Blackjack table

With a hard 8 against dealer's 2 (a weak upcard), hitting is optimal. Basic strategy recommends hitting all hard 8s regardless of dealer upcard, as the bust risk is minimal and the hand needs improvement.

With a hard 18 against dealer's 2 (weak upcard), standing is optimal. The dealer busts frequently from a 2, and hitting risks busting a strong hand.

With a hard 8 against dealer's 8, doubling down is optimal. Basic strategy calls for doubling on 8 vs 8 because the dealer has a moderate upcard, and the 10-value cards in a 6-deck shoe (32%) give a strong chance of reaching 18-20. Our expected value is positive when doubling here.

With a hard 5 against dealer's Queen (10-value), hitting is the correct basic strategy play. The hand has no bust risk and needs to improve significantly to compete against the dealer's strong upcard.

With a hard 13 against dealer's Queen (10-value card), hitting is the correct basic strategy play. The dealer is in a strong position, and standing on 13 gives the dealer a 59% win rate. Hitting offers the best expected value despite bust risk.

With a hard 16 against dealer's Jack (10-value), standing is the correct basic strategy play. Hitting would bust on any card 6 or higher (6 cards out of 13), while standing gives the dealer a chance to bust. Doubling would be mathematically unfavorable in this situation.

With a hard 18 against dealer's Jack (10-value), standing is optimal. Hard 18 wins against most dealer upcards and only loses to dealer 19-21; doubling would risk 20 chips to gain only 10, an unfavorable risk-reward at this strength.

With a hard 19 against dealer's 9, standing is optimal. My hand is very strong and likely to win. Hitting risks busting, and doubling would only increase risk without meaningful benefit.

With a hard 8 against dealer's 4 (a weak upcard), doubling down is optimal basic strategy. The dealer's 4 is a bust card, and doubling maximizes value when the dealer is vulnerable.

With a hard 13 against dealer's 7 (a strong dealer card), hitting is the mathematically correct play. The dealer's 7 indicates a likely 17 when counting the hole card, so we must improve our hand rather than stand on 13, which loses to most dealer outcomes.

With a hard 16 against dealer's 4, standing is optimal. The dealer's weak upcard (4) has high bust probability (around 40%), making it better to let the dealer bust rather than risk busting on a hit with the 40% chance of drawing 10+ value cards.

Hard 17 vs dealer 3 is a classic stand situation. The dealer's weak upcard (3) suggests a high bust probability, making it better to stand and let the dealer risk busting rather than hit and risk busting ourselves.

With a hard 12 against dealer's 6 (weak upcard), standing is optimal. Dealer busts frequently from 6, and hitting 12 risks busting. Doubling is mathematically inferior here.

With a hard 6 against dealer's 3 (a bust card), hitting is the optimal play. The dealer is likely to bust, but my hand is too weak to stand on; I need to improve to 12 or higher to have a reasonable chance of winning.

With a hard 16 against dealer's 3 (a bust card), hitting is the correct basic strategy play. The dealer is likely to bust, but my hand is still weak and needs improvement.

I have 19, a strong hand. The dealer shows a 3 (bust card), making it likely they will bust or have a weak hand. Standing maximizes the value of this hand.

I have a soft 18 (7+As) against dealer's Ace. Dealer peeks for blackjack and will stand on soft 17, so my 18 wins most scenarios. Doubling risks busting or drawing a card that weakens my hand; standing maximizes expected value here.

Splitting 8s against dealer's 10 is standard basic strategy. This reduces the risk of the hard 16 and gives two chances to improve to 18 or better.

With a hard 17 against dealer's 10 (weak upcard for player), standing is the correct basic strategy play. The probability of busting on a hit (7 cards) is too high, and dealer's 10 upcard means they likely have 17-20, making 17 a reasonable stand.

With 13 against dealer's 10, hitting is the mathematically correct play. A 13 is a stiff hand with significant bust risk, but standing against a 10 is worse; the dealer likely has 17-20, making a stand futile. Doubling is not favorable given the poor hand strength.

With a hard 19 against the dealer's 4 (a weak upcard), standing is the optimal play. The dealer is in a vulnerable position and likely to bust or make a weak hand; doubling risks losing additional chips when we already have a strong hand.