Showdown Hold'em table

Pocket eights is a pair of 3s or better, which the optimal preflop strategy raises 4x; maximizing the play bet with a strong preflop edge is the highest-EV play.

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

Flopped a hidden pair of fours (hole 4h with board 4d) with a queen kicker; standard flop strategy raises 2x with any hidden pair other than pocket deuces since we beat most non-qualifying and many qualifying dealer hands.

8-3 offsuit is far below the optimal 4x raising range, so checking preserves the option to raise 2x on a favorable flop or 1x on the river.

Bottom pair of threes with an 8 kicker on an A-K-3 two-diamond board is the weakest possible made pair; the dealer pairs an overcard or draws out often enough that committing 2x now is roughly break-even at best, so I keep the option to bet 1x or fold with full river information.

Bottom pair of threes on A-K-T-4-3 board: dealer beats me with any A/K/T/4/3 in hand, 55+ pocket pair, QJ or 52, roughly 60% of 990 holdings, but when the dealer misses it usually doesn't qualify so I only risk the play bet. EV of raise ≈ -14 chips vs -20 for folding, so calling 1x is correct.

7-9 offsuit is well outside the optimal 4x raising range (no pair, no ace, no qualifying K/Q/J combo), so checking preserves the option to raise 2x on a favorable flop or 1x on the river.

We hold a pair of sevens using a hole card plus an open-ended straight draw (6 or J) on an uncoordinated board; a hidden pair alone is a standard 2x raise and the draw adds substantial equity.

JTo is in the published optimal 4x preflop raising range (JTo qualifies), so raising the maximum preflop has the highest expected value.

K9 offsuit falls within the published optimal 4x preflop raising range (K5o+), so raising the maximum is the highest-EV play.

6-4 suited is well below the optimal 4x raising range (no pair, no ace, no qualifying K/Q/J hand), so checking preflop and waiting to see the flop is correct.

4h6h on Ts 5d 9c is only a gutshot (7-8) with no pair and no flush draw; the flop 2x raise requires roughly a pair or strong draw, so checking and deciding on the river is correct.

We hold only the board pair of tens with a 6 kicker; nearly every dealer holding (any card 7+ or any pair) beats us, so raising 1x loses about 27 chips in expectation versus 20 for folding.

Any ace is in the published optimal 4x raising range for Ultimate Texas Hold'em-style play; A6o has enough equity against a random dealer hand to justify the maximum preflop raise.

A4 offsuit is any ace, which falls inside the published optimal 4x preflop raising range; raising max preflop is higher EV than waiting.

2-3 offsuit is far outside the optimal 4x raising range (no pair, no ace, weak kicker), so checking preserves the option to raise 2x on the flop or 1x on the river only when the board improves the hand.

Only an open-ended straight draw (need an A or 6) with no pair and the lowest possible hole cards; standard flop strategy checks draws and waits to see the river before committing 2x.

With 2c3h on 5d7h4d7s8d I only play the board (pair of sevens, 8-5-4 kickers); the dealer always qualifies and beats me with virtually any holding, so folding loses 20 versus ~30 expected from raising.

T5 offsuit is well below the optimal 4x raising threshold (no pair, no ace, not K/Q/J strong enough), so checking preflop and waiting for the flop is correct.

Ten-high with no pair on a 4-9-7 board, only a backdoor flush draw and weak gutshot; standard flop strategy says check without a pair or strong draw, so check and see the river.

Board trips 9s with my T kicker only beats dealer holdings of two unpaired cards from {2,3,5,6,8} (~144/990, ~14.5% win, ~4.5% tie); EV of raising (~-21.4 chips) is slightly worse than folding (-20), so fold.

6s4s is not in the optimal 4x raising range (needs 33+, any ace, K2s+, Q6s+, J8s+ etc.), so checking preflop and waiting for the flop is correct.

Flopped a hidden pair of sixes with a 4 kicker and a small backdoor straight draw; standard flop strategy raises 2x with any hidden pair other than pocket deuces, as the dealer's unpaired holdings miss often enough to make the 2x bet +EV versus checking.

8c2c is well outside the optimal 4x raising range (no pair, no ace, no qualifying king/queen/jack hand), so checking preflop and waiting for flop/river information is the EV-maximizing play.

8c2c on Ac-7d-6s gives no pair, only a backdoor flush and weak straight draws; standard flop strategy says check and see the river.

Two pair (sixes and deuces, ace kicker) wins against roughly 55% of the 990 dealer holdings with some ties; EV of raising is about -0.4 chips versus -20 for folding, so raise.

A6 suited is any-ace, which is in the published optimal 4x preflop raising range for Ultimate Texas Hold'em-style play; raising 4x maximizes EV.

Q7 offsuit is below the published 4x threshold (Q8o+ or Q6s+), so checking preflop and waiting for flop/river information is the higher-EV line.

Qh7s on 5s5d8h gives only the board pair with a queen kicker, no draws; standard flop strategy says raise 2x only with a hidden pair, two pair or better, or a strong flush draw, so I check and reevaluate on the river.

Two pair sevens and fives with a queen kicker loses to only roughly 30% of the 990 dealer holdings (any 5, any 8, 7A/7K, 99+, 64/69, 77/22), so raising 1x is far better than forfeiting the ante and blind.

J6 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.

Top pair (jacks) on a dry flop is a clear 2x raise under standard Ultimate Texas Hold'em flop strategy; checking would only cost equity against the dealer's 990 holdings.

