Showdown Hold'em table

Any ace is in the published optimal 4x preflop range, so raising 4x maximizes expected value.

3h-2h is below the optimal 4x raising range (33+, any ace, strong K/Q/J hands), so checking preserves the option to raise 2x on a favorable flop or fold later.

With 3h2h on Qh8sKc I have only a weak backdoor flush draw and low pair outs, far too weak to commit a 2x raise. Checking preserves the option to raise 1x or fold on the river after seeing the full board.

My Ace-high is just the board playing (A-K-Q-T-8), so I can never beat the dealer, only tie; any dealer pair qualifies and beats me, making raising worse than folding.

A7o is any ace, which is in the published optimal 4x preflop range, so raising 4x maximizes expected value.

A4 offsuit is any ace, which is in the published optimal 4x preflop raising range.

Pocket eights are 33+ in the published optimal 4x preflop table, so raising the maximum preflop maximizes expected value.

ATo is an ace hand, which is in the optimal preflop 4x raising range, maximizing value before the board.

9-3 offsuit is below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves option to raise later or fold cheaply.

Second pair of 9s with a weak 3 kicker on a J-9-5 board is only a modest favorite and is vulnerable to overcards and a jack; its equity is below the threshold to commit 2x now versus checking and deciding for 1x with full board information.

Two pair 9s over 5s with K kicker beats 561 of 990 dealer holdings, ties 68 and loses 361; with the paired board dealer always qualifies, raising EV is about +0.4 chips versus -20 for folding.

7-2 offsuit is far below the optimal 4x raising range (33+, any ace, strong K/Q/J), so checking preserves the option to raise 2x on the flop or 1x/fold on the river.

With 7-2 and no pair or meaningful draw on a K-J-8 board, raising 2x would put chips in as a large underdog at a forced showdown; checking is free and preserves the option to fold or raise on the river if I improve.

On the paired board I have only pair of 8s with K-J-7 kickers; dealer always qualifies and beats this with any 8, K, J, 5, pocket pair, or kicker above 7, winning only about 8.5% with 4.5% ties, so raising 1x has lower EV than folding.

A2 offsuit is any ace, which is in the published optimal 4x preflop raising range, maximizing value before the board.

T5 offsuit is below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo+ etc.), so checking preserves the option to raise 2x on a good flop or 1x/fold on the river.

Flopped two pair, tens and fives, which is well ahead of a random dealer hand and benefits from putting the larger 2x bet in now rather than only 1x on the river.

K6 offsuit meets the published optimal 4x threshold of K5o+, so raising the maximum preflop maximizes expected value.

T9 offsuit is below the optimal 4x raising range (JTo+ for jack-ten type hands), so checking preserves option to raise later with more information.

Flopped two pair tens and nines on an ace-high rainbow board, beating a lone ace and most dealer holdings. Raising 2x now gets more value while ahead and charges draws that could overtake us, versus only 1x available on the river.

JTo is in the published optimal 4x preflop range (J8s+ or JTo), so raising 4x maximizes expected value.

8-2 offsuit is well below the optimal 4x raising range (33+, any ace, strong kings/queens/jacks), so checking preserves the option to raise later only if the flop improves it.

With 8-2 and no pair on a K-J-9 board, only a Ten for a straight or pairing gives showdown value; checking is free and preserves optimal river fold/raise option, while a 2x raise risks extra chips as a clear underdog.

Bottom pair beats all dealer high-card hands; raising loses less on average (-12.5 chips) than folding for -20, with about 404 wins and 38 ties out of 990 dealer holdings.

5c2h is well below the optimal 4x raising range (33+, any ace, strong K/Q/J), so checking preserves option to raise 2x or 1x later with more information.

With 5c2h on a 4s4cQh board we only have the board pair with weak kickers, far too weak to commit a 2x raise; checking is free and preserves the option to fold or raise 1x on the river if we improve.

