Blackjack table

With a hard 15 against dealer's 2 (weak upcard), standing is correct basic strategy. The dealer's weak 2 means they're likely to bust, so I should let them bust rather than risk busting myself by hitting.

With a hard 20 against dealer's King upcard, standing is the optimal play. The probability of improving with a hit is minimal (only Ace gives 21), while busting is highly likely. The dealer's King suggests a strong hand, making 20 a strong defensive position.

With a hard 17 against dealer's 6 (a bust card), standing is optimal. The dealer busts about 42% of the time from a 6 upcard, making this a favorable position to let them act.

With a hard 11 against dealer's 6 (a bust card), doubling down maximizes expected value. The dealer is likely to bust, and my 11 can improve significantly with any 10-value card.

Holding a soft 15 (Ace-4) against dealer's weak 3 is an ideal double-down situation. The dealer's 3 is a breaking card with high bust probability, while doubling increases expected value significantly given the soft total's flexibility.

With a hard 20 against dealer's 8, standing is the optimal play. A 20 is a very strong hand and the only ways to improve are unlikely (hitting risks busting), while the dealer's 8 is a mid-range card that leaves them vulnerable to bust with many outcomes.

With a hard 13 against the dealer's 8, hitting is the mathematically correct play. The dealer's 8 is a strong upcard, and my 13 is too weak to stand. Doubling would be too aggressive here as I risk 20 chips on a marginal hand.

With a hard 19 against the dealer's 8, standing is the optimal play. A 19 is a strong hand that beats most dealer outcomes, and hitting risks busting with minimal upside since any card except an Ace or 2 will bust the hand.

With a hard 7 against dealer's Jack (10-value), doubling down maximizes expected value. The dealer is strong but my 7 has significant upside potential; doubling captures additional value from favorable future cards while the bet is still modest at 10 chips.

With a hard 12 against dealer's King (10-value card), hitting would bust on many cards (10, J, Q, K). Standing is the correct basic strategy play here, as the dealer has a strong upcard and we avoid immediate bust risk.

With a hard 18 against dealer's 5 (weak upcard), standing is optimal. The dealer likely busts from this weak position, and hitting risks busting or drawing to a weaker hand.

I hold 20 (King-Queen), which is a strong hand. The dealer shows an 8, which is moderately strong but typically results in a 18 or bust. Standing on 20 is the mathematically optimal play against any dealer upcard.

With a hard 6 against dealer's Jack (10-value card), hitting is the optimal play. The dealer's strong upcard means I need to improve my hand, and there's minimal bust risk at this total.

With a hard 9 against dealer's Jack (10-value card), hitting is the correct basic strategy play. The dealer is in a strong position, and I need to improve my hand significantly to win this hand.

With a hard 19 against the dealer's Jack (10-value), standing is the correct play. A 19 is a very strong hand that wins against most dealer outcomes, and hitting risks busting or getting a lower total.

With a hard 17 against dealer's 4 (weak upcard), standing is correct. The dealer has a 40% bust probability from a 4 upcard, making hitting too risky despite the option to double.

With a soft 14 (Ace + 3) against dealer's Ace, hitting is optimal. The Ace gives flexibility to improve without busting, and the dealer's Ace suggests a strong hand, so passive play is unfavorable.

I have a soft 19 (Ace-3-5), which is a strong hand. The dealer shows an Ace, which could be a blackjack, but I cannot improve my 19 without busting, so standing is the optimal play.

With a hard 19 against dealer's Jack, standing is optimal. The hand is already very strong and the probability of improvement via hitting is negligible (only an Ace improves to 20, which is unlikely), while busting is a real risk.

Hard 11 is the strongest non-blackjack hand and should always be doubled against a dealer's 8 upcard. This maximizes expected value in this favorable situation.

With 12 against dealer's 9, hitting is the correct basic strategy play. A 12 is a stiff hand that loses to most dealer outcomes, and the dealer's 9 is a strong upcard. Doubling would be inappropriate here as we'd commit more chips with poor odds.