Showdown Hold'em table

Pocket tens are well inside the optimal 4x preflop raising range (33+), so the maximum raise gives the highest expected value.

74s is well outside the optimal preflop raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking to see the flop for free is correct.

7-high with only backdoor straight and flush draws and no pair is far too weak to raise 2x on the flop. Checking keeps the option to fold or raise on the river.

I only have king-high with no pair or straight. Raising would lose about 24 chips on average against the dealer's possible hands, while folding loses exactly 20.

9-3 offsuit is not in the optimal preflop 4x raising table, so checking keeps the extra risk off and waits for the flop.

9-3 offsuit on a K-T-4 flop gives no pair and only a weak gutshot (needs a Q and J), so raising 2x would be -EV. Checking is free and keeps the river decision open.

With only A-K-T-9-7 high, the dealer pairs about 60% of the time. Enumerating dealer holdings puts raising at about -20.8 chips versus -20 for folding, so folding is slightly better.

9-5 offsuit is well outside the optimal preflop 4x range, so checking is the higher-EV play. It keeps the flop and river decisions available at no extra cost.

Two pair (queens and nines) with a hidden pair of nines. That beats most dealer holdings, so the standard flop strategy is to raise 2x rather than check.

Q5 offsuit is below the optimal 4x preflop threshold (Q8o+ for offsuit queens), so I check and reassess on the flop.

Queen-high with no pair and no real draw on 6-T-2 rainbow falls well short of the standard 2x flop raise, which needs at least a pair using a hole card. Checking keeps the option to decide on the river.

King-high (KQT65) beats roughly 220 of the 990 possible dealer holdings. A win gains 10 more than folding, and a qualified-dealer loss costs 10 more. Since 3×220 > ~609 qualifying hands, raising has a slightly higher EV than folding.

The published optimal preflop strategy raises 4x with any ace, and A5 offsite is on that list. Raising the maximum is higher EV than checking.

T2 offsuit is well outside the optimal preflop 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking to see the flop for free is correct.

T2 misses the K-9-K flop entirely: I have no pair of my own and no draw, only the board's kings. Checking keeps the option to decide on the river rather than putting 2x at risk now.

We hold kings and tens with a 9 kicker, and the dealer only beats that with a king, the last ten, a QJ straight, or a pocket pair of JJ or higher. Raising needs just over a 20% win rate to beat folding, and we win far more often than that.

The published optimal preflop strategy says to raise 4x with K5o or better, and K6 offsuit qualifies, so the 4x raise has the higher expected value.

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

K2 offsuit is below the optimal 4x threshold (K5o+), so checking preflop and deciding on the flop has higher expected value.

A hidden pair of deuces with a king kicker, plus backdoor straight chances on 5-2-3, meets the standard flop 2x raise threshold. Raising is higher EV than checking.

Offsuit 9-5 falls well outside the optimal preflop 4x raising range, so checking keeps our risk at the ante and blind until we see more cards.

Standard flop strategy is to raise 2x with any pair that uses a hole card. Here the 9 pairs the board, and middle pair should be ahead of most dealer holdings, so raising 2x has higher expected value than checking.

JTs is on the published optimal 4x preflop table (J8s+), so raising the maximum is the best play.

A6 suited falls under 'any ace' in the published optimal 4x preflop table, so raising the maximum is the reference play.

9-8 offsuit is not on the optimal 4x preflop table (it needs JTo or better among unpaired non-ace/king/queen offsuit hands), so checking and reassessing on the flop is correct.

Middle pair of eights using a hole card, with a 9 kicker, meets the standard flop strategy of raising 2x with a hidden pair. It plays well against the dealer's range.

J7 offsuit is below the optimal preflop 4x threshold, which calls for JTo or better among offsuit jacks. Checking keeps the option to raise 2x on the flop or 1x on the river more cheaply.

Standard flop strategy is to raise 2x with any hidden pair that uses a hole card, except pocket deuces. Our pair of sevens with a jack kicker is well ahead of the dealer's average holding.

T8 offsuit is not on the optimal 4x preflop raising chart (which only includes JTo among J/T offsuit hands), so checking is best. That keeps the flop and river decisions open.

T8 high on an A-Q-4 board has no pair and no real draw, so it falls well below the flop 2x raise threshold. Checking keeps the option to decide on the river.

Aces and tens with a queen kicker beat most dealer holdings; the dealer only wins with an ace, a queen, a diamond flush, KJ, KK or a ten with a king, roughly 28%. Calling is worth about +5 chips, versus -20 for folding.

KQo is well inside the published optimal 4x preflop range (K5o+), so the maximum raise has the best expected value.

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

9-high with no pair and only a backdoor straight draw falls well short of the flop 2x raise threshold (two pair, a hidden pair, or a strong flush draw). Checking keeps the river decision open at no cost.

