Blackjack table

With a hard 17 against dealer's 8, standing is optimal. The dealer likely has 18 (10-value card in hole), making hitting too risky with a 46% bust probability on the next card.

With a hard 10 against dealer's 10-value card, doubling down is the mathematically optimal play. This hand benefits significantly from one additional card and doubles expected value compared to hitting.

With a hard 17 against dealer's 6 (a weak upcard), standing is optimal. The dealer is likely to bust, and hitting risks busting our hand with only a 4-card (Ace) helping us. Basic strategy recommends standing on hard 17 against dealer's 6.

With 13 against dealer's 10, hitting is the mathematically optimal play. Standing gives a very low win probability, while hitting offers a reasonable chance to improve to 17+ without busting (we can draw 2-8).

I have a hard 20 (Jack-King), which is an excellent hand. The dealer shows an Ace, but standing on 20 is the correct play—any hit risks busting, and 20 beats most dealer outcomes.

With 14 against dealer's 6 (a bust card), standing is optimal. The dealer has a high probability of busting from this weak upcard, making it unnecessary to risk busting our hand by hitting.

With a hard 18 against dealer's 6 (a bust card), standing is optimal. The dealer busts roughly 42% of the time from a 6 upcard, making this a strong position without needing to risk busting with a hit.

With a hard 12 against dealer's 9, hitting risks busting (any 10-value card busts). Standing gives the dealer a chance to bust, as dealer must hit on hard 17 or less and 9 is a strong upcard that often leads to dealer busting or reaching 17-21 where we lose anyway.

With 13 against dealer's 3, hitting is optimal. The dealer's weak upcard (3) suggests they're likely to bust, but my 13 is too weak to stand; hitting gives me a strong chance to improve without excessive bust risk.

With a hard 8 against dealer's 9, hitting is the correct basic strategy play. The hand is too weak to stand, and doubling on 8 is not recommended since we need low cards to improve and the expected value of hitting is better.

With a soft 19 (Ace-5-3), I have a strong hand. The dealer shows a 9, which is a strong upcard, but my 19 beats it. Standing is the correct play as hitting risks busting or improving to a worse outcome.

With a soft 20 (Ace-9), I have an excellent hand that beats most dealer outcomes. Standing is optimal since hitting risks busting or at best pushing, while the dealer's Jack upcard suggests a strong hand that makes doubling unnecessary.

With a hard 7 against dealer's 7, hitting is the correct play. The dealer's 7 is a strong card, and my 7 is too weak to stand. Doubling down would be too aggressive with such a low total and uncertain upside.

With a hard 17 against dealer's 7 upcard, standing is the correct basic strategy play. The dealer has a moderate bust probability, and hitting risks busting (any card 5+ busts this hand) while gaining minimal advantage.

With a soft 15 (Ace-4) against dealer's 6 (weak upcard), doubling down is mathematically optimal. The dealer's 6 is a bust card, and doubling maximizes expected value when we have a soft hand that can improve to 17-21 with a single card.

With a hard 20 (Queen-King) against dealer's 7, standing is the optimal play. A 20 is a very strong hand and the probability of improvement by hitting is minimal while the bust risk is substantial.

With a pair of 2s against dealer's King (10-value), splitting gives two chances to reach 12+ without busting immediately. Hitting would risk a bust on the next card (>2), while standing at 4 loses to dealer's likely 17+. Splitting maximizes expected value.

With a hard 5 against dealer's King, hitting is the optimal play. A hard 5 cannot bust on the next card, and I need to improve significantly to win against a strong dealer upcard.

Hand 0 is a soft 16 (Ace-2-3), which is weak against the dealer's King upcard. Hitting gives a good chance to improve without busting since the Ace can count as 1, and reaching 17+ is needed to compete against likely dealer 17-20.

I have 13 (2-3-A-7) against dealer's King. This is a stiff hand needing improvement. Hitting is standard basic strategy against a dealer's strong 10-value card.

I have a soft 13 (Ace-2) against the dealer's King. Doubling down is the mathematically optimal play here, as it increases my expected value significantly by allowing me to capitalize on a favorable situation where the dealer's stiff card is unlikely to bust.

With a hard 7 against dealer's 5 (a weak upcard), hitting is the mathematically optimal play. The dealer's 5 is vulnerable to busting, but my 7 needs improvement regardless, and doubling would risk more chips without sufficient advantage at this stage.

With a hard 17 against dealer's 5 (weak upcard), standing is the correct play. The dealer has a high bust probability, and hitting risks busting with a likely losing hand.

With 16 against dealer's 4 (a bust card), standing is optimal. The dealer is likely to bust, and hitting 16 risks busting myself while the dealer has significant bust probability.

With a hard 6 against dealer's 8, hitting is the mathematically correct play. A 6 is a weak hand that needs improvement, and the dealer's 8 is a strong upcard. I cannot bust on the next card (best case Ace=17, worst case King=16), so hitting maximizes expected value.

With a hard 16 against dealer's 8, hitting is the mathematically correct play. The dealer's 8 is strong (likely making 18), and standing on 16 loses to most dealer outcomes. Hitting gives a chance to improve to 17+ or bust, but the expected value favors hitting in this spot.

Hand total is 20 (2+4+Q+4), which is a very strong hand against the dealer's 8 upcard. Standing is the correct play as hitting risks busting and the probability of improvement is minimal.

With 13 against dealer's 7, hitting is optimal per basic strategy. The dealer's 7 is a strong upcard, so I need to improve my hand. Doubling would be reckless with such a weak total.

I have 20 (8-5-7), which is a very strong hand. The dealer shows a 7 upcard. Standing with 20 gives me an excellent chance to win, as the dealer would need 21 to beat me, which is unlikely.

Player has 20 (King-Queen), which is a very strong hand. Dealer shows Queen (10-value card). Standing is the mathematically correct play here—hitting risks busting while the hand is already strong, and doubling is not justified when the dealer's upcard is already high value.