Showdown Hold'em table

K9 offsuit is in the published optimal 4x range (K5o+), so raising 4x preflop maximizes EV.

Pocket threes are in the published optimal 4x range (33+), so raising the maximum preflop is the highest EV play.

4-2 offsuit is far outside the optimal 4x raising range, so checking preflop and waiting for the flop or river is correct.

Hidden pair of deuces (2c pairs the board 2h) with a backdoor straight draw; standard flop strategy raises 2x with any hidden pair except pocket deuces, so I take the larger bet now rather than a smaller one on the river.

9-6 offsuit is well outside the optimal 4x raising range (no pair, no ace, no qualifying king/queen/jack), so checking preserves the option to raise 2x on a favorable flop.

We hold a hidden pair of nines on a J-Q-9 board; standard flop strategy is to raise 2x with any hidden pair (except deuces), as we are ahead of most random dealer holdings despite the drawy texture.

2c3d offsuit is far below the published 4x raising range (needs 33+, any ace, K5o+, etc.), so checking preflop and waiting for the flop is correct.

Bottom pair of deuces using a hole card on K-J-2 is a hidden pair; standard flop strategy raises any hidden pair except pocket deuces, and our extra outs to two pair/trips put equity slightly above the 2x breakeven.

9-3 offsuit is well below the 4x raising threshold (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.

9-high with only a gutshot draw (J for a straight) on Qs 5h Ts; no pair, no flush draw. Far below the 2x raise threshold, so check and see the river for free.

Queen-high with a 9 kicker on a three-heart board (we hold only one heart): the dealer beats us with any heart, any A/K/J, any pair of the board or pocket pair — roughly 28+ outs, far above the ~21-out threshold, so folding loses less than calling 1x.

Q2 offsuit is below the published 4x threshold (Q8o+ / Q6s+), so checking preflop and waiting for the flop or river is optimal.

Q2 offsuit with a paired board (5-5-4) gives no hidden pair, just a queen high with a weak gutshot; standard flop strategy says check and wait for the river decision.

Board pair of fives with A-Q-7 kickers; dealer beats me with roughly 704 of 990 holdings (~71%), but folding costs 20 for sure while calling 1x costs ~16 in expectation, so the 1x raise is +EV relative to folding.

Any ace is a published 4x raise in Ultimate Texas Hold'em strategy; A3 suited has an added flush/wheel bonus edge, so raising the maximum preflop maximizes EV.

K8 offsuit is within the published optimal 4x range (K5o+), so raising the maximum preflop is the highest-EV play.

9-6 offsuit is well below the optimal 4x raising threshold (needs 33+, any ace, K5o+, Q8o+, JTo), so checking to see the flop is correct.

Hidden pair of sixes using a hole card plus a gutshot to the 8 for a straight; standard flop strategy raises 2x with any hidden pair (except deuces), and the draw adds equity.

Q3 offsuit is below the published 4x threshold (Q6s+ or Q8o+), so checking preflop and waiting for the flop is the higher-EV line.

Only an open-ended straight draw with queen high and no pair; standard flop strategy raises 2x only with two pair+, a hidden pair, or a strong four-flush, so checking keeps the cheaper 1x river option if the straight comes in.

I hold a 6-high straight (3h with 2-4-5-6 on board), well ahead of the vast majority of dealer holdings; only a 7, two diamonds, or a full house/quads beat me, so raising 1x is clearly +EV and the blind pays 1:1 on the straight.

K2 suited is in the published optimal 4x range (K2s+), so raising the maximum preflop has the highest expected value.

Pocket kings are a premium holding well inside the optimal 4x range (33+), so raising the maximum preflop maximizes expected value.

T8 offsuit is below the published 4x raising threshold (not a pair, no ace, not K/Q/J-high qualifying), so checking preflop and deciding on the flop is optimal.

Middle pair of tens using a hole card is a standard 2x raise on the flop in this variant; the pair beats most dealer holdings often enough to make raising clearly better than checking to the river.

Any ace is in the published optimal 4x preflop raise range for Ultimate Texas Hold'em-style play, so A4o should be raised the maximum preflop.

Pocket nines are well within the optimal 4x preflop raising range (33+), so maximizing the play bet now has the highest EV.

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.

T6 offsuit is well below the optimal 4x raising threshold (no pair, no ace, not K/Q/J-high strong enough), so I check and wait to see the flop before committing chips.

Flopped a full house (sixes full of tens) with Tc6h on Td-6s-6d; this is a monster that crushes nearly all dealer holdings, so raising 2x now maximizes EV and sets up the 3:1 blind payout.

K2 offsuit is below the published 4x threshold (K5o+ or K2s+), so checking preflop and waiting for the flop is the higher-EV line.

King-high with no pair and no draw on 3-8-T rainbow; standard flop strategy is to check and reevaluate on the river.

King-high on a 3-8-T-4-9 board loses to any ace, any king with a better kicker, any pair, and several straights; enumeration gives roughly 17% win equity, making the 1x raise EV (~-21 chips) slightly worse than folding (-20).

4-2 offsuit is far below the published 4x raise threshold (33+, any ace, K2s+/K5o+, etc.), so checking preflop and waiting for the flop is optimal.

Hidden pair of deuces plus a four-flush draw: standard flop strategy raises any hidden pair, and the flush outs add enough equity against a random dealer holding to make 2x profitable versus checking into a 1x river decision.

2-4 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.

Flopped a pair of deuces using a hole card; standard flop strategy raises 2x with any hidden pair (excluding pocket deuces), and the dealer frequently fails to pair on a K-J-2 board, so betting now has higher EV than checking.

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

Pocket deuces unimproved on a J-8-4 board is the one hidden pair the optimal flop strategy says to check; any dealer pair beats us, so wait for the river and the 1x decision.

Pair of deuces on an unpaired board: dealer needs a pair or straight to beat us (~64% of holdings), but folding costs 20 while raising has EV around -16, so the 1x raise is the better of two bad options.

QJ offsuit is in the published optimal 4x range (Q8o+), so raising the maximum preflop is the highest-EV play.

A7 offsuit is any-ace, which is a published 4x raise preflop in Ultimate Texas Hold'em strategy; raising 4x maximizes EV versus checking.

K5 suited is in the published optimal 4x raising range (K2s+), so raising the maximum preflop maximizes EV.

K9 offsuit is within the published optimal 4x range (K5o+), so raising 4x preflop maximizes EV.

J9 suited is in the published optimal 4x range (J8s+), so raising 4x preflop maximizes EV.

Any ace is a 4x raise per the optimal preflop strategy; A3o has positive EV at the max raise.

8-6 offsuit is well below the optimal 4x raising range, so checking preserves the option to raise 2x on a favorable flop or 1x on the river.

Flopped trips with 8h on a paired board of 8d Js 8c; trips or better on the flop is a clear 2x raise with strong equity against the dealer's range.

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

King-high with no pair, no draw on a 5-J-T flop; standard flop strategy calls for checking without a hidden pair or strong draw, so I take the free card and decide on the river.

Pair of deuces with a king kicker on an unpaired, no-flush board; the dealer fails to qualify roughly 40% of the time and folding costs 20, so a 1x raise has clearly better expected value than folding.