T9 offsuit is not in the optimal 4x raising range (needs JTo or better for ten-high offsuit), so I check and see the flop before committing chips.

Ten-nine high with no pair, no flush draw, and only a two-card backdoor straight draw on 4-5-8 does not meet the flop raise threshold; check and reevaluate on the river.

Only the board pair of fours with a ten kicker; the dealer always qualifies here and has roughly 31 outs (any A/K/Q/J, 5/7/8/4 for two pair or trips, 6 for a straight), so winning chance is under 10% and folding loses less than raising.

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

Any ace is in the published optimal 4x preflop raise table for Ultimate Texas Hold'em style play against the dealer; A2o is a marginal but positive-EV 4x raise.

Any ace is a published 4x raise preflop in Ultimate Texas Hold'em strategy; A2o has positive EV for the max raise against the house dealer.

K2 offsuit is below the published 4x threshold (K5o+ for offsuit kings), so checking preflop and reevaluating on the flop is the higher-EV line.

King-high with only an open-ended wheel/six draw on 3-4-5; standard flop strategy does not raise 2x on a bare straight draw without a pair, so check and decide on the river with full information.

Board pair of 8s with K kicker; dealer always qualifies here, and enumeration gives roughly 210 wins, 9 ties out of 990 dealer holdings. Raise EV ≈ -19.1 chips vs fold -20, so raising is marginally better.

9c4c is well below the published 4x raise threshold (not a pair, no ace, not K/Q/J high), so checking preflop and waiting to see the flop is optimal.

9c4c on a 5s6s Js flop gives me nothing but a weak gutshot (need 7 and 8... actually 7-8 for a straight with 4-5-6), no pair, no flush draw on a monotone board; this is well below the 2x raise threshold, so check and see the river.

Pair of nines on a four-spade board is weak (dealer wins ~64% with any spade, 7, J, or two pair), but raising 1x still beats folding: fold costs 20 chips for sure, while the raise's expected loss is roughly 13 chips given ~34% wins.

9-3 suited is well below the optimal 4x raising range (needs pairs, any ace, K2s+, Q6s+, J8s+); checking preserves the option to raise 2x on a favorable flop.

Flopped a hidden pair of threes on a dry 3-6-T board; standard flop strategy raises any hidden pair (except pocket deuces) since it beats the dealer's many unpaired holdings and raising 2x now beats waiting for a 1x river bet.

Q5 suited is below the published 4x threshold (Q6s+), so checking preflop and waiting for flop or river information is the higher-EV line.

Four to a flush with a hidden queen-high heart on a two-heart board; standard flop strategy favors a 2x raise with a strong flush draw including a high hidden card.

5-6 offsuit is well below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking preflop and waiting for the flop is correct.

Flopped a hidden pair of fives (5d with the 5h on board); standard optimal flop strategy raises 2x with any hidden pair except pocket deuces, as the pair beats a non-qualifying dealer often enough to make the larger bet +EV versus waiting for a 1x river bet.

4h3d offsuit is far below the optimal preflop 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking to see the flop is correct.

Pair of threes using a hole card on a T-2-3 rainbow board is a hidden pair, which standard flop strategy raises 2x (only pocket deuces are excluded); plus minor straight equity with the 4. Betting now with an edge beats waiting to bet only 1x on the river.

9-4 offsuit is well below the optimal 4x raise threshold, so checking preflop and waiting for the flop is the EV-maximizing play.

4c9h on 6s7sTh gives only a gutshot (8) with no pair; flop 2x raise requires roughly a pair or strong draw, so checking to see the river for free is the better play.

Pair of nines on a K-T-9-7-6 board; dealer needs a K, T, 8 (straight), better kicker nine, two pair or overpair to beat us, roughly 45% of holdings, so raising 1x loses far less than the -20 of folding.

Pocket deuces fall just below the published optimal 4x range (33+), so checking preflop and reassessing on the flop is the higher-EV line.

Pocket deuces are the one hidden pair the flop strategy excludes from raising, and the T98 board gives the dealer many straight and overcard outs, so check and reevaluate on the river.

Pocket deuces only beat a non-qualifying dealer, but about 29% of dealer holdings (no board pair, no J, no pocket pair) miss entirely; raising 1x yields roughly -18 chips EV versus -20 for folding, so the call is marginally better.

T5 offsuit is well outside the optimal 4x raising range (needs JTo+ or J8s+ for ten/jack high), so check and wait for the flop.

Ten-high with no pair on a Q-9-3 board and only a backdoor flush draw is far too weak for a 2x flop raise; standard strategy is to check and reevaluate on the river.

Board pair of 3s with only a ten kicker; dealer always qualifies and beats me with any A, K, J, Q, 9, 6, 3, pocket pair, or diamond flush (~800 of 990 holdings), so raising 1x costs more in expectation (about -21.7 chips) than folding (-20).

7-5 offsuit is far below the optimal 4x raising range, so checking preflop and waiting to see the flop is the EV-maximizing play.

Open-ended straight draw with no pair; standard flop strategy only raises 2x with pairs/two pair/strong flush draws, so check and reevaluate on the river.

I hold an 8-high straight (4-5-6-7-8) on a board with no flush or pair possibilities; only a dealer 9T makes a higher straight, so raising is clearly +EV and the blind pays 1:1 on the straight.