Showdown Hold'em table

45 offsuit is not on the optimal preflop 4x raise table (which starts at 33+, any ace, and select kings, queens and jacks), so checking to see the flop is correct.

4-5 offsite on A-T-9 has no pair and no straight draw, just two low cards, so raising 2x would lose money. Checking keeps the option to fold for 2 antes on the river or raise if the turn and river improve the hand.

The board already gives the dealer a qualifying pair of nines, and my only edge is a 5 kicker. That beats the dealer in only about 12 of 990 holdings, so raising would lose about 30 chips almost every time, versus losing 20 by folding.

74 suited is not in the optimal 4x raise range (33+, any ace, K2s+, Q6s+, J8s+), so checking to see the flop is the correct play.

I have a four-card flush draw with only low hole cards (the 7c and 4c) and no pair. Standard flop strategy raises a flush draw only when the hidden flush card is ten or higher, so I check and decide on the river.

Pair of fours: enumerating dealer holdings gives calling an EV of about -8.6 chips. That beats folding's certain -20, because the dealer often fails to qualify.

3-5 offsuit is well outside the optimal preflop 4x raising range, so I check to see the flop for free.

3-5 on a 6-7-J board has no pair and only a gutshot draw to a straight with a 4, which is far too weak to raise 2x. Checking keeps the option to fold on the river cheaply.

My 3-5 with the 4-6-7 on board makes a seven-high straight, which beats most dealer holdings and pays the blind 1:1 when it wins. Raising is clearly better than folding.

Q2 offsuit falls outside the optimal 4x table (queen offsuit needs Q8o+), so check preflop and reassess on the flop.

Queen-high with no pair and no flush or straight draw is far below the flop 2x raise threshold (two pair, a hidden pair, or a strong flush draw). Checking keeps the river option open at no extra cost.

The paired board guarantees the dealer qualifies. Against the 990 possible dealer hands I win about 264 and tie 57, so calling is worth about -15 chips versus a certain -20 for folding.

A pocket pair of sevens falls within the published optimal 4x table (33+), so raising the maximum preflop gives the best expected value.

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

8-high with only a gutshot (needs a 5) and a weak backdoor flush draw has too little equity to raise 2x. Checking keeps the option to see the river for free and fold if it misses.

Jack-high with no pair or straight wins only about 28 of 990 dealer holdings. Raising has an EV of about -25 chips, worse than the -20 lost by folding.

Suited 8-2 is well outside the optimal 4x raising chart (needs 33+, any ace, K2s+, Q6s+, J8s+), so checking to see the flop for free is correct.

A flush draw plus a gutshot to a 6 gives about 12 outs, roughly a 45% chance to make a flush or straight by the river. My rough estimate puts raising now slightly ahead of checking, mainly because the blind pays extra on a made flush.

AKs is a premium hand and falls well inside the optimal preflop 4x raising range (any ace), so the maximum raise gives the highest expected value.

The reference optimal preflop strategy calls for a 4x raise with any ace, so A3o is a raise. This is essentially Ultimate Texas Hold'em strategy against a dealer who qualifies with a pair.

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

I have a pair of fours that uses one of my hole cards, with an eight kicker. Standard optimal flop strategy raises 2x with any such hidden pair other than pocket deuces.

9-6 offsuit is not on the optimal preflop 4x raising table (which needs 33+, any ace, or strong kings, queens and jacks), so checking to see the flop for free is correct.

A hole-card pair of sixes plus gutshot equity meets the standard flop 2x threshold, since a hidden pair other than pocket deuces is a raise. The dealer also fails to qualify often, which favours raising over checking.

K7 suited falls within the published optimal 4x preflop range (K2s+), so raising the maximum is the highest-EV play.

The published optimal strategy says to raise 4x preflop with any ace. A2 suited clears that bar and adds flush potential for the blind paytable.

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

Nine high with only backdoor straight and flush draws does not meet the flop 2x raise threshold of two pair, a hidden pair, or a strong flush draw, so checking to the river preserves the option to fold cheaply.

Nines and threes with a king kicker beats every single pair and most dealer holdings, losing only to higher two pair, sets and straights. Raising is clearly better than folding away the ante and blind.

AKo is a strong starting hand and falls within the optimal preflop 4x raising range (any ace), so the maximum raise gives the highest expected value.

J3 offsuit is not in the optimal preflop 4x raising range (needs JTo or J8s+), so checking to see the flop is correct.

Jack-high with no pair and only weak backdoor straight draws on a K-Q-6 board is well behind the dealer's range, so checking keeps the river fold option available instead of putting more chips at risk.

Our two pair (queens and jacks, king kicker) beats the dealer in about 662 of 990 holdings and ties in about 76. Raising has an EV of roughly +6 chips, versus -20 for folding.

Q6s is on the published optimal 4x preflop table (Q6s+), so raising 4x is the reference-optimal play.

