Showdown Hold'em table

9-3 offsuit is well below the published 4x/3x raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking preserves the cheap flop and river decision points instead of risking 30-40 chips on a weak hand.

We hold two pair (tens and nines), beating the dealer's board-only two pair and all single-pair holdings; raising 1x is clearly better than folding this strong river hand.

87o is well below the 4x/3x raise threshold (33+, any ace, K+), so checking and playing the flop is optimal.

The board gives me trip sevens (77 on K-7-7), a very strong made hand that warrants max aggression.

2d3h is far below the published 4x/3x raising range (33+, any ace, K/Q/J thresholds), so checking keeps the ante-blind exposure minimal and preserves the 2x flop raise option if the board improves us.

My pair of threes beats the dealer whenever the dealer fails to qualify (~78% of holdings), so raising 1x has EV about +1.2 ante versus folding for a sure loss of 2 antes.

9d3d is far below the published 4x/3x raising range (33+, any ace, K2s+, Q6s+, J8s+), so checking preserves flexibility to raise 2x on a favorable flop or fold cheaply on the river.

I hold two pair (aces and sixes); raising 1x risks only 10 more versus folding 20 already posted, and I beat many dealer no-pair holdings while two pair wins often enough that raising dominates folding.

85o is far below the optimal 4x/3x raising range (33+, any ace, K/Q/J-combos), so checking preserves the ante and keeps the flop decision cheap.

9-8 offsuit falls outside the optimal 4x preflop range (pairs 33+, any ace, K/Q/J suited or strong offsuit hands), so checking preserves the option to raise 2x on a favorable flop.

Pair of 8s plus an open-ended straight draw (any J or 6) on 8-7-T is far above the flop raise threshold; raising 2x maximizes value against the dealer's qualifying range.

93o is well below the 4x/3x raising range, so checking and deciding on the flop minimizes risk.

With 9-high and only a backdoor flush draw (needing two running clubs) on Q-8-A, raising 2x would commit 20 chips with almost no equity; checking keeps the option to fold cheaply on the river if we don't improve.

Q4 offsuit fails the published 3x/4x raising criteria, so checking keeps the ante and blind in play with low risk.

Bottom pair with a middling kicker rarely clears the bar for committing 2x on the flop; checking preserves the cheap 1x-or-fold river decision and lets me see whether I improve before risking more.

Q9o meets the published optimal 4x preflop raise threshold (Q8o+ offsuit), so raising 4x maximizes expected value versus checking.

7-4 offsuit is far below the published 4x raise range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the ante/blind and keeps the 2x flop raise available if the board helps.

K7o is above the K5o+ cutoff in the optimal preflop raise table, so raising 4x the ante maximizes EV versus checking.

K8s meets the optimal preflop 4x raise criteria (any suited king), which is the highest-EV line for this holding.

94 offsuit is far below the published 4x/3x raising range (pairs 33+, any ace, K/Q/J-combos), so raising would be -EV. Checking preserves the option to raise 2x on the flop if the board helps.

I play the board's two pair (Q-Q-8-8-J); the dealer beats me only with an A, K, Q, J or 8 in the hole or a 9+/TT pocket pair (564/990), ties 393/990, and I win 33/990, making the 1x raise (EV about -16.4) better than folding (-20).

Q2 offsuit is well below the optimal 3x/4x raise range (Q8o+/Q6s+), so checking keeps the flop option open with minimal risk.

Q2o on T-high board is far too weak to put 20 more chips at risk; checking keeps the river fold option and minimizes expected loss.

8-3 offsuit is far below the published 4x/3x raise range (pairs 33+, any ace, decent kings/queens/jacks), so raising would be strongly -EV; checking keeps the flop option open with only ante and blind at risk.

Ad2d is any ace, which meets the published optimal preflop 4x raise criteria (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so the play bet of 40 is the correct max raise.

