Showdown Hold'em table

Ace-3 offsuit is in the published optimal 4x range (any ace), so I raise the maximum preflop rather than check.

32s is below the published 4x range (no pair, no ace, and too low for king/queen/jack suited thresholds), so checking preserves the option to raise 2x if the flop connects.

32 of hearts has no pair and only a backdoor flush draw on Qh-8s-Kc, so a 2x raise is not justified. Checking preserves the option to raise 1x or fold on the river.

Our best hand is the board (A-K-Q-T-8), so we can only tie or lose. Raising risks the play bet in spots where the dealer qualifies and beats us, which is worse than folding for a certain loss of the ante and blind.

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

Any ace is in the published optimal 4x range, so Ad4o raises the maximum preflop.

Pocket eights are in the published optimal 4x range (33+), so I raise the maximum preflop.

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

93o is well below the published optimal preflop 4x range (33+, any ace, K2s+/K5o+, Q6s+/Q8o+, J8s+/JTo), so checking preserves the option to raise later with a made hand.

Second pair with a weak kicker is too thin to raise for 2x; checking keeps the river fold option if I do not improve.

We have two pair, nines and fives with a king kicker, and the dealer always qualifies on the paired board. We win about 561 of 990 holdings and tie 62, so a 1x raise is clearly better than folding.

72o is far below the published 4x range, so checking preserves the option to raise only if the flop improves the hand.

7-2 offsuit has no pair, no flush draw, and no straight draw on K-J-8. Checking keeps the river fold option instead of committing a 2x raise with almost no equity.

A2o is in the published optimal preflop 4x range (any ace), so I raise the maximum.

T5 offsuit is well below the published 4x range (JTo+, Q8o+, suited broadways and pairs), so checking preflop is the +EV default.

Two pair (tens and fives) is well ahead of a random dealer hand, so I want the larger 2x play bet in now rather than a possible 1x later.

K6o is in the published optimal 4x range (K5o+), so raise the maximum preflop.

T9 offsuit is outside the published optimal 4x range (JTo+ and stronger), so checking preserves the option to raise 2x on a favorable flop or fold on the river.

Two pair (tens and nines) is ahead of nearly all dealer holdings on this flop, so raising 2x captures more value than checking and only betting 1x on the river.

JTo is in the published optimal 4x range (J8s+ or JTo), so raising four times the ante is the correct preflop play.

82 offsuit is well below the published preflop raising range, so I check and keep the option to raise later if the board improves.

8-2 offsuit has no pair, no draw, and no connection to K-J-9. Checking keeps the option to fold on the river rather than putting 2x more in with air.

Pair of deuces beats every non-qualifying dealer hand and the dealer qualifies only about 59% of the time, so a 1x raise has higher EV than folding.

52 offsuit is well below the published preflop raise range, so checking preserves the option to raise 2x only if the flop improves the hand.

5-2 offsuit has no pair, no flush draw, and no straight draw on 4-4-Q. Raising 2x with air is -EV; check keeps the river fold option if I don't improve.

I have two pair, fours and twos, and the dealer always qualifies on the paired board. Exact enumeration shows raising wins or ties often enough that its expected loss is under 1 chip versus 20 for folding.

63 offsuit is well below the published 4x range, so checking preserves the option to raise only if the flop improves the hand.

6-3 offsuit has no pair and only backdoor straight or flush possibilities on A-8-7, so a 2x raise is not justified.

I have a ten-high straight, which only loses to the 170 jack holdings and ties 117 six holdings. The other 703 runouts win, so a 1x raise is clearly +EV versus folding.

A3o is in the published optimal 4x range (any ace), so I raise the maximum preflop.

K6 suited is in the published optimal 4x range (K2s+), so I raise the maximum preflop.

96s is below the published optimal 4x range (J8s+), so checking preserves the option to raise later with a made hand or strong draw.

Board pair only with a 9 kicker and no flush or straight draw; raising 2x is -EV against most dealer holdings. Check and reassess on the river.

Board pair of aces with four diamonds means the dealer flushes, two-pairs, or outkicks 9-8-6 on the vast majority of holdings. Win rate is only about 5%, far below the ~20% needed for a 1x raise to beat folding.

QTo is in the published optimal preflop 4x range (Q8o+), so I raise the maximum.

Pocket kings are in the published optimal 4x range (33+), so I raise the maximum preflop.

K9o is inside the published optimal 4x range (K5o+), so I raise the maximum preflop.

T9s is below the published 4x range (J8s+), and a 3x raise is not the value size for this hand, so checking preserves the flop decision.

Two pair (tens and nines) plus a diamond draw is well ahead of a random dealer hand, so putting the 2x play bet in is clearly +EV.

T5s is below the published optimal 4x range (J8s+), so checking preflop is the correct play.

Two pair (tens and eights) is ahead of most random dealer holdings, so a 2x flop raise is the value play.

QTo is in the published optimal 4x range (Q8o+), so I raise the maximum preflop.

Pocket aces are the top of the published optimal 4x range (33+, any ace), so I raise the maximum preflop.

Q6 offsuit is below the published preflop 4x range (Q8o+ or Q6s+), so checking preserves the option to raise later with more information.

Queen-high with only a backdoor club draw has little equity, so checking preserves the option to fold on the river if I miss.

I have an 8-high flush and the dealer can beat it only with one of six higher clubs, about 25% of holdings. Raising wins the pot most of the time and is far better than folding for -20.

T7o is outside the published optimal 4x range (no pair, no ace, and not a qualifying king/queen/jack hand), so checking preserves the option to raise later with more information.

Top pair on the flop is a made hand worth a 2x raise under standard Casino Hold'em flop strategy.

78o 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 only if the flop connects.

Two pair (eights and sevens) plus a spade flush draw is well ahead of a random dealer hand, so the 2x raise is clearly +EV.

QJo is in the published optimal 4x range (Q8o+), so I raise the maximum preflop.