Showdown Hold'em table

Any ace is in the published optimal 4x preflop raising table for Ultimate-style play, so A3o should raise the maximum.

32 suited is well outside the optimal preflop 4x raising range (33+, any ace, strong kings/queens/jacks), so I check and look at the flop for free.

3-2 high on a K-Q-8 board leaves no pair, no meaningful draw and only a weak backdoor flush chance, so raising would lose money. Checking keeps the option to see the river for free.

My 3-2 does not improve on the board, so the best I can do is tie by playing the board, and any dealer pair, nine, jack or club flush beats me. Raising risks about 30 chips on most outcomes and wins nothing, so folding for 20 is cheaper.

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

The published optimal strategy says to raise 4x preflop with any ace, and A4o falls in that range. The 4x raise has higher EV than checking.

Pocket eights fall within the published optimal 4x preflop range (33+). A 4x raise maximizes expected value with a made pair.

Any ace is on the published optimal 4x preflop raise table, so ATo calls for the maximum raise.

9-3 offsuit is well outside the optimal preflop 4x raising range, so check and see the flop for free.

A hidden pair (middle pair of nines using a hole card) is a standard 2x flop raise under optimal strategy, and the backdoor spade draw adds a little extra equity.

7-2 offsuit is not in the preflop 4x raising range, so checking is correct. Checking costs nothing extra and keeps the flop and river decisions open.

7-2 offsite on a K-J-8 flop has no pair, no draw and no real equity, so raising 2x would lose money. Checking is free and keeps the river decision open.

The board's pair of eights means the dealer always qualifies. I only win when the dealer holds two unpaired cards below a 7 (about 8.5%), so raising is worth about -24 chips versus -20 for folding.

Any ace is on the published optimal preflop 4x raising table, so A2 offsuit gets the maximum raise.

T5 offsuit is well outside the optimal preflop 4x raising range (which needs JTo or better among unpaired non-ace, non-king hands), so checking is correct. This keeps cheaper options open on the flop and river.

Top two pair (tens and fives) on the flop is a strong favorite against a random dealer hand, so raising 2x maximizes expected value.

K6 offsuit falls within the published optimal 4x preflop range (K5o+), so raising 4x has higher expected value than checking.

T9 offsuit is outside the optimal 4x preflop range (only JTo+ among offsuit jack/ten hands), so checking is correct. That keeps flop and river options open for cheaper decisions.

Two pair (tens and nines) on the flop is a strong favorite over a random dealer hand. Raising 2x maximizes expected value; checking would give up too much.

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

82 offsuit is far below the optimal preflop 4x raising threshold, so I check and see the flop for free.

8-2 offsuit on a K-J-9 flop has only a gutshot (needs a 10) and no pair, which is far too weak to raise 2x. Checking keeps the river decision open for free.

Bottom pair of 2s raises to about -1.19 ante in expectation, because the dealer misses qualifying in roughly 404 of 990 holdings and we then win the play bet. That beats the certain -2 from folding.

5-2 offsuit is far outside the optimal 4x raising range (33+, any ace, strong kings/queens/jacks), so checking to see the flop for free is correct.

52 offsuit on a 4-4-Q flop has only a gutshot (needs a 3) and a 5-high kicker, so it is too weak to raise 2x. Checking costs nothing extra and keeps the option to fold or raise 1x on the river.

I have two pair, fours and twos with a queen kicker, which beats any dealer hand that only plays the board pair of fours. Raising needs to win only about 20% of the time to beat folding, and I win far more often than that.

6-3 offsuit is far outside the optimal preflop 4x raising range (33+, any ace, strong kings/queens/jacks), so checking to see the flop is correct.

With 6-high and only backdoor straight and flush draws, this hand is well short of the usual flop raising threshold (two pair, a hidden pair, or a strong flush draw). Checking keeps the river decision open at lower risk.

I hold a ten-high straight (6 through T), which beats every dealer holding except one containing a jack, and no flush is possible on this board. Raising gets paid on the play bet, the ante and the 1:1 blind straight payout.

Any ace is in the published optimal preflop 4x raising range, so A3 offsuit gets the maximum raise.

K6 suited falls within the published optimal 4x preflop table (K2s+), so raising 4x maximizes expected value.

96 suited is outside the optimal 4x preflop table (33+, any ace, K2s+, Q6s+, J8s+), so checking is correct. That keeps the option to raise on the flop or river if the hand improves.

With 9-6 offsuit on an A-A-2 board I have only 9 high and no draw, so checking keeps the river option without adding risk. The board pair already gives the dealer a qualifying hand, which makes a 2x raise clearly negative here.

The board's pair of aces means the dealer always qualifies and beats our A-A-9-8-6 with any higher kicker, any pair, a diamond flush or a straight. We win only about 5% of the time, well below the roughly 20% needed for raise_1x to lose less than folding.

QTo meets the published optimal 4x preflop threshold of Q8o or better, so a maximum raise has positive expected value.

Pocket kings are far inside the optimal 4x preflop raising range, so the maximum raise gives the highest expected value.

K9 offsuit falls within the published optimal 4x preflop range (K5o+). Raising the maximum is the correct play here.

T9s is not on the optimal 4x preflop table (which needs J8s+ for suited jacks and does not include suited ten-nines), so checking and re-evaluating on the flop is correct.

Top two pair (tens and nines) on the flop is a strong favorite over a random dealer hand, so raising 2x maximizes expected value.

T5 suited is not on the optimal 4x preflop table (no ace, not K/Q/J high, not a pair 33+), so checking is the stronger play. The flop can then decide whether to raise 2x.

A ten in my hand pairs the top board card and combines with the board's eights for two pair. This beats most dealer holdings, so the 2x flop raise should be clearly profitable, in line with the standard bet-any-hidden-pair flop strategy.

QTo is offsuit and falls within the published optimal 4x range (Q8o+), so raising 4x preflop maximizes expected value.

Pocket aces are the strongest preflop hand and fall well inside the optimal 4x raising table, so committing the maximum play bet maximizes expected value.

Q6 offsuit is below the optimal 4x threshold (Q8o+ for offsuit queens), so checking keeps the option to raise 2x on the flop or 1x on the river.

Queen-high with only backdoor flush and straight draws is well below the flop raise threshold (a hidden pair or a strong four-flush), so checking and deciding on the river is better.

I hold an 8-high flush (8c-7c-6c-5c-3c), which beats every dealer holding except one containing a higher club or the 4c. Raising gains the play bet, the ante, and the 3:2 blind payout in the large majority of cases.

T7 offsuit is not in the optimal 4x preflop range (JTo is the weakest offsuit hand with a ten that qualifies), so checking is correct. That keeps the option to raise on the flop or river.

Top pair of tens using a hole card is a hidden pair, and optimal flop strategy raises 2x with any hidden pair because it is well ahead of the dealer's range.

Offsuit 8-7 is outside the optimal preflop 4x raising range, so I check and re-evaluate on the flop.

Two pair (8s and 7s) on the flop is well ahead of a typical dealer holding. It also has full house outs and a backdoor flush draw for the blind, so raising 2x has clearly higher EV than checking.

QJo falls inside the published optimal preflop 4x raising range (Q8o+), so raising 4x maximizes expected value.