Blackjack table

With 13 against dealer's Ace, standing is optimal. The dealer shows Ace (likely 11 or 21), and hitting 13 risks busting with high probability while doubling down increases exposure to a likely dealer blackjack or strong hand.

With hard 13 against dealer's 5 (weak upcard), standing is optimal. Dealer busts roughly 42% of the time on 5, while hitting risks busting my hand immediately. Basic strategy recommends standing on 13 vs 5.

With 16 against dealer's 7 (a breaking card), standing is optimal. The dealer has a 38% bust rate but hitting 16 gives only 25% win rate versus 46% when standing. This is a mathematically sound decision in basic strategy.

I have 20 (Queen-Queen), which is an excellent hand. The dealer shows a Queen (10-value), giving them a likely 10-20 range. Standing on 20 is the mathematically optimal play; hitting risks busting or drawing a card weaker than what I already have.

With a hard 19 against dealer's King (10-value card showing), standing is optimal. A hard 19 is a strong hand that beats most dealer outcomes, and hitting risks busting while doubling only adds marginal value with limited upside.

With a hard 20 against the dealer's 10, standing is the mathematically optimal play. A 20 is a very strong hand that wins against most dealer outcomes, and hitting risks busting with minimal upside.

I have Ace-4 (soft 15) versus dealer's 3. Doubling down is optimal here because the dealer's weak upcard makes this a favorable situation to increase my bet, and I can improve to 16-21 with most cards.

With a hard 19 against dealer's Queen (likely 10-value), standing is optimal. The probability of improving is minimal and busting risk is high; dealer must hit on soft 17 or less, giving good winning chances.

With a hard 16 against dealer's 6 (a bust card), standing is optimal. The dealer busts approximately 42% of the time with a 6 upcard, making this a favorable situation to avoid the risk of busting on a hit.

With a hard 10 against the dealer's King (10-value card), doubling down is the mathematically optimal play. While the dealer's upcard is strong, doubling maximizes expected value when holding 10, as hitting risks busting while doubling gives us a better chance to reach 19-20.

With a hard 15 against dealer's Jack (10-value card), standing is optimal. Hitting risks busting with a 37% probability while the dealer's likely 20 will beat 15 anyway; standing gives the best expected value in this losing situation.

With a hard 16 against the dealer's King (10-value), standing is the mathematically correct play. Hitting risks busting on 10-value cards (which are abundant in a 6-deck shoe), while the dealer's strong upcard means we're likely losing anyway; doubling down would only increase losses in an unfavorable situation.

Hard 17 against dealer 9 is a marginally negative expectation hit, but standing avoids the high bust risk (92% chance to bust on hit). Basic strategy recommends standing on hard 17 versus dealer 9.

With a hard 9 against dealer's King (10-value), doubling is optimal. This is a classic doubling situation where the player has a weak hand but favorable odds of improving to 19 or better, and the dealer's strong upcard justifies aggressive play to maximize expected value.

Player has 15 against dealer's 5. The dealer has a weak upcard (5) and is likely to bust. Standing maximizes expected value by letting the dealer bust rather than risking busting on a hit.

With a hard 15 against dealer's 8, standing is optimal. Dealer's 8 is strong (likely 18 if hitting), but my 15 will bust if I hit (need 6 or less out of 13 bust cards). Basic strategy and odds favor standing here.

Hard 17 against dealer 8 is a standoff situation where hitting risks busting (any card 5+ busts) while standing gives a reasonable chance at winning. Basic strategy recommends standing on hard 17 regardless of dealer upcard.