Showdown Hold'em table

54 offsuit is far outside the optimal preflop 4x raising range (33+, any ace, strong kings/queens/jacks), so checking is correct and keeps the flop and river options open.

4-5 offsponsuit on A-T-7 has no pair and only a gutshot (needs a 6 plus an 8 or 3, which is runner-runner), so it is well behind the dealer and raising 2x would be -EV. Checking keeps the river decision open at no extra cost.

I'm playing the board (aces with T-8-7), so I can't beat the dealer, who always qualifies with the board's aces. I can only tie, in about 129 of 990 dealer holdings, so a 1x raise is worth about -26 chips versus -20 for folding.

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

ATo falls within the optimal 4x preflop raising range (any ace), so I take the maximum raise.

Pocket sevens are within the optimal 4x raise range (33+), so raising the maximum preflop maximizes expected value.

Any ace is on the published optimal 4x preflop table, so A9o earns the maximum raise.

4-3 offsuit is far outside the optimal preflop 4x raising range, so checking is the best play. It sees the flop for free with the option to raise later.

Holding 4-3 on a J-Q-A flop gives me no pair and only a weak gutshot needing runner cards, so raising 2x would be clearly negative EV. Checking keeps the river decision open at no extra cost.

Two pair (fours and threes) on an unpaired board beats every dealer one-pair hand. Only uncommon two-pair, trips or straight holdings beat it, so raising is far better than folding and losing 20.

T3 suited is outside the optimal 4x raising range (which needs J8s+ for jack-high suited hands), so checking to see the flop for free is best.

A pair of tens that uses one of my hole cards meets the standard flop rule of raising with any hidden pair. The monotone club board and weak kicker make it closer, but raising should still beat checking.

Q5 offsuit falls below the optimal 4x threshold (Q8o+), so checking and reassessing on the flop is better than raising.

I only have the board's pair of kings with a queen kicker and a backdoor flush draw, which is not strong enough for a 2x flop raise under standard flop strategy. Checking keeps the river decision open.

We play kings with an A-Q-9 kicker. The dealer always qualifies with the board pair, and we win against about 42% of dealer holdings and tie about 7%. That gives calling an EV of roughly -6.7 chips, versus -20 for folding.

T7 suited falls below the optimal preflop 4x raising threshold (J8s+), so checking is the right play. We'll see the flop for free and decide there.

Ten-high with no pair and no real draw on a J-4-3 flop is far below the flop raise threshold, so checking to see the river for free is better than putting in 2x.

Ten-high with no pair. Enumerating the dealer's hands gives raising an EV of about -21.6 chips versus -20 for folding, because the dealer qualifies about 64% of the time and we rarely win even when the dealer does not qualify.

54 offsuit is not in the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so checking to see the flop is correct.

A pair of fives that uses a hole card is a hidden pair. Standard flop strategy for this game raises 2x with any hidden pair except pocket deuces, so the raise has positive expected value against a random dealer hand.

T5 offsuit is well outside the optimal preflop 4x raising range (needs JTo+ for unsuited jacks/tens), so checking to see the flop is correct.

Standard flop strategy is to raise 2x with any pair that uses a hole card. Middle pair of tens is far enough ahead of the dealer's range that raising beats checking.

K2 offsuit falls below the optimal 4x raising threshold (K5o+ or K2s+), so checking is better than raising preflop.

King-high with no pair and only a backdoor flush draw falls short of the standard flop raise threshold of a hidden pair, two pair, or a strong four-flush. Checking keeps the river decision open.

Ks with four spades on board gives a king-high flush, which loses only to the As, a straight flush, or a board-pairing full house or quads. Raising is clearly +EV, and a win also earns the 3:2 blind payout.

8-2 suited is far below the optimal preflop 4x raising range (pairs 33+, any ace, strong kings, queens and jacks), so checking to see the flop for free is correct.

8-2 on a 7-T-3 board has no pair and only a weak backdoor flush draw and a gutshot-ish draw, so it is far behind a random dealer hand. Checking keeps the river fold option open.

The dealer always qualifies because the board is paired, and our 3s with an 8 kicker win only about 84 of 990 dealer holdings. That makes raising worth about -24.4 chips versus -20 for folding, so we fold.

72 offsuit is the weakest starting hand and falls far outside the optimal 4x raising range, so I check and take a free look at the flop.

Seven-high with only backdoor flush and straight draws is too weak to raise 2x. Checking keeps the option to see the river and fold for free if nothing improves.

I am only playing the board (a pair of fives with J-9-8), so I can at best tie. A tie happens only about 11% of the time, which makes raising worth roughly -27 chips against -20 for folding.

8-6 offsuit is well outside the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo), so the best play is to check and see the flop for free.

8-6 offsuit on a 7-3-J board is only 8-high with a gutshot (needs a 5 for 3-4-5-6-7... wait, 4-5 needed; a 5 makes 5-6-7-8 plus another card only on two cards), so it's too weak to raise 2x. Checking is free and leaves the river decision open.

I only have the board's pair of sevens with 8-6 kickers, and the dealer always qualifies on this board. By my count I beat the dealer in only about 52 of 990 holdings, far below the roughly 20% win rate needed for a 1x raise to beat folding, so folding loses less.

8-3 offsuit is far below the optimal preflop 4x raise threshold, so I check and keep the option to raise on the flop or river.