Two pair 4s and 2s beats a dealer who only plays the board pair of 4s; exact count is 544 wins, 54 ties, 392 losses out of 990, giving about -0.9 chips versus -20 for folding.

6-3 offsuit is well below the optimal 4x raising range of pairs 33+, any ace, and strong king/queen/jack holdings, so checking preserves the option to raise later or fold cheaply.

Only three diamonds and weak straight possibilities with 6d-3c on Ad-8d-7s; runner-runner draws are too weak to commit 2x now, so check to see turn and river cheaply.

I have a ten-high straight (6-7-8-9-T). Dealer only beats me with a Jack for a higher straight and only ties with a Six, so raising 1x has strongly positive EV versus folding.

Any ace is in the published optimal 4x preflop range, so raising 4x maximizes expected value with As3c.

Ks6s is K2s+ suited, which is in the published optimal preflop 4x raising range.

9h6h suited is below the optimal 4x/3x preflop raising range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves option to raise 2x on a favorable flop or 1x/fold on the river.

With only the board pair of aces and a 9 kicker on Ad-Ac-2d, my equity is well below the roughly 57% needed for a 2x raise to profit. Checking is free and preserves the option to raise 1x only if the runout improves me, otherwise fold on the river.

On this paired, four-diamond board I only have a pair of aces with a 9 kicker; any diamond, ace, board pair, straight, or high kicker gives the dealer a better hand, so my win probability is far below the threshold needed to call.

QTo is above the Q8o+ threshold in the published optimal 4x preflop table, so raising 4x maximizes expected value.

Pocket Kings are well above the published 4x threshold of 33+, so raising the maximum preflop maximizes value.

K9 offsuit meets the published optimal 4x preflop table (K5o+), so raising the maximum preflop maximizes expected value versus checking.

T9 suited is not in the optimal preflop 4x range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking to see the flop cheaply has higher expected value than committing 3x or 4x.

Flopped top two pair tens and nines on a rainbow board, ahead of almost all dealer holdings except rare sets, with high showdown equity that favors committing the larger 2x play bet now over checking for only 1x on the river.

T5 suited is below the optimal 4x preflop range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise 2x on a favorable flop or 1x/fold on the river.

Two pair, tens and eights, on the flop is a strong made hand that beats dealer high-card and lower-pair holdings; raising 2x maximizes value versus checking for only a 1x river raise.

QTo is above the Q8o+ threshold in the optimal preflop 4x table, so raising 4x maximizes expected value.

Pocket aces are in the published optimal 4x range (33+ and any ace), maximizing value with the strongest preflop hand.

Q6 offsuit is below the published 4x threshold of Q8o+ (Q6s+ suited), so checking to see the flop preserves EV over raising.

Q-high with no pair and only a backdoor club draw is too weak to commit 2x on the flop; checking preserves the option to raise 1x or fold on the river after seeing the full board.

I have an 8-high flush using the 6c; dealer only beats me with one of the six higher remaining clubs, about 25% of holdings, while a win also pays 3:2 on the blind for a flush. Raising 1x has strongly positive EV versus folding and losing ante and blind.

T7 offsuit is below the optimal 4x raising range (JTo or better for ten-high), so checking preserves the option to raise 2x on the flop or 1x/fold on the river.

Top pair on the flop likely has above-even showdown equity against a random dealer hand, and I will raise the river on most runouts, so making the larger 2x play bet now has positive expected value.

7s8c offsuit is below the optimal 4x raising range (33+, any ace, K5o+, Q8o+, JTo etc.), so checking preserves the option to raise 2x on the flop or 1x on the river with more information.

Flopped two pair, eights and sevens with a jack kicker, is a strong made hand likely ahead of a random dealer holding; raising 2x now maximizes value and protects against overcards and draws.

QJo meets the published optimal 4x preflop threshold (Q8o+), so raising 4x maximizes expected value over checking.