A8o falls under 'any ace' in the published optimal preflop table, so raising 4x antes maximizes expected value versus checking.

2d3d is well below the published 4x/3x raising range (33+, any ace, K2s+, etc.), so checking keeps the flop 2x option open while limiting risk on a weak suited connector.

My 2d-3d pairs with 6d-9d-Kd on the board for a king-high flush, and the dealer (who always qualifies via the board's pair of sevens) only beats me with a seven in the hole, pocket kings, or two higher diamonds (~111 of 990 holdings). Raising 1x wins +35 when I win vs -30 when I lose, for EV of about +27.7 chips versus -20 for folding.

T8 offsuit falls below the published 4x preflop raise range (needs JTo or better among non-pairs), so checking to see a free flop and preserving the option to raise 2x later is optimal.

9-7 offsuit is far outside the published 3x/4x raising ranges (needs pairs, aces, strong kings/queens/jacks); checking keeps the ante-blind exposure minimal and preserves flop options.

With 9-high on a K-high board I have almost no equity against a dealer pair, so raising 2x would burn 20 more chips on a likely loser. Checking keeps the ante and blind at risk and preserves the river fold option if the turn and river do not improve my hand.

Ace-queen offsuit is a standard 4x preflop raise under the optimal table (any ace), maximizing play bet value against the qualifying dealer.

5c2c is far below the 4x/3x raising range (needs 33+, any ace, or strong kings/queens/jacks), and folding surrenders 20 chips immediately. Checking keeps the ante and blind live while preserving the flop 2x raise option, which is the lowest-EV-loss line for this trash hand.

I have a pair (fives) plus open-ended straight potential on 6-5-4; the dealer needs a pair to qualify, so betting 2x here has positive EV versus checking.

5-4 offsuit is well below the published 3x/4x raise range, so checking and seeing the flop minimizes risk while keeping all options open.

4-5 offsuit with no draws is far too weak to put 20 more chips at risk; check and only continue on the river with a made hand worth a 1x raise.

My best hand is only the board's pair of sevens with a Q-8-5 kicker, and the dealer always qualifies off the board pair. Enumerating the 990 dealer holdings: I win just 21 (dealer doubles 3s/4s), push 24, and lose 945, so raise_1x EV is about -28.2 chips versus -20 for folding.

T8 offsuit falls below the published raising range (needs J8s+/JTo or better), so checking preserves the cheap 2x flop option instead of committing 30-40 chips with a weak hand.

I flopped top pair (tens) on a dry board, which is well ahead of the dealer's random holding range; getting 2x in now maximizes value since I'd raise the river anyway with this strength.

QTs is inside the published optimal 4x preflop range (Q6s+), so the player edge justifies the maximum 40-chip play bet rather than a smaller 3x raise or checking.

8d3s offsuit is far below the published 4x/3x raising range (33+, aces, K/Q/J requirements), so checking keeps only the ante and blind at risk and defers to the flop decision.

I hold 8-high with no real draw (only a backdoor 5-6 straight, ~1.5%), so a 2x raise would risk 20 chips with roughly 13% equity. Checking preserves the cheap river option to fold for just the ante+blind or raise 1x if I improve.

Pocket deuces fall below the 33+ threshold in the optimal 4x preflop raise table, so checking preserves the cheap flop decision and set-mining equity without risking 30-40 extra chips.

Pocket deuces on K-6-5-9-J give me only a weak pair, and the dealer needs just a pair to qualify, so I lose to nearly every dealer holding and tie only against a bigger pair of deuces. Raising 1x risks 10 more chips with almost no chance of winning, while folding costs nothing extra beyond the ante and blind already committed.

K9s falls squarely in the published optimal 4x preflop range (any suited king), so raising the maximum is the highest-EV play.

Q3 offsuit is well outside the optimal raising range (needs Q8o+/Q6s+), so raising 3x or 4x has negative EV; checking preserves the flop option and minimizes risk on the final hand.