Showdown Hold'em table

45o is far below the published 4x/3x raising range, so checking to see the flop is optimal.

4-high with no draw on an ace-high board has almost no equity; raising 2x would lose ~20 more chips on average. Check and only invest on the river if the board improves us.

Our pair of aces beats the vast majority of dealer holdings; only ~8% of the 990 dealer hands beat us, so raising 1x (EV ≈ +7 chips vs. folding for -20) is clearly better.

Pocket queens is well inside the standard 4x range (pair of queens+); raising max now maximizes value against the dealer's qualification requirement.

Aces-up preflop: any ace is in the published 4x raise range, and raising maximizes EV against the dealer's pair-or-better qualification requirement.

Pocket sevens are well above the published 4x threshold (33+), so max value with the strong raise.

A9o meets the published optimal preflop raise table (any ace), so raising 4x maximizes EV versus checking.

43o is far too weak to raise; checking keeps the ante at risk with a chance to raise later if the flop improves.

4h3d has no pair, no draw, and only ace-high potential that rarely beats the dealer; raising 2x here is a clear negative-EV bluff against a qualifying house hand, so I keep the pot small and decide on the river.

My best five is just the board (ace high); I can only tie a non-qualifying dealer or lose to any pair, so raising 1x has no winning outcomes. Folding saves the extra 10-chip play bet.

Td3d is far below the published 4x/3x raising range (needs K-high suited or better); checking keeps the ante/blind at minimum risk and preserves flop options.

I've flopped a pair of tens, which beats the dealer's qualification threshold often enough that betting 2x has positive expected value versus checking.

Q5o misses the 4x/3x preflop raising range (needs Q8o+); checking keeps the flop 2x option and lower variance.

Queen-high with no pair on a paired king board is too weak to put 2x at risk; check and decide on the river with full information.

With Q5 I only hold pair-of-kings-with-AQ from the board; most dealer holdings (any ace, pair, or higher king-kicker) beat me, so the typical win probability falls well below the ~2/3 needed for a 1x river raise. Folding sacrifices only the 20 already at risk.

T9s is below the published 4x/3x raising range (needs J8s+ suited), so checking and deciding on the flop is optimal.

Ten-high with no pair, no draw worth 2x; checking keeps the option to fold cheaply on the river if the board doesn't improve.

My best hand is T-high; the dealer only fails to beat me with two unpaired hole cards all seven or lower (~6% of holdings), so raising 1x loses about 10 more chips on average than folding. Folding locks in the fixed -20 instead of an expected ~-27.

5-4 offsuit is not in the preflop raise table (needs K2s+/any ace or better), so checking preserves the option to raise 2x on the flop if it pairs well.

Bottom pair with a weak kicker - raising 2x here is roughly break-even against the dealer's qualifying range, so I'll keep the bet small and decide on the river with full information.

My pair of fives only loses to dealer holdings that out-kicker the board or make a bigger hand; folding forfeits 20 chips for certain, while raising 10 wins in the rare cases the dealer's hole cards don't improve the board pair.

T5o offsuit is well below the published 4x/3x raising range (needs K5o+ or better), so checking and deciding on the flop minimizes risk.

I flopped top pair (tens) on QT4; against a dealer needing a pair to qualify, raising 2x has positive EV, and it locks in value before worse runouts.

K2 offsuit falls below the published 4x/3x raising range (K5o+ minimum), so checking and re-evaluating on the flop is optimal.

King-high with no pair on Q-high board is far too weak to risk 2x; checking keeps the river fold option alive.

The paired board with three spades gives me a king-high flush, which likely beats the dealer's range most of the time; folding forfeits 20 chips for certain, so raising 1x is clearly better.

82o is far below the published 4x/3x raising range, so checking minimizes risk and keeps the flop decision open.

8-high with no pair on T73 gives almost no showdown value; raising 2x would risk 20 more chips on a hand that rarely beats a qualifying dealer. Check and reassess on the river.

With 8-high on a board pairing the 3 with an ace, the dealer almost surely has a pair and I can only beat nothing; folding saves the 1x play bet, risking only ante and blind.

2h7d is far too weak to raise; checking keeps the ante and blind in play and lets me decide on the flop with more information.

72o missed the J95 flop with no draws; raising 2x would be a large losing investment, so check and evaluate on the river.

2h7d makes at best 7-high on this board; we lose to nearly every dealer holding including most no-pair hands, so raising 1x is far worse than folding.

86s is well below the published 3x/4x raising range (needs J8s+ suited), so checking to see the flop minimizes risk.

8-6 high with no draw on 7h3dJs has little equity; raising 2x here is a losing bluff against a qualifying dealer, so I keep the option to evaluate on the river.

The board pairs 7s, so the dealer always qualifies; I only tie when both dealer hole cards are 6 or lower (about 15%), otherwise my J-8-6 kicker loses. Raising nets roughly -14 chips versus a certain -20 fold... actually raising EV is worse than folding only if tie chance pays; folding saves the extra 10x stake with negative equity.

3s8h is far below the 3x/4x raising range and checking keeps the option to raise 2x on a favorable flop; folding just surrenders the ante and blind.

3-high with no draw on a paired board has almost no equity; raising 2x would just add 20 chips to a likely losing showdown. Check and fold cheaply on the river if the board doesn't improve me.

I hold 3s8h on a paired, ace-high board with no draw realized; the dealer very likely pairs the board or better, so my win equity is far below the single Required raise threshold.

