Showdown Hold'em table

86 offsuit is well outside the optimal preflop 4x raising range, so checking to see the flop for free is the higher-EV play.

Our 6 pairs the board, which standard flop strategy says to raise 2x with. We also have a gutshot straight draw (any 7) and a backdoor heart flush draw, so 2x should be worth more than checking.

K3 offsuit is below the optimal 4x threshold (K5o+), so checking preflop and waiting for the flop is better.

Kings and eights two pair, using a hole card, is a strong made hand that beats most dealer holdings. The standard flop strategy is to bet two pair or better here.

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

T4 offsuit is well outside the optimal preflop 4x raising range (JTo is the lowest offsuit ten-high hand that qualifies), so I check and keep the flop and river options open.

T4 offsite on a 3-Q-6 board with two hearts gives me only a weak backdoor flush draw, a gutshot (5 for 3-4-5-6) and ten high. That is far too weak to raise 2x, so I check and decide on the river.

A pair of fours makes calling worth about -1 ante, better than the -2 ante lost by folding. Raising also wins when the dealer fails to qualify or holds only 3s or less.

The optimal preflop strategy calls for a 4x raise with any ace, so A3o qualifies. Raising beats checking in expected value.

85 offsuit is well outside the optimal preflop 4x raising range, so checking preserves a free look at the flop.

85 offsuit has nothing on a T-K-J board: no pair and only a weak gutshot-free backdoor, so raising 2x would be -EV. Checking keeps the option to see the river for free.

Enumerating dealer holdings gives an EV of about -11.3 chips for a 1x raise with our pair of eights, mainly because the dealer often fails to qualify. Folding costs a sure 20 chips, so calling is better.

T2 suited is not in the optimal preflop 4x raising range (Q6s+, J8s+, K2s+, any ace, 33+), so I check and wait for the flop.

Ten-high with only a gutshot to broadway (no pair, no flush draw) falls well short of the standard flop 2x raise threshold. Checking keeps the river decision open.

Our aces and tens with a king kicker beat about 465 of the 990 possible dealer holdings, tie 63 and lose 462. That makes raising worth about -0.46 ante, compared with -2 for folding.

T9 offsuit is not on the optimal 4x preflop table, which needs JTo or better for offsuit connectors, so checking to see the flop is correct.

Top pair (nines, using a hole card) with a ten kicker on a 9-7-2 flop is well ahead of the dealer's typical holdings. Standard flop strategy is to raise 2x with any pair that uses a hole card.

82 suited is well outside the optimal preflop 4x raising range (no pair, no ace, no qualifying K/Q/J), so checking to see the flop is correct.

8-high with no pair and no draw on a K-4-9 board is far behind; checking keeps the river option to fold or call cheaply.

With only ace-high (AKJ98) and no draw left, the dealer qualifies about 65% of the time. Counting all 990 dealer holdings, raising has an EV of about -21.4 chips, versus a sure -20 for folding, so folding is slightly better.

Pocket nines fall within the published optimal 4x raising range (33+), so the maximum preflop raise has the best expected value.

Offsuit 7-4 is far outside the optimal preflop 4x raising range, so checking to see the flop for free is correct.

Seven-high with no pair and only weak backdoor straight potential falls far short of the flop 2x raise threshold. Checking keeps the option to fold or bet 1x on the river cheaply.

The board already holds trip deuces, so the dealer always qualifies, and my best hand is only 2-2-2-T-7. Out of 990 possible dealer hands I win just 40 and tie 33, so raising is worth about -27 chips versus -20 for folding.

Any ace is in the published optimal preflop 4x raising table, so A6 offsuit raises 4x rather than checking.

AJo is any ace, which falls inside the published optimal 4x preflop raising range, so raising the maximum is correct.

Q4 offsuit is not in the optimal 4x table (Q8o+ needed), so I check and keep the option to raise on the flop or river.

Second pair of queens made with a hole card falls under the standard flop strategy of raising 2x with any hidden pair. Its showdown equity against a random dealer hand makes the 2x raise more profitable than checking.

Pocket sixes fall within the published optimal 4x raising range (33 and above), so the maximum preflop raise has the highest expected value.

J3 offsuit falls outside the optimal 4x preflop table, which requires J8s+ or JTo for jack-high hands. Checking keeps the flop and river decisions available at no extra cost.

J-3 offsite has no pair of its own and no draw on a paired 7-T-T board; the tens are shared with the dealer. Standard flop strategy only raises 2x with a hidden pair or better or a strong flush draw, so I check and decide on the river.

