Blackjack table

With a hard 9 against the dealer's Ace, doubling down is optimal. This hand has strong equity against a weak dealer position, especially considering potential natural blackjacks are already off the table.

With a hard 14 against dealer's 5, standing is optimal. The dealer's 5 is a weak upcard with high bust probability (around 42%), making it more profitable to let the dealer act rather than risk busting with a hit.

With 16 against dealer's Ace (which counts as 11), I have a losing hand in most scenarios. Hitting risks busting at 67% probability, while standing gives a small chance the dealer busts or has a weak total. Doubling would be counterproductive with such a weak hand.

With 17 against dealer's 7, standing is the optimal play. Doubling risks busting or making only 18-20, while the dealer's likely bust rate with a 7 upcard makes standing the highest expected value decision.

With a hard 12 against dealer's 2 (weak upcard), standing is optimal. Hitting a 12 into a dealer's 2 is a classic mistake—the bust risk (4 cards bust: K,Q,J,A) outweighs the benefit of trying to improve, and the dealer's weak upcard makes it likely they'll bust themselves if we don't.

With a hard 19 against dealer's 4 (a bust card), standing is optimal. The dealer has a high bust probability, and doubling risks losing chips on an already strong hand.

With a hard 18 against dealer's 5 (a weak upcard), standing is optimal. Basic strategy dictates standing on 18 regardless of dealer upcard, as the probability of improvement is minimal while bust risk on hit is substantial.

With a hard 7 against dealer's 8, hitting is the correct basic strategy play. The hand is too weak to stand, and doubling on 7 is not a strong position despite the option being available.

With 15 against dealer's 8, hitting is the mathematically correct play. The dealer's 8 is a strong card (likely makes 18), so standing on 15 loses most of the time. Hitting gives a chance to improve to 17+ or at worst bust, but the expected value favors hitting here.

With 15 against dealer's 4 (a bust card), standing is optimal. The dealer has a high probability of busting, and hitting 15 increases my bust risk significantly.

With a hard 11 against dealer's 3 (weak upcard), doubling is the optimal play. This maximizes expected value by doubling the bet when the dealer is most likely to bust and my hand has high probability of reaching 21.

With 14 against dealer's 7, hitting is the optimal play. The dealer's 7 is a strong card (likely to make 17+), so I need to improve my hand. Basic strategy calls for hitting 14 against 7 rather than standing or doubling.

With a hard 19 against dealer's 7, standing is optimal. A 7 upcard is moderately strong for the dealer, but my 19 is a powerful hand that beats most dealer outcomes. The risk of busting by hitting far outweighs any potential gain.

With a hard 15 against dealer's 6 (weak upcard), standing is correct. The dealer's 6 is a bust card, so the dealer's bust probability is high. Hitting risks busting my 15 while doubling is mathematically unfavorable here.

With a hard 20 against the dealer's 4 (a weak upcard), standing is the mathematically optimal play. A 20 is an excellent hand and the risk of busting on a hit far outweighs any potential gain.

I have 20 (Queen and Jack), which is a very strong hand. With the dealer showing a 7, standing is optimal as the probability of improving is minimal while the risk of busting is high.

With a hard 7 against dealer's 10-value card, hitting is the optimal play. The hand is too weak to stand, and doubling down would be poor expected value since we'd only get one more card and risk doubling the bet.

Player has 17 (4+3+10) against dealer's Jack (10). Standing on 17 is the correct basic strategy play; hitting risks busting with a 40% chance while dealer must hit on soft 17 or less, giving the player favorable odds.

With 12 against dealer's King (10-value), standing is optimal. Hitting has high bust risk (any card 10+ busts), while dealer likely has 10 or blackjack already. Doubling 12 is mathematically poor and unnecessary here.

With a pair of 8s totaling 16 against a dealer 10, splitting is the mathematically optimal play. A hard 16 versus a 10 is a losing position, but splitting 8s into two separate hands gives each an 8, allowing both to potentially reach 18 or better with reasonable draws. This significantly improves win equity compared to standing or hitting on 16.

I have a soft 19 (8+Ace) against dealer's 10. Soft 19 is a strong hand—standing is the optimal play here since hitting risks busting or at best improving marginally, while the dealer's 10 suggests they likely have 20 or 10+10=20.

Hand 1 has 18 against dealer's 10 upcard. While doubling is legal, standing on 18 is the correct basic strategy—doubling would risk 20 chips for marginal expected value when the dealer likely has 20. Hand 0 (19) is already complete and winning.

With a hard 15 against dealer's 4 (a weak upcard), standing is correct. The dealer busts frequently from 4, and hitting 15 risks busting myself with high probability (any card 7+ busts). Doubling here is mathematically inferior to standing.