Blackjack table

With a hard 9 against dealer's 3 (bust card), doubling down is the mathematically optimal play. The dealer is in a weak position and we're likely to improve our hand significantly with one card.

With a hard 16 against dealer's 7, standing is the mathematically optimal play. The dealer's 7 is a moderate-strength card, and hitting a 16 is too risky given the high probability of busting (over 61%) compared to the dealer's bust probability from 7 upcard.

Hard 17 against dealer's 2 is a favorable stand. The dealer is in a weak position and likely to bust, while hitting risks busting myself or getting a worse hand.

Player has 20 (Jack and King), which is a very strong hand. Dealer shows Jack (10-value card). Standing on 20 is the correct play as hitting risks busting with minimal upside, and the hand already beats most dealer outcomes except blackjack or 21.

With a hard 20 against dealer's 9, standing is the mathematically optimal play. The hand is already extremely strong, and any hit risks busting while the dealer is likely to bust or make at most 19.

With 16 against dealer's King (10-value), hitting is statistically unfavorable (bust probability ~38% vs dealer bust probability ~42%). Standing is the mathematically optimal play in this classic 16 vs 10 scenario.

With a hard 15 against dealer's 10, standing is optimal. Hitting gives high bust probability (54%), while dealer's 10 likely makes 17-20. Basic strategy recommends standing in this unfavorable situation.

With a hard 12 against dealer's Ace, standing is the optimal play. Hitting risks busting (any card 10+ busts), while the dealer's Ace suggests a strong hand. Basic strategy recommends standing on hard 12 vs Ace.

With 12 against dealer's Ace showing, standing is optimal. The dealer likely has 21 (blackjack) or a strong hand, and hitting would bust on many cards (10-K worth 10). Basic strategy recommends standing on hard 12 versus Ace.

I have 20 (King-Ten), which is a strong hand. The dealer shows 8 and will likely bust or make a weak hand. Standing is the optimal play here, as hitting risks busting and doubling unnecessarily exposes more chips for minimal benefit.

I have 20 (10+K), which is a very strong hand. The dealer shows a 5, which is a weak upcard. Standing is the correct play here as hitting risks busting while the dealer is likely to bust or have a weak hand.

With a hard 12 against dealer's 10, hitting risks busting on any card 10 or higher (4 in 13 outcomes). Doubling 12 against a 10 is mathematically poor. Standing gives the dealer pressure to draw to 17+ with their 10 upcard, where they'll bust roughly 35% of the time on subsequent draws.

With a hard 14 against the dealer's Jack (10-value card), standing is correct. Hitting risks busting while the dealer is in a strong position, and doubling would be mathematically unfavorable with this weak total.

With a hard 17 against dealer's Ace (which could be blackjack or a 10-value card), standing is the optimal play. Hitting risks busting, and doubling increases variance without improving expected value against a dealer Ace.

With a hard 20 against dealer's 10-value card (Jack), standing is the correct play. A 20 is an extremely strong hand, and the probability of improving is low while the risk of busting is significant.

I have 18 against dealer's Queen (10-value card). Standing on 18 is optimal strategy as hitting risks busting while doubling or splitting would be disadvantageous given my strong hand relative to the dealer's likely 17-20 total.

With a hard 14 against dealer's King (10-value), hitting is the correct basic strategy play. The dealer's strong upcard means standing on 14 is too weak; we need to improve our hand.

With 16 against dealer's King (10-value card), hitting is the optimal play. The dealer likely has 10+ and will bust only rarely, so standing on 16 loses almost certainly. Hitting gives a chance to reach 17+ or at least improve the hand.

With a hard 19 against dealer's King (likely 10 value), standing is optimal. A 19 is a strong hand that wins against most dealer outcomes, and hitting risks busting.

With 13 against dealer's 6 (a bust card), standing is optimal. The dealer has a high bust probability, and hitting 13 risks busting myself while doubling down would needlessly increase exposure to a losing scenario.

With a hard 12 against the dealer's Ace, standing is optimal. The dealer shows Ace which likely results in a strong hand (17+), and hitting a 12 gives a high bust probability (around 42%), making stand the mathematically superior play.

With 13 against dealer's 5, hitting is the standard basic strategy play. The dealer's 5 is a weak upcard but my 13 is even weaker, and the probability of improving outweighs the risk of busting.

I hold 19 (3-Q-6), a strong hand against the dealer's 5 upcard. Dealer busts in ~42% of cases from a 5, and my 19 wins most non-bust scenarios. Hitting risks busting or receiving a card that doesn't improve my position.