98 offsuit is not on the optimal 4x preflop table (it is unpaired with no ace, king, queen or jack), so checking and deciding on the flop or river gives the better expected value.

Nine-high with an open-ended straight draw and no pair is below the optimal flop 2x raise threshold (hidden pair or better, or a strong flush draw). Checking keeps the option to bet 1x or fold on the river once the board is complete.

The river raise EV is about (144×2 − 789×3)/990 ≈ −2.10 antes, versus −2 for folding. We only play the board pair with a 9 kicker, which loses to any dealer pair or any A, K or J, so folding loses slightly less.

87 offsuit is not on the optimal 4x raise table (it needs 33+, any ace, K5o+, Q8o+ or JTo), so checking and reassessing on the flop is correct.

A pair of sevens using a hole card plus an open-ended straight draw (a 5 or T makes the straight and pays the blind) is well ahead of the dealer's random range. Standard flop strategy raises 2x with any hidden pair.

84 offsuit is well outside the optimal 4x raising range (33+, any ace, strong kings, queens and jacks), so checking and reassessing on the flop is correct.

With 8-high, no pair and only a gutshot to a 5, a 2x raise is too weak by standard flop strategy. Checking keeps the option to fold or bet 1x on the river.

I have a pair of eights with an A-K-7 kicker, which beats every dealer hand with no pair or a lower pair. Raising 1x has a much better expected value than folding, which costs a certain 20 chips.

T8 offsuit is not in the optimal preflop 4x raising table, which requires JTo or better among offsuit non-ace, non-king hands, so checking and reassessing on the flop maximizes EV.

The paired queens are on the board and shared with the dealer, so I have only T-8 high with no real draw. That falls well short of the usual 2x flop raise threshold (two pair using a hole card, a hidden pair, or a strong flush draw), so I check and decide on the river.

The board's trip queens guarantee the dealer qualifies, and my ten kicker wins, ties or loses often enough that calling has an expected value of about -11.8 chips. Folding loses 20, so calling costs less.

Any ace is in the published optimal preflop 4x raising table, so A8 offsuit should be raised 4x.

J3 offsuit is not on the optimal preflop 4x raise table (J8s+ or JTo), so checking to see the flop is correct.

A pair of jacks using one of my hole cards is a hidden pair, which basic flop strategy says to raise 2x despite the weak kicker and the king on board. The pair beats enough of the dealer's holdings that raising is worth more than checking.

J6 offsuit is not on the optimal 4x raising chart (it requires JTo or J8s+), so the higher-EV play is to check and see the flop.

J6 offsuit on a Q-9-2 rainbow flop has only jack-high and a weak gutshot-free backdoor draw, well below the flop 2x raise threshold. Checking keeps the option to see the river cheaply and fold if the hand misses.

A pair of sixes on this board beats most dealer holdings: every hand where the dealer fails to qualify, plus low pairs. Roughly 30% of dealer hands beat me, so the call is worth far more than folding and losing 20.

2-3 offsuit is far outside the optimal preflop 4x raising range (33+, any ace, etc.), so checking keeps options open for the flop and river at no extra cost.

2-3 offsite on an A-Q-8 board has no pair and no flush draw, only a weak gutshot needing a 4 and 5 (backdoor wheel), so raising 2x has negative EV. Checking keeps the option to see the river for free.

The board plays (A-Q-J-T-8), so the best I can do is tie. A tie only happens when the dealer holds two unpaired cards from 2 to 7, about 20% of dealer holdings, which makes raising worth about -23.9 chips versus -20 for folding.

Offsuit 7-3 is well outside the optimal preflop 4x raising range, so checking and seeing the flop for free is correct.

Seven-high with no pair and only a weak backdoor straight draw is well below the standard flop 2x raise threshold (two pair, a hidden pair or a strong flush draw). Checking keeps the river decision open.

The board pair gives the dealer at least a pair of 4s, so the dealer always qualifies. My 7 kicker beats only about 4% of dealer holdings, which makes calling worth about -2.7 antes versus -2 for folding.

KQ offsuit (K5o+) is in the published optimal preflop 4x raising range, so raising the maximum is best.

The published optimal preflop strategy says to raise 4x with any ace, and A2o is on that list. Raising the maximum has higher expected value than checking.

The published optimal table says to raise 4x with K5o or better, and K5 offsuit just meets that threshold. Raising 4x is favored over checking here.

T5 offsuit is not in the optimal 4x preflop raising range. Checking keeps the flop and river decisions available at no extra cost.

T5 offsuit on a 4-8-2 board has no pair and only a weak gutshot (needs a 3 for 2-5), plus overcards that are no better than ten high. Raising 2x is clearly -EV, so I check and keep the option to play or fold on the river.

With only king-ten high and no pair, the dealer qualifies about 60% of the time. When the dealer misses, I win only about 96 of 990 holdings, far below the roughly 199 needed for calling 10 more to beat folding. Folding loses 20 chips, which is less than the expected loss from raising.