Blackjack table

With 14 against dealer's 7, hitting is correct basic strategy. The dealer's 7 is a strong card (likely makes 17 or better), so standing on 14 loses in most scenarios. Hitting gives us a chance to improve to 17+ or bust less frequently than the expected loss from standing.

With a hard 16 against dealer's 7, hitting is the mathematically optimal play. The dealer's 7 is a strong upcard (likely makes 17+), so standing on 16 loses; hitting gives a chance to improve to 17-21 while accepting bust risk is preferable to the high probability of losing if we stand.

With a hard 8 against dealer's 9, hitting is the optimal strategy. The hand is too weak to stand (dealer 9 is strong), and doubling on 8 is mathematically unfavorable. I need to improve this hand significantly.

With a hard 16 against dealer's 9 (strong upcard), hitting is the mathematically correct play. Standing on 16 vs 9 has a very negative expected value, while hitting gives a reasonable chance to improve the hand.

With a hard 20 against dealer's 9, standing is optimal. A 20 wins against most dealer hands, and hitting risks busting. Doubling or splitting K-Q is not strategically sound.

Hard 17 vs dealer 7 is a classic hold position. Dealer's 7 is strong but not guaranteed to bust; hitting risks busting while standing gives a reasonable chance to win or push.

With a hard 10 against dealer's 10-value card (Jack), doubling down is the mathematically optimal play. A hard 10 is a strong doubling opportunity that maximizes expected value even against a strong dealer upcard.

With 11 against dealer's Ace, doubling is the strongest play. A hard 11 has excellent doubling potential (10-value cards give 21), and the dealer's Ace showing doesn't change the math significantly given dealer hits soft 17 is false.

Player has 11 (7+4) against dealer's 5. Doubling down on 11 against a weak dealer upcard (5) is a mathematically optimal play—the dealer has a high bust probability, and doubling maximizes expected value in this favorable situation.

With a hard 12 against dealer's 4 (a bust card), standing is the optimal play. The dealer is in a weak position and likely to bust, so hitting risks busting our hand while standing lets the dealer's weak upcard work in our favor.

With a hard 19 against dealer's 7, standing is optimal. The hand is strong and statistically beating most dealer outcomes; hitting risks busting while the probability of improving to 20 or 21 is too low relative to the risk.

Pair of 8s totaling 16 against dealer 10 is a classic split situation. Splitting gives two chances to improve to 18+ rather than hitting and likely busting or standing on a weak 16. Splitting 8s is correct basic strategy.

With a hard 18 against the dealer's 10 upcard, standing is the correct basic strategy play. A hard 18 is a strong hand that beats most dealer outcomes, and hitting risks busting while the probability of improvement is minimal.

Hand total of 12 vs dealer's 10 is a stiff hand in a bad spot. Hitting is the mathematically correct play here; doubling 12 against a 10 would be poor EV. Hand 0 already has 18, so we have decent backup value.

Hand total is 17 against dealer's 10 upcard. Standing on 17 is optimal basic strategy; hitting risks busting (any card 5 or higher busts), and the 17 has reasonable equity against the dealer's likely 17-20.

With 15 against dealer's 8, standing is optimal. The dealer's 8 is a moderately strong card (likely 18 if they hit), and hitting 15 risks busting with a 37% chance while standing has a better expected value.

Hard 12 vs dealer 3 is a critical decision. Basic strategy recommends standing on hard 12 against a dealer 3, since the dealer's weak upcard (likely to bust with a 40% bust probability) makes it better to let the dealer act rather than risk busting ourselves at 12.

With a hard 14 against the dealer's 6 (a weak upcard), standing is optimal. The dealer has a high bust probability, and hitting risks busting myself with most cards (K, Q, J bust immediately). Basic strategy recommends standing here.

With a hard 17 against the dealer's 7, standing is the correct basic strategy play. The dealer's 7 is a strong upcard, but doubling 9-8 is not mathematically favorable, and hitting risks busting with a high probability of drawing 10-value cards.

With a hard 12 against dealer's 10, hitting is unfavorable (high bust risk of 31% with any card 10+), and doubling is mathematically poor. Standing gives the best expected value by avoiding bust while hoping the dealer busts on their 10.

With 14 vs dealer's Ace (counting as 11 for dealer's potential blackjack), hitting is the mathematically correct play. Standing on 14 loses to most dealer outcomes. The slight bust risk (36% with 8/13 cards busting) is outweighed by the high likelihood that standing 14 loses to the dealer's likely strong hand.