Showdown Hold'em table

KJo is in the published optimal 4x range (K5o+), so raising four times the ante is the highest-EV preflop action.

67 offsuit is outside the published optimal 4x range (no pair, no ace, and below the king/queen/jack thresholds), so checking preserves the option to raise 2x on a favorable flop.

67 offsuit has no pair, no flush draw, and only weak straight outs on 8s Qs 3d, so a 2x raise is not justified. Check and reassess on the river.

I have an 8-high straight. Only 90 of 990 dealer holdings make a flush and beat me, so a 1x raise is strongly +EV versus folding.

Any ace is in the published optimal 4x range, so I raise the maximum preflop with Ad5h.

Q7 offsuit is below the published 4x range (Q8o+ or Q6s+), and 3x is not a substitute for a value raise, so checking preserves the option to raise later.

Top pair of queens is ahead of most dealer holdings and runouts, so a 2x flop raise captures value rather than checking to a thin river decision.

95o is well below the published 4x range (no pair, no ace, and neither card is high enough), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

5-9 offsuit completely missed this flop with no pair or draw, so a 2x raise has no value. Check to keep the river decision.

I have two pair, nines and twos, and the board pair means the dealer always qualifies. I win about 676 of 990 holdings and tie 46, so a 1x raise is clearly +EV versus folding.

6-2 offsuit is far below the published preflop 4x range (no pair, no ace, no suited broadway), so checking preserves the option to raise later only if the board improves.

6-2 offsuit has no pair and only a backdoor diamond draw on this flop, so checking preserves the option to fold on the river if it misses.

The board is already a pair of threes with Q-T-9, and neither hole card improves it, so the dealer always ties or wins. Raising loses about 24 chips in expectation versus 20 for folding.

J5 offsuit is outside the published preflop raise range (J8s+ or JTo), so checking preserves the option to raise on later streets if the board improves.

J5 offsuit has no pair and no draw on 8-7-4 rainbow, so a 2x raise is not justified. Check and reassess on the river.

Pair of fives beats all non-qualifying dealer hands and every worse pair, so a 1x raise loses about 12 chips in expectation versus 20 for a fold.

AQ offsuit is in the published optimal preflop 4x range (any ace), so I raise the maximum.

QTs is in the published optimal preflop 4x range (Q6s+), so I raise the maximum rather than check.

J9 offsuit is below the published 4x range (JTo+ offsuit, J8s+ suited), so checking preserves the option to raise later only if the board improves the hand.

Top pair of jacks is ahead of a random dealer hand often enough that a 2x play bet is +EV versus checking and relying on a later 1x or fold.

67o is outside the published optimal 4x range (no pair, no ace, and not a qualifying broadway), so checking preserves the option to raise later if the board improves.

Pair of sevens is weak on a king-ten board, so I check to decide on the river with full information.

Pair of sevens wins about 49% of dealer holdings and ties 6%, so calling loses far less than folding the ante and blind.

J7 offsuit is below the published optimal 4x range (JTo is the cutoff for offsuit jacks), and 3x is not worth it with this weak holding, so I check to see the flop.

No pair and only backdoor straight or flush possibilities, so checking preserves the option to raise or fold on the river.

Ace-high AKQJ7 beats 332 of 990 dealer holdings and ties 9, so a 1x raise loses about 16 chips in expectation versus 20 for a fold.

J9 offsuit is outside the published optimal 4x range (JTo+ for offsuit jacks), so checking preserves the option to raise later with more information.

J9 offsuit has no pair, no flush draw, and no straight draw on K52. Checking keeps the option to fold on the river if the board does not improve.

With a pair of nines, raising 1x is about -12 chips versus -20 for folding: I win enough unqualified and lower-pair runouts that the play bet is worth taking.

45s is outside the published optimal 4x range (no pair, no ace, below K/Q/J thresholds), so checking keeps the flop 2x option instead of committing 3x or 4x.

Two pair (kings and fours) is ahead of most dealer holdings that only share the board pair, so a 2x flop raise is the +EV play.

AJs is in the published optimal 4x range (any ace), so I raise the maximum preflop.

9-5 offsuit is outside the published optimal 4x range (no pair, no ace, and below the king/queen/jack thresholds), so checking is the correct preflop action.

Top pair of nines is ahead of most dealer holdings and worth a 2x value raise before overcards or club draws arrive.

K4o is below the published optimal 4x range (K5o+), so checking preflop is the correct play.

King-high with no pair and no draw on Q-T-3; raising 2x is -EV, so check and reassess on the river.

