Showdown Hold'em table

K2 offsuit falls outside the published optimal 4x table (K5o+ is the offsuit threshold). Checking keeps the option to raise 2x on the flop or 1x on the river at no extra risk.

A hole card pairs the board's 2 (a hidden pair, with a king kicker and a backdoor club draw). Standard flop strategy is to raise 2x with any hidden pair except pocket deuces.

The published optimal strategy says to raise 4x preflop with any ace, and A6o qualifies. Raising 4x has higher expected value than checking.

9-4 offsuit falls outside the optimal preflop 4x raising range (33+, any ace, K5o+, Q8o+, JTo, among others). Checking lets me see the flop for free.

9-high with a gutshot (needs a 2 for A-5... actually needs 2 or 6 for a straight) and no pair is well behind a random dealer hand, so raising 2x is -EV. Checking keeps the river fold option open.

We only play the board's pair of threes with T-9-8 kickers, and the dealer always qualifies on this paired board. We beat roughly 8.5% of dealer hands and tie about 4.5%, so raising has an EV well below the -20 chips lost by folding.

J8 offsuit falls outside the optimal 4x table, which needs J8 suited or JTo for jacks. Checking keeps a free look at the flop.

With no pair, J-high, and only an open-ended straight draw, betting 2x on the flop has negative EV compared with checking. Checking keeps the river raise or fold available once the draw is resolved.

I have a jack-high straight (J-T-9-8-7). Only a dealer flush with two diamonds beats it, so raising is clearly profitable, and the straight also pays 1:1 on the blind if I win.

T2 suited is not in the optimal 4x raising table, so I check and see the flop for free.

T-high with no pair and no real draw on J-7-6 falls well short of the 2x flop-raise threshold (two pair, a hidden pair, or a strong flush draw). Checking keeps the option to fold on the river cheaply.

The board pair means the dealer always qualifies, and my jacks with a ten kicker win only about 11% of the time against the 990 possible dealer hands. Raising is worth about -23 chips, which is worse than the -20 from folding.

Pocket 55 falls within the optimal 4x preflop range (33+), so the maximum raise is correct here.

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

T4 offsuit is well outside the optimal preflop 4x raising range (JTo is the minimum ten-high offsuit hand), so checking is the better play.

A pair of tens that uses one of my hole cards sits in the standard flop 2x raising range, and it is ahead of most dealer holdings, which favors raising over checking.

J7 suited falls outside the optimal 4x table, which starts at J8s+ for jack-high suited hands, so checking and seeing the flop is the higher-EV play.

J7 offsuit on an A-6-3 two-heart flop is only jack-high with no pair and no real draw (just a gutshot-free backdoor), so raising 2x has negative EV. Checking keeps the option to play or fold on the river.

We hold jacks and sixes with an ace kicker, and the paired board means the dealer always qualifies. We beat any dealer hand without a jack or better pair, so a 1x call is far better than folding and losing 20.

98 offsuit is not in the optimal preflop 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking and seeing the flop is better.

Nine-high with only runner-runner flush and straight draws is far below the flop raise threshold of two pair, a hidden pair, or a strong four-flush. Checking keeps the option to fold or bet 1x on the river.

With only nine-high against this board, the dealer beats us whenever they qualify, which is about 60% of hands. Raising works out to roughly -20.5 chips versus exactly -20 for folding, so folding is marginally better.

2-3 offsuit is the weakest possible starting hand and far outside the optimal 4x raising range (33+, any ace, etc.), so checking preflop is correct.

A pair of deuces is the weakest possible pair and plays much like pocket deuces, the one hidden pair that basic flop strategy excludes from the 2x raise. Checking keeps the option to bet 1x or fold on the river.

Folding costs 20 chips. Raising risks 30 in total, but the dealer fails to qualify about 40% of the time, which wins us the 10-chip play bet. That makes raising roughly -14 EV, better than folding.

T8 offsuit is not in the optimal 4x preflop table (it requires JTo or better for offsuit jack-high and below), so checking and seeing the flop for free is correct.

T8 with no pair on a Q-A-J board has only a gutshot to a king and a runner-runner flush draw, well short of the usual flop raise threshold (two pair, a hidden pair, or a strong flush draw). Checking keeps the option to raise 1x or fold on the river.

The Ts with AKQJ on board gives me the nut Broadway straight, which loses only to a dealer flush. Raising is clearly better than folding, and a win also pays the blind 1:1.

The published optimal strategy raises 4x preflop with any ace, and A2o fits that rule. So raising 4x is the reference play here.

T9 offsuit is not in the optimal preflop 4x raising range (JTo is the weakest offsuit jack-high hand that qualifies), so checking preserves flop and river options at lower risk.

Ten-high with no pair and only backdoor straight and flush draws is too weak to put in a 2x raise on this flop. Checking keeps the river fold-or-bet option open.