Playing the board's two pair with a jack kicker loses most of the time, but it still beats or ties about 39% of dealer hands. That makes raising worth about -12 chips, versus a certain -20 for folding.

9-6 suited is outside the optimal preflop 4x raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking and deciding on the flop is the higher-EV play.

Standard optimal flop strategy is to raise 2x with any hidden pair except pocket deuces. Our 6 makes a pair of sixes with the board, so this hand qualifies, and raising beats checking in expectation.

2-3 offsuit is far below the optimal 4x raising threshold (33+, any ace, etc.), so checking preflop to see the flop for free is correct.

A pair of threes using a hole card plus an open-ended straight draw (any ace or six) is strong enough against the dealer's random hand. A straight would also pay the blind, so raising 2x on the flop has positive expected value.

K8 suited falls within the published optimal 4x preflop range (K2s+), so a maximum raise has the highest expected value.

Q4 offsuit is below the optimal preflop 4x threshold (Q8o+ for offsuit queens), so checking and reassessing on the flop is correct.

Queen-high with no pair and only backdoor draws falls well below the standard flop 2x raise threshold. Checking keeps the option to bet 1x or fold on the river.

Queen-high with no pair, straight or flush. Calling 1x is worth about -22.9 chips, because the dealer qualifies in roughly 65% of holdings and often out-kicks us otherwise, which is worse than the 20 chips lost by folding.

J9 offsuit falls below the optimal preflop 4x threshold (needs J8s+ or JTo), so checking and deciding on the flop is the higher-EV play.

Top pair of jacks using a hole card, plus an open-ended straight draw. Standard flop strategy is to bet 2x with any hidden pair, so raising has positive expected value here.

J7 offsuit is not on the optimal 4x table (that needs J8s+ or JTo), so checking preflop and seeing the flop for free is the better play.

J-7 with no pair and only a backdoor spade flush draw is far too weak to raise 2x on the flop. Checking keeps the river decision open at no extra cost.

Ace-high with a Jack kicker beats roughly 240 of the 990 possible dealer hands that fail to qualify, while 625 hands qualify. Calling is therefore about 1 chip better than folding: winning gains 30 chips relative to folding, and losing to a qualifying dealer costs only 10 more.

Q7 offsuit falls outside the optimal 4x raising table (Q8o+ for offsuit queens), so checking and re-evaluating on the flop has higher expected value.

Paired the 7 with a hole card for middle pair, plus a backdoor club draw. Standard flop strategy is to raise 2x with any pair that uses a hole card, and this hand fits.

4-2 offsuit is well outside the optimal preflop 4x raising range, so checking keeps the cost down and leaves the flop and river decisions open.

2-4 offsite on an 8-3-J board has no pair, only a gutshot to a 5 and a weak backdoor flush draw, which is well below the threshold for raising 2x on the flop. Checking keeps the option to fold or raise 1x on the river cheaply.

My hand only plays the board (33-J-8-5), so the dealer always qualifies and beats me with almost any card above a five. A tie is very unlikely, so folding (-20) beats raising, which would mostly lose 30.

KJo meets the published optimal preflop 4x threshold (K5o+), so raising 4x maximizes expected value over checking.

AK offsuit falls well inside the optimal preflop 4x raising range (any ace), so the maximum raise has the highest expected value.

Q3 offsuit is below the optimal preflop raise threshold (Q8o+), so I check and look at the flop for free.

The Qd pairs the board queen, so I hold queens and eights, a top-pair-strength hand. Standard optimal flop strategy raises two pair that uses a hole card, even with a weak kicker.

J5 offsuit is not on the optimal preflop 4x raise list (it calls for JTo or J8s+), so checking and seeing the flop is the higher-EV play.

Top pair of jacks using a hole card fits the standard flop 2x raise rule for a hidden pair. Against a random dealer hand it holds enough equity to justify the bet despite the connected board.

A2 suited is any ace, which the optimal preflop table says to raise 4x. Its suitedness also adds blind-paytable flush equity.

52 offsuit is far below the optimal preflop raising threshold, so checking is correct and keeps the flop and river options open at no extra cost.

There is no made hand, only a four-out straight draw (any 4) and possible low pairs. That is far too weak to put 2x at risk, so check and decide on the river.

The board (3-3-A-K-6) plays and my 2 and 5 add nothing, so I can at best tie and lose to most dealer hands. Raising loses about 29.4 chips on average versus a sure 20 by folding.