King-high loses to any qualifying dealer, but folding locks in -20. A 1x raise still wins about 220 of 990 holdings for +10 and ties 69, so its EV is about -18, slightly better than folding.

Ace-ten offsuit is in the published optimal 4x range (any ace), so I raise the maximum preflop.

T4 offsuit is outside the published 4x range (no pair, no ace, and too weak to raise 3x), so checking preserves the option to raise or fold later.

No pair, flush draw, or straight draw on this flop, so checking preserves the option to fold or raise 1x on the river.

Ace-high loses to every qualifying dealer hand, and only 116 of 990 holdings win the showdown. Raising costs about 22 chips in expectation versus 20 for folding.

9-5 offsuit is well below the published optimal 4x range (no pair, no ace, and neither card is high enough), so checking preserves the option to raise later only if the board improves.

No pair, no flush draw, and only remote straight chances with 9-5 on 3-4-T, so checking preserves the option to fold on the river if the board does not improve.

Dealer always qualifies on the board pair. My TTJ95 wins or ties too few of the 990 holdings for the 1x raise to beat folding.

J2 offsuit is outside the optimal preflop 4x range (JTo+ or J8s+), so checking preserves the option to raise later only if the board improves the hand.

J-2 offsuit has no pair, no flush draw, and no real straight draw on A-8-7. Checking keeps the option to fold on the river rather than committing a 2x raise with a weak hand.

Ace-high loses to 833 of 990 dealer holdings, and the raise EV is about -22 chips versus -20 for folding.

25s is well below the published 4x range (no pair, no ace, not K/Q/J suited strength), so checking preserves the option to raise 2x only if the flop connects.

Four spades give a ~35% flush draw whose blind bonus and win rate justify committing 2x now versus checking and only betting the rarer made flush.

J2o is well below the published 4x range (J8s+ or JTo), so checking preflop preserves the option to raise later if the board improves.

Jack-high with only a backdoor club flush and no pair is too weak to commit a 2x raise. Checking keeps the river fold option if the board does not improve.

River pair of jacks beats most dealer holdings (worse pairs and non-qualifying high-card hands) and is clearly +EV versus folding the ante and blind.

QJo is inside the published optimal preflop 4x range (Q8o+), so I raise the maximum rather than check.

48o is well below the published 4x range (no pair, no ace, and neither card is high enough). Checking keeps the option to raise 2x on a favorable flop or fold on the river.

4-8 offsuit has no pair and no real draw on a paired ten board, so a 2x raise is -EV. Check and reassess on the river.

River two pair (tens and fours) beats roughly 66% of the 990 dealer holdings, and the board pair means the dealer always qualifies. Winning pays +20 while losing costs -30, for about +3 chips EV versus -20 for folding, so I raise 1x.

A7o is in the published optimal 4x range (any ace), so I raise the maximum preflop rather than check.

98o is below the published 4x range and too weak to commit 3x preflop, so I check and keep the option to raise or fold later.

9-8 offsuit has no pair, no flush draw, and no straight draw on A-6-6, so a 2x raise is -EV. Check and reassess on the river.

Board pair means the dealer always qualifies, and 9-8 only makes sixes with an A-K-9 kicker. Only 134 of 990 dealer holdings lose to that, so a 1x raise is about -21.7 chips versus -20 for folding.

T2s is below the published optimal 4x range (J8s+), so checking preflop is the correct play.

Ten-high with an open-ended straight draw and only a backdoor flush. Checking keeps the option to raise 1x on the river if the draw hits and to fold if it misses, which is better than committing a 2x play bet on a currently unpaired hand.

Jack-high with no pair loses to almost every dealer holding, and the 1x play bet is -EV versus folding the ante and blind.

J5o is well below the published optimal 4x range (offsuit jacks start at JT), so checking preserves the option to raise later with more information.

J5 offsuit has only the board pair of fours and no draw, so a 2x raise is -EV; check and reassess on the river.

Board pair means the dealer always qualifies, and exact enumeration shows 208 wins and 69 ties against 713 losses. Raising returns about 2.6 chips more than folding.

K3 offsuit is below the published 4x range (K5o+), so checking preserves the option to raise later if the board improves.

King-high with no pair and no flush or straight draw is too weak to raise 2x; checking keeps the option to fold or raise 1x on the river.

Pair of kings wins about 454 of 990 dealer holdings, and many losses are already priced in; raising 1x is about -9 chips versus -20 for a fold.