Pair of tens with a king-high board still beats every non-qualifying dealer hand and many weaker pairs. Raising risks 10 more chips but has an EV far above the -20 guaranteed by folding.

Q6 offsuit falls outside the optimal 4x table (Q6 qualifies only when suited; offsuit needs Q8+), so checking preflop and deciding on the flop is best.

Queen-high with no pair and no real draw is well below the flop raise threshold of a pair, two pair or a strong flush draw. Checking keeps the option to fold or raise 1x on the river.

With Q-high the dealer usually qualifies, but raising loses about 18.5 chips on average, slightly better than the certain 20-chip loss from folding. This is because the ante pushes whenever the dealer holds no pair, and we win about 244 of the 990 possible dealer hands.

AJo contains an ace, and the optimal preflop strategy raises 4x with any ace. That makes raise_4x the highest-EV action here.

J8 offsuit is not on the optimal 4x table (J8s+ or JTo only), so checking is the higher-EV play. I'll reassess on the flop.

J8 offhand on a three-club Q45 board has no pair, no club, and no real draw, so raising 2x here would be -EV. Checking keeps the option to see the river for free and then fold or raise 1x.

With only jack-high, the dealer qualifies about 81% of the time on this four-club, ace-high board. Raising 1x works out to roughly -24.6 chips in expectation, versus a fixed loss of 20 chips for folding.

K4 suited falls inside the published optimal 4x preflop range (K2s+), so raising 4x maximizes expected value.

J6 offsuit falls outside the optimal 4x preflop table, which needs J8s+ or JTo for jack-high hands. Checking keeps the option to raise 2x on the flop or 1x on the river at no extra cost.

A hidden pair of sixes, which is top pair on the board with a jack kicker, is a standard flop raise under optimal Ultimate/Casino Hold'em strategy. The hand beats most dealer holdings, and the backdoor heart draw adds some equity.

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

6-2 offsuit is well outside the optimal 4x preflop raising range, so checking to see the flop for free is correct.

6-2 offsuit on a K-J-3 rainbow flop has no pair and no draw, so raising 2x is clearly -EV. Checking keeps the river decision free.

With only ace-high and a 6 kicker, I lose to any pair, any ten, or any 7-9 kicker. Raising is worth about -32 chips on average, compared with -20 for folding.

KTo falls within the published optimal 4x preflop range (K5o+), so raising 4x maximizes expected value.

QTo falls within the published optimal preflop 4x range (Q8o+), so raising 4x maximizes expected value.

Pocket sixes fall within the optimal 4x preflop range (33+), so the maximum raise gives the highest expected value.

Offsuit 4-3 is not in the optimal preflop 4x raising range (33+, any ace, strong kings/queens/jacks), so checking and seeing the flop for free is best.

4-3 offsod on a Q-K-5 flop has no pair and only a gutshot to a straight (needs a 2), so it is far too weak to raise 2x. Checking keeps the river decision open at no extra cost.

I have two pair, fives and fours with a king kicker, and I beat or tie roughly 63% of dealer holdings. Raising 1x is about breakeven, while folding loses 20 chips for sure.

K2 offsuit falls outside the optimal 4x table, which requires K5o or better, so checking preflop is correct. I'll reassess on the flop.

King-high with only a gutshot to Broadway and no made pair is too weak to raise 2x on the flop. Checking keeps the option to decide on the river with all five cards showing.

King-high loses 20 chips if I fold. Calling costs 10 more, and I beat every non-qualifying dealer hand without a king (about 30% of holdings), so raising has higher expected value than folding.

92s is well outside the optimal preflop 4x raising range (no ace, no pair, 9-high), so checking to see the flop is correct.

A middle pair of nines made with a hole card is a hidden pair. Standard optimal flop strategy raises 2x with it, since checking to the river gives up too much value.

86 offsuit is not in the optimal preflop 4x raising range (which requires pairs 33+, any ace, or strong kings/queens/jacks), so I check and look at the flop for free.

A hidden pair of sixes, made with a hole card, plus some straight potential. Standard flop strategy is to raise 2x with any hidden pair other than pocket deuces.

5-4 offsuit is well outside the optimal 4x preflop range, so checking is correct; I can still raise 2x on the flop or 1x on the river if the board helps.

With 5-4 on a T-7-7 flop I hold only the board pair and no real draw, far below the usual flop raise threshold of two pair, a hidden pair or a strong flush draw. Checking keeps the option to see the river and decide then.

The board plays for me (777-K-T), so I can at best tie. The dealer beats me in about 701 of 990 holdings, which makes raising worth about -21.2 chips versus -20 for folding.

Pocket 4s is within the optimal 4x raising range (33+), so raising 4x preflop maximizes expected value.