Showdown Hold'em table

9-3 offsuit is well outside the optimal preflop raising range (33+, any ace, strong kings/queens/jacks), so checking to see the flop for free is correct.

The dealer always qualifies on this paired board, and my two pair relies on the board tens with a weak 3 kicker. Any dealer ten, nine or higher kicker beats me, so my equity is too thin to raise 2x; check and reassess on the river.

Tens and nines with a jack kicker win about 42% against the dealer, who always qualifies with the board tens. Raising is worth about -0.75 ante in expectation versus -2 for folding.

T9s is not in the optimal preflop 4x raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo). Checking keeps the option to raise on the flop or river.

T9 on a 7-8-3 rainbow board is only an open-ended straight draw with two overcards and no made hand. My rough estimate puts checking and deciding on the river at least as good as a 2x raise, so I'll check.

The dealer always qualifies on this paired board, and our 33-A-T-9 beats only about 192 of 990 dealer holdings. Raising works out to about -20.03 chips versus exactly -20 for folding, so folding is marginally better.

87 offsuit is outside the optimal 4x preflop range (which needs 33+, any ace, or strong kings/queens/jacks), so checking to see the flop for free is correct.

Pairing my 7 gives me a hidden pair (bottom pair on an A-K-7 flop). Standard optimal flop strategy is to raise 2x with any hidden pair except pocket deuces, so raising should beat checking in expected value.

2-3 offsuit is far below the optimal 4x raising threshold, so checking is correct. It keeps flop and river options open at no extra cost.

I've paired the 3 on the board with a hole card, and standard optimal flop strategy says to raise 2x with any hidden pair except pocket deuces. Betting now should earn more than checking and relying on a 1x river bet.

9-3 suited isn't in the optimal preflop 4x raising range (Q6s+/K2s+/any ace/33+), so checking is correct and keeps the flop and river options open.

Nine-high with no pair and only backdoor straight chances is far below the flop 2x raise threshold. Checking keeps the river decision open.

The dealer always qualifies with the two pair on the board. Enumerating dealer hands gives raising an EV of about -19.9 chips, just better than the -20 from folding: I win 165 of 990 dealer holdings and tie 57.

The optimal preflop table does not include 8-5 offsuit, so checking is correct. It lets me see the flop for free and keeps the option to raise later.

The 5d in my hand pairs the board's 5, giving me a hidden pair. Standard optimal flop strategy says to bet 2x with any hidden pair except pocket deuces, so raising beats checking here.

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

A pair of eights made with a hole card, plus an open-ended straight draw (any J or 6 completes it), is a clear 2x raise under standard flop strategy. The draw also adds straight blind-payout equity.

9-3 suited is well outside the optimal 4x preflop raising range, so I check and keep the option to raise on the flop or river for free.

With 9-3 on a Q-8-A board I have no pair and only a backdoor flush draw, far below the flop 2x raise threshold. Checking keeps the option to see the river and fold cheaply.

The board pairs eights, so the dealer always qualifies, and my 9 kicker wins only about 144 of 990 dealer holdings. Raising works out to roughly -21 chips versus -20 for folding, so folding is marginally better.

Q4 offsuit falls below the optimal 4x raising threshold (Q8o+), so I check preflop and look at the flop for free.

A pair of fours that uses one of my hole cards is a hidden pair. Standard flop strategy raises 2x with that, and the backdoor heart draw adds a little equity.

Q9 offsuit is inside the published optimal 4x preflop range (Q8o+), so a maximum raise has higher expected value than checking.

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

A pair of sevens that uses one of my hole cards is a standard flop 2x raise under basic strategy. It beats most dealer holdings that didn't pair, and it also profits when the dealer doesn't qualify.

K7 offsuit falls within the published optimal 4x preflop range (K5o+), so raising 4x maximizes expected value.

K8 suited falls inside the optimal 4x preflop range (K2s+), so the max raise has the highest expected value.

9-4 offsuit is well outside the optimal preflop 4x raising range (33+, any ace, strong kings, queens and jacks). Checking keeps the option to act on the flop or river at no extra cost.

The board pair plays for the dealer too, and 9-high with no draw falls well short of the flop 2x raise threshold (two pair using a hole card, a hidden pair, or a strong flush draw), so I check and keep the river decision.

I am playing the board (QQ88 with a J kicker), so raising can only tie or lose. The dealer only matches that without beating it in about 414 of 990 holdings, giving a raise EV of roughly -17.5 chips versus -20 for a fold.

Q2 offsuit is below the optimal preflop raise threshold (Q8o+), so check and see the flop for free.

I hold a hidden pair of deuces made with my hole card. Standard Ultimate Texas Hold'em flop strategy bets 2x with any hidden pair except pocket deuces, so raising has higher EV than checking.

8-3 offsuit is well below the optimal 4x preflop raising threshold, so checking to see the flop for free is correct.

