Showdown Hold'em table

A pocket pair of 8s is in the published optimal 4x preflop range (33+), so raising the maximum is correct.

Q4 offsuit falls outside the optimal 4x preflop table, which needs Q8o or better for an offsuit queen. Checking keeps the option to raise on the flop or fold on the river at no extra cost.

Paired the 4 with a hole card (middle pair, queen kicker). Standard flop strategy is to raise 2x with a hidden pair other than pocket deuces, so raising should beat checking in expected value.

8-3 offsuit is far outside the optimal preflop 4x range (33+, any ace, strong kings/queens/jacks), so checking to see the flop for free is correct.

Standard optimal flop strategy is to bet 2x with any hidden pair except pocket deuces. My 3 pairs with the board's 3c, so I raise despite the high board.

97 offsuit falls well outside the optimal 4x preflop range (33+, any ace, K5o+, Q8o+, JTo), so checking is correct and keeps the flop and river decisions open.

A hidden pair of sevens plus an open-ended straight draw (a 6 or J completes it, and the blind pays on a straight) is a clear flop raise under standard strategy.

JTo is on the published optimal 4x raising table (JTo qualifies among jack hands), so raising 4x preflop maximizes EV.

K9 offsuit is K5o+, which falls in the published optimal 4x preflop raising range, so raising 4x maximizes expected value.

64 suited is not in the optimal preflop 4x raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking to see the flop is the higher-EV play.

With 6-high, no pair and no real draw (straights need runner-runner cards), this hand is well below the flop 2x raising threshold of a hidden pair or better. Checking keeps a free river decision.

The board already gives the dealer a pair of tens, so the dealer always qualifies, and my only edge is a 6 kicker. Almost any dealer card of 7 or higher, or any pair, beats me, so I win only about 4% of the time. Raising would lose about 30 chips on average versus 20 for folding.

Any ace is on the published optimal preflop 4x raising table, so A6o calls for the maximum 4x raise rather than a check.

Any ace is in the published optimal preflop 4x raising range, so A4 offsite should be raised the maximum.

2-3 offsuit is far below the optimal 4x raising threshold, so I check and keep the option to raise 2x on the flop or fold on the river.

An open-ended straight draw with low cards and no pair is too weak to raise 2x. Checking keeps the river option to bet 1x if the straight hits, or fold if it misses.

My hole cards don't play, so my best hand is the board's pair of sevens. The dealer always qualifies with that board pair, and I can at best tie in about 9 of 990 holdings, so folding for -20 beats raising for roughly -30.

T5 offsuit is far below the optimal preflop 4x raising range (which needs JTo or better among offsuit non-ace, non-pair hands). Checking keeps the hand alive for the flop at no extra cost.

T-high with no pair, only a backdoor flush draw and weak straight potential falls well short of the standard flop raise threshold (pair or better, or four to a flush). Checking keeps the river decision open.

The board plays trip nines, so the dealer always qualifies, and any A, K, Q or J, any pocket pair, or any 4, 7 or 9 in the dealer's hand beats our ten kicker. We win only about 144 of 990 dealer hands, so raising is worth about -21.4 chips against -20 for folding.

64s is outside the optimal preflop raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking keeps the option to see the flop for free.

I've paired the 6 using a hole card, and standard optimal flop strategy says to raise 2x with any hidden pair except pocket deuces. A pair of sixes beats a large share of dealer holdings, so raising now has higher expected value than checking.

82 suited is far below the preflop 4x threshold (33+, any ace, K2s+, Q6s+, J8s+), so checking is correct. I'll reassess on the flop for free.

With 8-high, no pair and no flush or straight draw, my hand is far too weak to raise 2x on the flop. Checking keeps the river decision open at no extra cost.

Two pair (sixes and deuces with an ace kicker) beats roughly 55% of dealer hands and loses to about 38%. Raising is worth about -0.04 ante, far better than the -2 ante loss from folding.

A6 suited contains an ace, and the published optimal strategy raises 4x preflop with any ace.

Q7 offsuit is below the optimal preflop 4x threshold (Q8o+ for offsuit queens), so checking and reassessing on the flop is better.

Queen-high with only the board pair (no hidden pair or strong draw) falls below the standard flop raise threshold, so I check and keep the river decision open.

Two pair (sevens and fives, queen kicker) beats roughly 70% of dealer holdings, and the dealer always qualifies on this paired board. Raising has positive EV compared with folding, which loses 20 chips.

J6 offsuit is not on the optimal 4x preflop list (it needs JTo or better offsuit), so checking keeps the option to raise on the flop or river.

Top pair of jacks using a hole card on a dry flop is a clear 2x raise under standard flop strategy, since it is well ahead of the dealer's range.

T9 offsuit is not on the optimal preflop 4x list (that needs JTo or better among unpaired offsuit non-ace/king hands), so checking and seeing the flop for free is correct.