The board pair means the dealer always qualifies, and my 9 kicker wins only about 15% of the time (144 of 990 dealer hands). Raising works out to roughly -21 chips versus -20 for folding, so folding is slightly better.

J4 offsuit is well outside the optimal 4x preflop range (JTo+ for offsuit jacks), so checking to see the flop is correct.

The only pair is the 6s on the board, so my hand is just jack-high with a backdoor flush draw (only three spades). That falls short of the usual flop 2x raise threshold of a hidden pair or a four-flush with a strong kicker, so I check and decide on the river.

I only have a pair of sixes (the board pair) with a jack kicker, and the dealer always qualifies on this board. I win against about 10.5% of dealer holdings, so raising is worth roughly -23.8 chips versus -20 for folding.

T6 offsuit falls outside the optimal 4x preflop range, which only includes offsuit tens as JTo. Checking lets me see the flop at no extra cost.

With only ten-high and a gutshot to a nine, we have no pair or strong flush draw, so a flop raise has negative expected value. Checking keeps the river fold-or-raise option open.

I hold top pair of tens, which beats most dealer holdings on this board. Folding forfeits 2 antes for certain, so raising 1x has clearly higher EV.

J5 offsuit is not on the optimal 4x preflop table, which needs JTo or better for offsuit jacks. Checking keeps the option to raise 2x on the flop or 1x on the river once more cards are seen.

Jack high with no pair and only backdoor straight draws falls well below the flop 2x raise threshold. Checking keeps the river decision open.

The dealer always qualifies on the paired board. I beat about 216 of 990 dealer holdings and tie 8, so raising has an EV of about -18.8 chips versus -20 for folding, which makes raise_1x slightly better.

The reference optimal strategy says to raise 4x preflop with any ace, and suited A2 falls in that range. Raising the maximum on hands in the published 4x table maximizes expected value.

65 offsuit is not in the optimal preflop 4x raising range (33+, any ace, strong kings/queens/jacks), so checking to see the flop is correct.

Standard flop strategy is to raise 2x with any hidden pair other than pocket deuces. Our pair of sixes, made with a hole card, clears that bar despite the overcard jack on the board.

A9 suited is any ace, which is in the published optimal 4x preflop raising range, so max raise is correct.

54 offsuit is well outside the optimal preflop 4x range (33+, any ace, K5o+, Q8o+, JTo), so checking and seeing the flop for free is correct.

This is an open-ended straight draw with low cards and no pair. Under standard flop strategy that is not strong enough for a 2x raise, so checking keeps the river decision open.

I'm just playing the board (KK-Q-7-6), so the dealer, who always qualifies here, can only tie me and beats me about 93% of the time. Raising would lose about 28 chips on average, while folding loses only 20.

Q4s is below the optimal 4x preflop threshold (Q6s+), so checking and deciding on the flop is higher EV.

Q4 on a K-9-9 flop gives me only the board pair with a queen kicker, no hidden pair and no flush draw. That is well below the usual 2x flop-raise threshold, so I check and will decide at the river.

Using the board pair of nines, I play 99-A-K-Q. Rough counts give about 42% wins and 48% losses, so raising is worth about -0.6 ante versus -2 for folding, even allowing for dealer spade flushes.

Q4 suited falls below the optimal 4x threshold, which starts at Q6s, so checking preflop is correct. I'll re-evaluate on the flop.

Queen-high with no pair and only backdoor draws is too weak to raise 2x on the flop. Checking keeps the option to reassess on the river, where I can raise 1x or fold.

With a weak pair of fours, raising has an estimated EV of about -19.1 chips against the 990 possible dealer hands. That is slightly better than the -20 lost by folding, mainly because the dealer often fails to qualify.

8-2 offsuit is far outside the optimal preflop 4x raising range, so checking to see the flop for free is correct.

With 8-2 offsuit on a T-7-5 rainbow flop I have no pair and no draw beyond backdoors, well below the flop raising threshold. Checking keeps the river raise-or-fold option open.

I only have the board's pair of fives with an 8 kicker, and the dealer always qualifies on this board. By my rough count the dealer beats me in about 89% of holdings, so raising is worth about -25 chips versus -20 for folding.

J5 offsuit is outside the optimal 4x preflop range (J8s+ or JTo), so checking to see the flop is correct.

Jack high with no pair and no flush draw falls well short of any flop raise threshold. Checking keeps the option to decide on the river with all cards seen.

With only Jack-high and no pair, raising returns about -21.1 chips against the dealer's possible holdings, because the dealer qualifies about 60% of the time. Folding loses exactly 20 chips, so it is slightly better.

The optimal 4x preflop table includes K5o and better, so K7 offsuit qualifies for the maximum raise. Raising 4x has higher expected value than checking.