A7 offsuit falls below the published preflop raise range (needs K5o+ or better for non-ace kickers beyond A2+... here only any ace raises, but A7o is an ace — however optimal play raises any ace 4x; still, A7o is marginal and checking preserves the flop 2x option with decent equity).

Top pair with an ace kicker beats most dealer holdings; raising 2x on the flop is clearly +EV versus checking and risking a river fold decision.

K7 offsuit falls below the published 4x/3x raising range (K5o+), so checking and deciding on the flop is optimal.

King-high air on a T63 board; the dealer likely holds a pair already. Check to let the river decide cheaply, since only two extra antes are at stake and folding now locks in a guaranteed loss.

The board makes me a pair of threes with a king kicker; the dealer only beats me with a real pair or trips/kicker improvement, so raising 1x is clearly better than folding away the ante and blind.

9h3d is far below the 3x/4x raise range; checking keeps the ante and blind in play with minimal added risk and lets the flop decide.

9-high with no draw on K66 is far too weak to put 20 chips in; checking preserves the option to fold cheaply on the river.

My best five is sixes with T-9 kickers — barely a bluff-catcher; the dealer pairs the K66T3 board far too often, and raising 1x only adds risk when I beat so few qualifying hands.

5-6 offsuit is far below the published preflop raising range, so checking to see a cheap flop is best.

56 on a 99K board has almost no equity against dealer holdings; raising 2x would be a large losing bet, so check and only commit on the river if the board improves.

I hold pair of nines with KQ7 on board; many dealer holdings miss or make smaller pairs, so raising 1x has better EV than folding 20 chips.

72s is far below the optimal 3x/4x raising range, so checking to see the flop cheaply is clearly best.

I flopped a pair of sevens; the 2x raise is clearly better than checking since the dealer will often fail to qualify and I have a made hand with backdoor spade potential.

K3 offsuit falls below the published 3x/4x raising range (K5o+ required), so checking keeps the ante and blind in play with minimal added risk.

King-high with no pair on an 8-2-4 board is too weak to risk 2x; checking preserves the option to raise 1x or fold cheaply on the river.

My K-high loses to every qualifying dealer pair (~74% of holdings, costing 30 when raised), and most non-qualifying A-high hands still beat me, so raising EVs about -24 vs -20 for folding.

J2 offsuit is far below the published 3x/4x raising range (J8s+/JTo+), so checking keeps the ante and blind in play with minimal risk.

Jack-high with a paired board is too weak to risk 2x; check and evaluate the river, where raising 1x or folding is cheap and optimal.

The board already pairs sixes, so the dealer always qualifies and always has at least a pair of sixes; my J-high can never win, so folding saves the 1x play bet.

Q6o is below the published 3x/4x raising range (Q8o+), so checking keeps the flop option open with minimal risk.

Q6o on a K-J-3 flop is a weak hand with little equity; raising 2x risks 20 more chips on likely second-best, so check and evaluate the river cheaply.

With queen-high we beat only a non-qualifying dealer hand (~15%), so raising 1x has EV around -24 versus -20 for folding; folding loses less.

3s5d is far below the 3x/4x raise range (33+, any ace, K5o+), so checking keeps the ante at risk with flop optionality.

3s5d on 6s7s8d is only an open-ended straight/flush draw without made hand or equity to justify 2x ante risk; checking minimizes loss since dealer likely qualifies often.

I hold a 3-5-6-7-8 straight using both hole cards, a strong made hand that should raise and likely win the play bet plus a 1:1 blind bonus.

Q6 offsuit falls below the published preflop raise threshold (Q8o+), so checking to see the flop is optimal.

Q6o with no draw on a 995 board is a weak holding; raising 2x has negative EV. Checking and folding marginal rivers is optimal.

The board's paired nines mean the dealer almost always qualifies, but my Q plays as the kicker: if the dealer's hole cards don't improve their 99K hand, my queen-high kicker wins. Folding surrenders 20 chips when raising wins far more often than not.

J7 offsuit is well below the published 3x/4x raising range, so checking keeps the ante and blind in play with cheap flop options.

J7o on Q95 has no pairs, draws, or overcards strength; raising 2x here is negative EV, while checking lets me retreat on the river based on equity.

I hold a pair of queens (J kicker), which beats many dealer holdings and likely makes the dealer qualify; raising 1x risks only 10 more versus folding away 20 already committed.

8c6d is well below the published 4x/3x raising range (33+, any ace, K-high+, etc.), so checking to see the flop is optimal.

8-6 no heart on Kh4h has essentially no equity; raising 2x would be throwing 20 more chips at a near-certain loss. Check and fold the river unless the board improves dramatically.

With 8-high on a paired board (T,K,4,9,4), the dealer almost certainly has at least a pair and beats us; raising 1x adds 10 chips to a near-certain loss, so folding saves the extra bet.

A9 offsuit is below the published 3x/4x raising range (needs Q8o+ or K-high), so checking keeps the flop option open with minimal risk.

A9o on a Q-high flop is too weak to risk 2x; check and decide on the river with full information.

I hold the ace-high straight (9-T-J-Q-A), an essentially unbeatable made hand; raising 1x is strictly better than folding.

T4o is far below the published 4x/3x raising range (needs T9o+ or better), so checking keeps the flop option open with minimal risk.

Two pair (tens and fours) on the flop is far too strong to slow-play; raising 2x maximizes value against the dealer's range.