Eight-high with only backdoor straight chances falls well short of the standard flop 2x raise threshold (two pair, a hidden pair, or a strong flush draw). Checking keeps the river fold option open.

With only ace-high (A-J-8-7-6), about 60% of dealer holdings make at least a pair and beat me. Raising would lose far more often than folding's fixed 20-chip loss, so folding has the higher expected value.

The optimal preflop strategy raises 4x with any ace, and A2 suited is well inside that range. Checking gives up value compared with raising.

The optimal strategy raises 4x preflop with any ace, so A8o qualifies. Raising 4x has higher EV than checking.

23s is not on the optimal preflop 4x table (which needs 33+, any ace, or high kings/queens/jacks), so checking keeps the flop and river decisions open at no extra cost.

A four-card flush draw with only low hole cards (2-3 high) and no pair falls short of the standard 2x flop-raise threshold, which needs a ten or better in hand to the flush. Checking keeps the option to decide on the river.

The 2d and 3d combine with the 6d, 9d and Kd for a king-high flush, a strong hand that pays 3:2 on the blind when it wins. The dealer only beats it with two diamonds or a full house, so raising is clearly better than folding.

T8 offsuit is not on the optimal preflop 4x table (which needs JTo+ for offsuit jack/ten hands), so checking to see the flop is the higher-EV play.

With only the board pair of nines plus an open-ended straight draw, a 2x raise is not justified. Standard flop strategy raises with two pair or better, a hidden pair, or a strong flush draw, so I check and keep the river decision.

The board's two pair plays for both hands, but my T kicker beats roughly a quarter of the dealer's holdings and ties some others. By my count, calling is worth about -16 chips against -20 for folding.

97 offsuit is not in the optimal preflop 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking keeps the flop and river options open at no extra cost.

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

Our hand is only the board's pair of threes with a 9 kicker, and 26 dealer outs beat us, so we win only about 8% of the time. Raising breaks even only above a 20% win rate, so folding loses less.

AQo contains an ace, so it falls inside the published optimal 4x preflop raising range. Raising the maximum gets the most value from a strong hand.

5-2 suited is well outside the optimal 4x preflop range (33+, any ace, K2s+ and so on), so I'll check and see the flop for free.

A pair of fives using a hole card, plus a draw to a straight with any 3, fits the standard flop rule of raising 2x with any hidden pair. The dealer often fails to beat a middle pair, and the blind pays extra if the straight comes in.

5-4 offsuit is well outside the optimal preflop 4x raising range, so checking is correct. It keeps the option to raise 2x on the flop or 1x on the river if the board helps.

5-4 offsite on Q-7-2 gives no pair and no draw beyond backdoors, well below the usual flop 2x threshold of a hidden pair or a strong flush draw. Checking keeps the option to reassess on the river.

The board already has a pair of 7s, so the dealer always qualifies, and our 5 kicker loses to almost any dealer holding. Raising risks about 30 chips with a tiny chance to win, while folding loses only 20.

T8 offsuit is not on the optimal preflop 4x raise table (which needs JTo or better among unpaired non-ace offsuit hands), so checking and reassessing on the flop is correct.

Top pair of tens using a hole card, plus an open-ended straight draw (a 7 or J completes it), is well ahead of a random dealer hand. Standard optimal flop strategy raises 2x with any hidden pair better than deuces.

QTs falls within the published optimal 4x raising range (Q6s+), so raising 4x preflop maximizes expected value.

8-3 offsuit is well outside the optimal 4x preflop raising range, so checking to see the flop for free is correct.

Eight-high with no pair and only backdoor straight draws is far too weak to put in a 2x raise. Checking keeps the option to decide on the river for free.

With only eight-high and no pair, raising loses on average about 24.6 chips, versus 20 chips for folding. The dealer pairs about 60% of the time, and most unpaired dealer hands still beat eight-high.

The optimal preflop 4x table starts at 33+, so pocket 2s are just below the raise threshold and checking is the higher-EV play. We can still raise 2x on the flop or 1x on the river if the hand improves.

Pocket deuces under a K-6-5 board are the classic flop exception: standard optimal strategy raises 2x with a hidden pair except deuces, so checking to the river is better.

A fold loses 20 chips. Raising wins about 10 when the dealer fails to qualify (about 31% of holdings), and ties with a dealer 2 push. That gives an EV of about -15, which beats folding.

K9 suited falls inside the optimal 4x preflop range (K2s+), so raising 4x maximizes expected value.

Q3 offsuit is well below the optimal 4x preflop threshold (Q8o+ for offsuit queens), so checking and re-evaluating on the flop is the higher-EV play.

The pair of fives is on the board and shared with the dealer, so Q3 is effectively just queen-high with no draw. Standard flop strategy only raises 2x with a hidden pair or better or a strong draw, so checking keeps the river decision open.

The Qc gives me a full house, queens full of fives, which beats almost every dealer holding. The river raise is clearly +EV, and a win also pays the blind 3:1.