I only have the board's pair of sevens, with a weak 8 kicker, a gutshot and a backdoor flush draw. That is too weak to put 2x at risk, so I'll check and decide on the river.

The board's pair of sevens with A-K-9 plays, so my hand can at best tie the always-qualifying dealer. I lose to roughly 80% of dealer holdings, so raising (EV about -24 chips) is worse than folding (-20).

Any ace is in the published optimal preflop 4x raising table, so A7o is a max raise.

K7 offsuit is inside the published optimal 4x table, which raises K5o and better, so raising 4x preflop maximizes expected value.

9-3 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.

The pair of sixes is on the board, so I hold only 9-high with no draw. Standard flop strategy is to raise 2x only with a hidden pair or better, or a strong flush draw, so I check and decide on the river.

We hold two pair (sixes and threes with a king kicker). The dealer always qualifies here because of the board pair, and we beat a majority of dealer hands. Raising is roughly break-even or better, versus a guaranteed loss of 20 chips from folding.

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

6-5 on a 9-9-K board makes no pair of our own and holds only weak backdoor straight draws, well below the usual flop raising threshold. Checking keeps the cost low and leaves the river decision open.

My hole cards don't play, since the board's pair of nines plays for both hands. The dealer always qualifies and at best ties me (only about 13% of holdings), so raising (about -2.6 antes) is worse than folding (-2 antes).

72s is well outside the optimal preflop 4x raising range, so checking is best; I'll see the flop for free and reassess.

A pair of sevens that uses my hole card, plus a backdoor spade draw, fits the standard 2x flop raise for a hidden pair. Its edge over checking to the river should be positive, though it is thin with only a deuce kicker.

K3 offsuit falls below the optimal 4x raising threshold (K5o+), so I check and keep the option to raise 2x on the flop or 1x on the river.

King-high with no pair and only a backdoor straight draw on 8-2-4 does not meet the flop raise threshold of a hidden pair or better, so checking keeps the river option open.

K-high with no pair wins only about 19% of the time and wins just the 1x play bet when it does. Calling has an EV of about -2.05 antes, slightly worse than the -2 from folding.

J2 offsuit is not in the preflop 4x raising range (offsuit jacks need JTo or better), so checking is better. I'll see the flop for free and decide on a 2x raise or the river.

J-high on a paired 6-8-6 board gives no hidden pair or draw, so this is well below the flop 2x raise threshold. Checking keeps the option to see the river for free.

Folding loses 20 chips. With the board pair of sixes and a K-J-8 kicker, I estimate about a 21% chance to win and 4% to tie, which puts raising at roughly -18 chips, slightly better than folding.

Q6 offsuit falls outside the optimal 4x table, which requires Q8o or better for offsuit queens. Checking keeps the option to raise 2x on the flop or 1x on the river at no extra cost.

Q6 has no pair and no flush draw on a J-K-3 flop, which falls well short of the standard 2x flop raise threshold. Checking keeps the river option open.

Our pair of queens beats every unpaired dealer hand and any lower pair, so we win well over half the time. Raising has an expected value of roughly -3 chips, far better than the sure -20 from folding.

3-5 offsuit is well outside the optimal 4x raising range, so I check and keep the option to raise 2x on the flop or 1x on the river.

I have only an open-ended straight draw with low hole cards and no pair. That falls short of the standard flop 2x raise threshold (two pair, a hidden pair, or a strong flush draw), so I check and decide at the river.

Enumerating dealer holdings, raising with a pair of fives gives an EV of about -19.2 chips. Folding loses 20 chips outright, so the 1x raise is slightly better, mainly from the 220 non-qualifying dealer hands that pay +10.

Q6 offsuit falls below the optimal 4x threshold (Q8o+ / Q6s+), so checking preflop has higher EV than raising.

Q6 offsuit on a paired 9-9-5 board has only queen-high with a weak gutshot-free holding, so raising 2x is clearly negative EV. Checking keeps the option to fold or raise 1x on the river.

The paired board means the dealer always qualifies. My 99-K-Q-6 beats about 313 of 990 dealer holdings and ties 8, so calling has an EV of about -14 chips versus -20 for folding.

J7 offsuit is outside the optimal preflop 4x range (JTo is the minimum offsuit jack), so checking to see the flop is correct.

With jack-high, no pair and only backdoor draws on Q-9-5, my hand is too weak to raise 2x. Checking keeps the option to see the river for free and fold if I miss.

With QQ-J-9-7 the paired board guarantees the dealer qualifies. Counting dealer holdings, I win about 26% and lose about 73%, so raising is worth roughly -16.8 chips against -20 for folding.

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

8-6 offsuit on a K-T-4 flop has no pair and only a weak gutshot-free backdoor, so raising 2x is clearly negative EV. Checking keeps the option to fold or raise 1x on the river at no extra cost.

My hole cards don't play, so my best hand is just the board (44KT9). The dealer always qualifies and can at best tie, with only about 20% tie odds. Raising loses about 24 chips on average versus 20 for folding, so I fold.

Any ace is on the published optimal 4x preflop raise table, so A9 offsuit should raise the maximum to get the most out of its positive expectation.

T4 offsuit is not in the preflop 4x raising range, so checking is best and keeps the option to raise or fold on later streets.

Two pair (tens and fours) on the flop is a strong favorite against a random dealer hand, so raising 2x maximizes expected value.