Blackjack table

Hard 12 against a dealer 6 is a standing situation in basic strategy; the dealer's bust risk with a 6 up outweighs the modest gain from hitting.

Hard 18 against a dealer 6 is a clear stand; hitting risks busting a strong hand while the dealer is likely to bust from 6.

Hard 18 against a dealer 3 is a strong standing hand; basic strategy says stand, and doubling risks ruining a likely winner.

Hard 20 is nearly unbeatable; standing maximizes expected value against a dealer 7 upcard.

Hard 15 vs dealer 2 is a basic-strategy stand in 6-deck S17; the dealer's bust risk on small upcards outweighs the chance of improving without busting.

Hard 5 against a dealer 8 is far below 17; hitting is mandatory since standing loses almost always and doubling is not justified with such a weak total.

Hard 15 against a dealer 8 is a losing standing position; basic strategy calls for a hit since the dealer's expected total beats 15 too often.

Hard 20 is a made hand; standing is clearly optimal against a dealer 8.

Hard 10 against a dealer 8 is a standard basic-strategy double: the expected value of doubling exceeds hitting, since many draw cards improve to strong made hands while the dealer 8 is vulnerable.

Hard 15 against a dealer 5 is a standard stand; the dealer's high bust probability makes hitting riskier than letting them play out.

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.

Hard 15 against a dealer 7 is a basic-strategy hit; standing leaves the hand too weak against a likely dealer 17-20.

Hard 19 is a made hand; standing is clearly optimal against a dealer 7, as hitting or doubling risks a strong position for negligible gain.

Hard 9 against a dealer 6 is a textbook double: the dealer's weak upcard gives high bust probability, so maximizing the bet on this favorable spot is correct.

Hard 18 against a dealer 6 is a clear stand; hitting risks busting a strong hand while the dealer is likely to bust from 6.

Hard 11 against a dealer 2 is a textbook double in a 6-deck S17 game; expected value is maximized by doubling rather than hitting.

Hard 12 against a dealer ace is a clear hit per basic strategy; standing loses far more often than hitting, and doubling is not justified.

Hard 16 against a dealer 6 is a standard stand: the dealer's bust probability is high and hitting risks busting. Standing maximizes expected value here.

A pair of aces should always be split: two hands starting with an ace have far higher expected value than a soft 12, especially against a weak dealer 4 upcard.

Hard 20 against a dealer King is a near-lock winner; standing maximizes expected value with no risk of busting.

Hard 18 against a dealer 4 is a strong standing hand; basic strategy says stand, as hitting risks busting a likely-winning total and doubling is too risky.