Ten-high with no pair, no flush draw and only a weak backdoor straight draw falls well below the flop 2x raise threshold. Checking preserves the river decision.

The board pairs 4s, so the dealer always qualifies. My hand plays 4-4 with T-9-8 kickers, which beats only about 6-7% of dealer holdings. Raising would cost roughly 2.6 antes on average versus 2 for folding.

Any ace falls within the published optimal 4x preflop raising range, so ATo should be raised the maximum.

Any ace is in the published optimal 4x preflop raising table, so A2 offsuit should be raised the maximum.

The reference optimal preflop strategy raises 4x with any ace, so A2 offsuit qualifies. Raising beats checking in expected value.

K2 offsuit is not in the optimal preflop 4x range, which needs K5o or better, so checking is correct. We keep the option to raise 2x on the flop or 1x on the river.

King-high with an open-ended straight draw and only a backdoor flush draw is not strong enough to raise 2x on the flop. Checking keeps the option to raise 1x or fold on the river once the draw resolves.

We play the board pair of eights with a king kicker, and the dealer always qualifies. We win about 27% of dealer holdings, above the roughly 20% needed for calling 1x (EV about -16 chips) to beat folding (-20 chips).

94 suited is far outside the optimal preflop 4x raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking to see the flop for free is correct.

9-4 offsuit on a 5s6s-Js monotone flop is a weak gutshot (needs a 7 or 8 for a straight, or a 3) with no pair and no flush draw, far below the raise threshold. Checking keeps the river option of fold or raise_1x.

Our pair of nines beats a non-qualifying dealer and many weak dealer hands. Calling only needs to win roughly 22% of the time to beat the certain 20-chip loss from folding, and our estimated win chance is above that.

93 suited is well outside the optimal preflop 4x raising range, so checking keeps the option to see the flop at no extra cost.

Our 3c pairs the board's 3d, giving a hidden pair. Standard flop strategy for this game is to raise 2x with any hidden pair other than pocket deuces, even bottom pair, rather than check.

Q5 suited is below the optimal 4x threshold of Q6s+, so checking keeps the hand alive for a cheaper flop or river decision.

Four to a heart flush with a hidden queen of hearts meets the standard flop raise threshold (a flush draw with a hidden card of ten or better). The flush draw equity and the bonus blind payout make betting 2x better than checking.

65 offsuit falls outside the optimal 4x preflop table, which starts at 33+ and needs much stronger high cards. Checking costs nothing and keeps the flop and river decisions open.

Pairing a hole card with the board (fives) is a hidden pair. Standard optimal flop strategy makes the 2x raise with any hidden pair except pocket deuces, so raising should beat checking here, even with bottom pair.

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

Standard flop strategy is to raise 2x with any pair that uses a hole card, except pocket deuces. Our pair of 3s uses a hole card and beats the board's lowest card, so raising has higher expected value than checking.

9-4 offsuit falls well outside the optimal preflop 4x raising range, so checking is correct. I'll see the flop for free and reassess.

I have only nine-high with a gutshot to an eight and no pair, which is well short of the usual flop 2x raise threshold of a hidden pair or better. Checking keeps the river option open at no extra risk.

My pair of nines loses to roughly 68% of dealer holdings, but the dealer often fails to qualify. Raising is worth about -17 chips against -20 for folding, so calling the 1x is the better option.

The optimal preflop strategy raises 4x only with 33 or better, so pocket deuces are a marginal hand. Checking keeps the option to raise 2x on the flop or 1x on the river.

Pocket deuces under a coordinated T-9-8 board are the classic exception to raising a hidden pair on the flop. Almost any dealer pair beats us, so checking and deciding on the river is the better play.

Against all 990 possible dealer hands, raising with pocket 2s loses about 18.8 chips on average, compared with a certain 20-chip loss from folding. About 240 dealer hands fail to qualify and pay our play bet, and 49 tie, which more than offsets the 701 hands that beat us.

T5 offsuit is far outside the optimal preflop 4x range (JTo is the weakest offsuit ten), so checking keeps the option to raise later or fold cheaply.

Ten-high with only backdoor straight and flush draws is well below the usual flop raise threshold of a pair or a strong four-flush. Checking keeps the option to raise 1x or fold on the river.

We only play the board's pair of threes with a T-9 kicker. That beats roughly 13.5% of dealer hands and ties about 5%, so raising is worth about -21.7 chips against -20 for folding.

Offsuit 7-5 is well outside the optimal preflop 4x raising range, so checking keeps the flop and river options open at no extra risk.

With only 7-high and an open-ended straight draw, I have no pair yet, which is well short of the usual 2x flop-raise threshold. Checking keeps the river option, where I can raise 1x if the straight or a pair comes in, or fold cheaply.

5s-7d with the 8-6-4 on the board makes an 8-high straight, which is beaten only if the dealer holds 9-T. With no flush possible, raising is clearly better than folding, and a win also gets the 1:1 straight payout on the blind.