Blackjack table

Hard 11 against a dealer 10 is a textbook double in basic strategy; the expected value of doubling exceeds hitting.

A hard 20 is nearly unbeatable; standing has by far the highest EV against a dealer 9, while doubling or splitting queens would only destroy value.

Hard 20 is a near-made hand; standing wins against all dealer outcomes except a made 20/21, and doubling or splitting tens against a queen would destroy a dominant position.

Hard 13 against a dealer 10 is a basic-strategy hit; standing loses too often, and doubling 13 vs 10 is not profitable.

Hard 13 against a dealer 8 is a basic-strategy hit; standing risks losing to a likely dealer 18, while one card cannot bust me.

Hard 17 is a pat hand; standing is correct against a dealer 8 since hitting risks busting with no upside.

Hard 11 vs dealer 8 is a strong double per basic strategy; doubling maximizes expected value versus hitting.

Hard 10 vs dealer 7 is a standard double: dealer 7 upcard yields a strong but beatable average (~18), and one more card gives me a good chance of 19-21. Doubling maximizes EV versus hitting.

Hard 12 against a dealer 5 is a basic-strategy stand: the dealer's bust rate is high on 4-6, and hitting risks busting with 10/face cards. Standing maximizes expected value here.

Hard 18 vs dealer 2 is a stand per basic strategy; hitting risks busting a made hand with little gain.

Hard 14 against a dealer 9 is a basic-strategy hit; standing only wins if the dealer busts, which is unlikely with a 9 upcard.

Hard 17 vs dealer 9 is a standing hand in basic strategy; hitting risks busting with little gain since only 2-4 improves the hand meaningfully.

Hard 13 vs dealer Ace; dealer peeked so no blackjack, and basic strategy says hit hard 13 against an Ace rather than stand or double.

Hard 10 against a dealer 6 is a textbook double-down: strong drawing hand plus high dealer bust probability maximizes expected value.

Hard 13 against a dealer 4 is a basic-strategy stand; the dealer's high bust probability with a 4 upcard makes hitting unnecessary risk.

Hard 14 against a dealer 10 is a basic-strategy hit; standing loses more often than drawing since the dealer likely makes 17-20. Doubling is too risky with a weak total.

Hard 14 against a dealer 8 is a basic-strategy hit; standing leaves me losing to any dealer 18, and the risk of busting is outweighed by the dealer's strong upcard.

Hard 19 is a strong made hand; standing is clearly optimal against a dealer 8.

Hard 13 vs dealer 7 is a hitting situation; standing gives poor expected value since dealer 7 likely makes 17+.

Hard 14 against a dealer 10 is a basic-strategy hit; standing loses more often than drawing one card, and doubling is too risky here.

Basic strategy: hard 16 vs dealer 7 is a hit, since standing loses against the likely dealer 17+ anyway; only vs 2-6 would I stand.

Hard 18 vs dealer 7 is a standing hand; hitting only risks busting against a likely dealer push/loss scenario.

Hard 19 is a strong made hand; basic strategy says stand against any dealer upcard, including a ten. Hitting or doubling risks ruining a near-winning total.

Hard 18 against a dealer 5 is a strong standing hand; basic strategy says stand, as hitting risks busting a likely winner and doubling 18 is too risky.