Blackjack table

I have 20 (K-T), which is a very strong hand. The dealer shows a 5, which is a weak upcard that often leads to a bust. Standing is the correct basic strategy play here, as hitting risks busting and the hand is already excellent.

With 13 against dealer's King (10-value), hitting is optimal. The dealer's strong upcard means I'm in a weak position and need to improve my hand. Standing on 13 gives me only a ~23% win rate against a 10-value card.

I have 17 against dealer's King (10-value card). The dealer has a strong upcard, but hitting 17 risks busting (any card 5 or higher). Standing on 17 against a dealer's 10-value card is the mathematically correct basic strategy play.

With a hard 17 against dealer's 9, standing is the optimal play. The probability of busting on a hit (any card 5 or higher) is very high, and 17 already beats most dealer hands except 18, 19, 20, or 21. Doubling would be unnecessarily risky given the strong dealer upcard.

I have 20 (Jack-Queen), and the dealer shows a King. Standing on 20 is correct basic strategy as the probability of improving is minimal and the risk of busting on a hit is high. The dealer's 20 or blackjack is possible but standing maximizes expected value.

With a hard 12 against dealer's King (10-value card), hitting risks busting on 10+ cards. Standing is the mathematically correct play as the dealer's bust probability doesn't justify the high bust risk of hitting.

With a hard 20 against the dealer's 3, standing is the optimal play. A 20 is an excellent hand that wins against most dealer outcomes, and the risk of busting by hitting far outweighs any potential gain.

Splitting aces is the mathematically optimal play in blackjack. Each ace becomes a new hand with potential for 21, and this maximizes expected value against the dealer's queen upcard.

With a hard 15 against dealer's King (10-value card), standing is the optimal play. Hitting risks busting with a high probability (64% chance with 16+ cards remaining), while the dealer must hit on 16 and lower, making standing the mathematically superior choice.

With a hard 18 against the dealer's 4 (weak upcard), standing is the correct play. Dealer's 4 is a bust card, so my 18 is very likely to win without taking additional risk.

With a hard 9 against dealer's 3 (a bust card), doubling down is the mathematically optimal play. The dealer is likely to bust, and doubling maximizes expected value in this favorable situation.

With 15 against dealer's 6 (a bust card), standing is optimal. The dealer has a high probability of busting, and hitting 15 risks going bust myself while the dealer is likely to lose from their weak upcard.

I have 18 (8+Q) against dealer's 9. With a hard 18, doubling is risky since I can't improve without busting, and the dealer's 9 upcard is moderately strong. Standing is the optimal play—my 18 wins if the dealer busts or has 17 or less.

With a hard 10 against the dealer's weak 6 upcard, doubling down is the optimal play. The dealer is likely to bust (showing 6), and a 10 gives us a strong probability of reaching 20 or 21 on the next card.

With a hard 11 against dealer's weak 3, doubling down is mathematically optimal. This hand has strong equity against the dealer's upcard, and doubling maximizes expected value by doubling the wager when the odds favor the player.

With a soft 18 (Ace-7) against the dealer's weak 6 upcard, standing is optimal. The dealer busts approximately 42% of the time on a 6, making this a favorable spot. Doubling risks busting or drawing a card that doesn't improve the hand sufficiently to justify the extra risk.

With a hard 10 against dealer's weak 3, doubling down is optimal. The dealer has a high bust probability, and my 10 is a strong position to double on according to basic strategy.

Hard 15 vs dealer 4 is a dealer bust scenario. Standing maximizes expected value as doubling risks busting while dealer has high probability of busting with this weak upcard.

With a hard 9 against dealer's 10-value card, doubling is the mathematically optimal play. This follows basic strategy: a 9 should be doubled against dealer upcards 3-6, and while a 10 is harder, the double bet maximizes expected value when drawing a single card has favorable odds of improvement.

With a hard 15 against dealer's 9, standing is the mathematically optimal play. Hitting risks busting (any card 7 or higher busts), while the dealer's 9 upcard suggests a strong hand, making doubling down an unfavorable risk-reward proposition.