Showdown Hold'em table

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

The published optimal strategy for this Ultimate Texas Hold'em-style game says to raise 4x preflop with pocket threes (33+). A pair has enough equity that the maximum raise beats checking.

4-2 offsuit is well below the optimal 4x raising threshold (33+, any ace, K5o+, etc.), so checking to see the flop for free is correct.

Standard flop strategy is to raise 2x with any hidden pair other than pocket deuces. Our 2 pairs the board with a hole card, so it qualifies and should beat checking toward a likely river fold.

9-6 offsuit is well outside the optimal preflop 4x raising range (33+, any ace, strong kings/queens, J8s+/JTo), so checking is correct to see the flop for free.

I have a pair of nines using one of my hole cards. Standard optimal flop strategy raises 2x with any hidden pair except pocket deuces, so raising beats checking here.

2-3 offsuit is far below the optimal preflop 4x raise threshold, so checking is the right play. It keeps the option to raise on the flop or river for free.

A deuce in my hand pairs the board for a hidden pair, and there is a backdoor diamond draw. Standard flop strategy is to raise 2x with any hidden pair except pocket deuces.

9-3 offsuit is well outside the optimal preflop 4x raising range, so checking is correct. That lets us see the flop for free.

Nine-high with no pair and only runner-runner straight and flush draws is far too weak to put 2x at risk on the flop. Checking keeps a free look at the river, where I can play or fold.

Queen-high with no pair cannot beat any dealer pair, and the dealer also beats or ties most unpaired hands. Raising is worth about -23 chips, which is worse than the -20 from folding.

Q2 offsuit falls below the optimal 4x raise threshold (Q8o+ for offsuit queens). Checking keeps the option to raise on the flop or river at no extra cost.

Only the board pair of fives plus a queen kicker with no hidden pair and no strong draw, which falls below the usual flop 2x raising threshold. Checking keeps the river decision open.

My best hand is a pair of fives with A-Q-7 kickers, and the dealer always qualifies on this paired board. I estimate about a 26% win and 3% tie rate, so calling is worth roughly -1.6 antes versus -2 for folding.

Any ace is on the published optimal 4x raising table, and A3 suited also adds flush potential for the blind bet. Raising 4x preflop is the highest-EV option.

K8 offsuit falls within the published optimal 4x preflop range (K5o+), so a 4x raise is the higher-EV play than checking.

96 offsuit falls outside the optimal preflop 4x raising range, so checking is correct. Checking keeps the option to raise on the flop or river for free.

A pair of sixes made with my hole card, plus a 9 kicker and a gutshot to an 8, meets the standard flop strategy of betting 2x on a hidden pair. Raising should beat checking and deciding on the river.

Q3 offsuit is below the optimal 4x preflop threshold (Q8o+), so checking and seeing the flop for free is correct.

Queen-high with an open-ended straight draw and only a backdoor flush is too weak for a 2x raise. Checking lets me see the river and then raise 1x if I make the straight or fold cheaply if I miss.

We hold a 6-high straight (2-3-4-5-6), which beats most dealer holdings; only two diamonds for a flush, a higher straight, a full house or quads beat it. Raising is clearly better than folding.

K2 suited is included in the published optimal preflop 4x raising range (K2s+), so raising 4x has higher expected value than checking.

Pocket kings are a premium hand, well inside the optimal 4x preflop raising range, so I take the maximum raise.

T8 offsuit falls outside the optimal preflop 4x raising range (that range needs JTo or better among offsuit jack-high hands), so checking keeps the flop and river options open.

A hidden pair of tens, even under the queen, clears the standard 2x flop raising threshold, which is any hidden pair except pocket deuces. A 2x bet is worth more than checking down to the river.

The published optimal strategy says to raise 4x with any ace, and A4 offsite fits that rule. Raising 4x preflop has higher EV than checking.

Pocket nines are well inside the published optimal 4x preflop range (33+), so the maximum raise is the highest-EV play.

K7 offsuit falls within the published optimal preflop 4x range (K5o+), so raising the maximum is the highest-EV play.

T6 offsuit is well outside the optimal preflop 4x raising range (which needs a pair 33+, any ace, or strong king/queen/jack hands), so checking is correct.

Flopped a full house (sixes full of tens), a huge favorite with the blind paying 3:1 on a win, so raising the maximum available on the flop is clearly best.

K2 offsuit falls outside the optimal 4x preflop range, which needs K5o or better offsuit, so I check and reassess on the flop.

King-high with no pair and no flush or straight draw falls well short of the flop 2x raise threshold. Checking lets me see the river for free before deciding whether to raise 1x or fold.

With only king-high, the dealer qualifies about 65% of the time. Counting all dealer holdings, raising costs about -21.1 chips versus -20 for folding, so folding loses slightly less.

4-2 offsuit is well outside the optimal preflop 4x raising range, so checking keeps the option of a cheap flop or river decision.

I hold a hidden pair of deuces plus a four-card spade flush draw. That combination is well above the flop raise threshold, and a flush would also pay the blind 3:2.

4-2 offsuit is far below the optimal preflop raising threshold, so checking keeps the play bet at zero and lets me see the flop for free.

Bottom pair of deuces, made with a hole card, has enough equity against a random dealer hand. Raising 2x should lose less than checking, which would often end in a river fold costing the ante and blind.

The published optimal preflop 4x table raises 33 and higher, so pocket deuces fall just below the threshold. Checking keeps the option to raise on the flop or river once more cards are known.

Pocket deuces below all three board cards are too weak for a 2x raise; standard flop strategy explicitly excludes pocket deuces, so checking keeps the river option open.

Counting dealer holdings, my pair of 2s wins only about 240 of 990 (about 24%), and every win comes against a non-qualifying dealer, so it pays just +10. That makes raising worth about -20.3 chips versus -20 for folding, so folding is marginally better.

QJ offsuit is inside the published optimal 4x preflop range (Q8o+), so raising the maximum gives the highest expected value.

Any ace is in the published optimal preflop 4x raising range, so A7 offsuit gets the maximum raise.

K5 suited falls inside the published optimal preflop 4x table (K2s+), so raising 4x is the highest-EV play here.

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

J9 suited falls inside the published optimal 4x preflop raising range (J8s+), so a max raise has higher expected value than checking.

The published optimal preflop strategy calls for a 4x raise with any ace, so A3 offsuit is a raise. Raising 4x gives a higher expected value than checking.

86 offsuit is far below the optimal preflop 4x raising threshold (33+, any ace, K5o+, Q8o+, JTo), so I check and decide on later streets.

Trip eights with the flop is a strong favorite over a random dealer hand, so raising 2x maximizes expected value.

K2 offsuit is below the optimal 4x threshold (K5o+), so checking preflop and reassessing on the flop maximizes EV.

King-high with no pair and no flush draw on 5-J-T does not meet the standard flop 2x raise criteria, so checking and deciding on the river is better.

Our pair of deuces with a king kicker wins against every non-qualifying dealer hand and some weaker deuces. By rough enumeration that gives the call an EV of about -11.7 chips, compared with a certain -20 for folding.