo), so checking preflop and waiting for the flop or river is the higher-EV line.

J6 offsuit on a 5-9-3 rainbow board gives me nothing but jack-high with a weak gutshot; standard flop strategy only raises 2x with a pair or strong draw, so checking to see the river is correct.

Board two pair with J kicker; dealer beats me with roughly 19 singleton outs plus some pocket pairs (~70% of holdings), but raising 1x still loses less (~-16.5 chips) than folding (-20) since wins pay 20 and ties push.

Pocket aces is the strongest preflop holding and is a clear 4x raise per the optimal strategy table; maximizing the play bet with maximum equity has the highest expected value.

T8s is not in the optimal 4x raising range (needs J8s+ or any ace/pair etc.), so checking preflop and waiting for the flop is higher EV.

Flopped middle pair (8s) plus a flush draw with Ts8s on an 8d-As-2s board; pair plus flush draw is a standard 2x raise on the flop in Ultimate Texas Hold'em strategy with strong equity against a random dealer holding.

3-4 offsuit is far outside the optimal 4x raising range, so checking preflop and waiting for a favorable flop is correct.

3-4 offsuit with no pair on a Q-Q-7 board; we have only a weak gutshot and nothing else, so raising 2x is clearly -EV. Check and see the river for free.

Our 3-4 doesn't play; we hold only the board (QQ with A-J-7 kickers). Dealer beats us with any 7+ or pair in hand and can at best tie with two unpaired small cards (~13%), so raising 1x costs more in expectation (~-26) than folding (-20).

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

AQ offsuit is well within the optimal 4x preflop raising range (any ace), so raising the maximum maximizes EV.

JTo is in the published optimal 4x range (JTo qualifies), so raising 4x preflop maximizes EV.

KQ offsuit is well within the optimal 4x preflop raising range (K5o+), so raising the maximum preflop maximizes expected value.

T6 offsuit is well outside the optimal 4x raising range (needs JTo, Q8o+, K5o+, or any ace), so checking preserves the option to raise 2x on a favorable flop or 1x on the river.

T6 offsuit on Q-7-A with no pair, no draw and no overcards is far too weak to raise 2x on the flop; check and reevaluate on the river.

My hole cards don't play; I hold the board (A K Q 7 7) so I can only tie or lose, but dealer beats me only ~49% of the time (any A/K/Q/7, pocket pair, or JT). Raising costs 30 on a loss and 0 on a tie, EV ≈ -15 vs -20 for folding.

4c5s offsuit is well below the optimal 4x raising range (no pair, no ace, no high cards), so checking and waiting for the flop is correct.

Just a gutshot (any 6) plus a weak backdoor club draw with no pair on Ac 7c 8s; standard flop strategy says check without a pair, two pair, or a strong flush draw and decide on the river.

My 4-5 adds nothing to the board's pair of sevens; dealer always qualifies via the board pair and beats me with any pair, any club flush, or simply any kicker above a 5. Raising loses 30 on ~97% of holdings versus a flat -20 from folding, so folding is clearly higher EV.

Any ace is in the published optimal 4x preflop raising range for Ultimate Texas Hold'em-style play; A4o has an edge against a random dealer hand, so raising the maximum now has the highest EV.

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

Jh5h on Qd 2c 7s is just jack-high with no draw (two hearts only); standard flop strategy requires a pair or strong draw to raise 2x, so checking and deciding on the river is better.

Board two pair QQ77 with my J kicker; dealer beats me only with Q, 7, K, A, or 22 (~47%), ties ~9%, loses ~44%. Raising EV ≈ -5 chips vs folding -20, so raise 1x.