Blackjack table

With 13 against dealer's 3 (weak upcard), standing is optimal. Basic strategy dictates standing on hard 13 when dealer shows 3, as the dealer is likely to bust and hitting risks busting myself.

Splitting 8s against dealer's 6 (weak upcard) is optimal basic strategy. This converts a stiff 16 into two separate chances to reach 18, leveraging the dealer's bust likelihood.

Hand totals 17 against dealer's 6 (a weak upcard). Standing is optimal; hitting risks busting while the dealer has a high probability of busting on 16 or less.

Hand 1 (17) is already complete. On hand 2 (13 vs dealer's 6), doubling is optimal: the dealer's weak upcard makes this a favorable spot, and doubling maximizes expected value against a likely dealer bust.

With a soft 18 (Ace-7) against dealer's 5 (a weak upcard), standing is optimal. Dealer busts roughly 42% of the time with a 5 showing, and hitting risks busting or improving to a worse hand while giving up a strong total.

With a hard 20 against the dealer's 6 (a weak upcard), standing is optimal. The dealer is likely to bust, and hitting risks busting our strong hand.

I have a hard 20 against the dealer's Ace. Standing is optimal here because hitting risks busting, and 20 is a very strong hand that wins against most dealer outcomes.

With a hard 13 against dealer's 3 (bust card), standing is optimal. The dealer busts roughly 40% of the time with a 3 showing, and hitting 13 risks busting immediately (any card 9+ busts). Basic strategy favors standing in this spot.

With a hard 11 against dealer's Queen (10-value), doubling down is the mathematically optimal play. The probability of drawing a 10-value card (16 in a 6-deck shoe) to make 21 is high, and even non-10 cards often create a strong hand that puts pressure on the dealer's stiff position.

With 14 against dealer's Jack (10-value card), hitting risks busting while standing gives a reasonable chance the dealer busts or we win. Basic strategy recommends standing on hard 14 versus 10.

I have a hard 20 (Td+Qc) against dealer's 10 upcard. This is an excellent hand that beats most dealer outcomes. Standing is the correct basic strategy play here, as hitting risks busting and doubling would waste chips on an already strong hand.

With a hard 15 against dealer's King (10-value), hitting risks busting. Standing gives the best chance—the dealer must hit to 17+ and could bust, while hitting my 15 gives only a ~58% bust probability but minimal improvement to winning hands.

With a hard 6 against dealer's 2, hitting is the mathematically optimal play. A 2 is a weak dealer upcard, but my hand is too weak to stand. Doubling risks too much chips for this weak initial total. I need to improve my hand.

With a hard 10 against dealer's 2 (weak upcard), hitting is the mathematically correct play. A hard 10 is rarely a good time to stand, and the dealer's 2 means hitting has positive expected value to improve the hand.

With a hard 20 against dealer's 2 (weak upcard), standing is optimal. The hand is already very strong and hitting risks busting with only small probability of improvement.

With a soft 15 (Ace-4) against the dealer's weak 3, doubling down is optimal. The Ace gives flexibility, and the dealer's bust probability is high, making this a +EV play.

With a soft 16 (Ace-5) against dealer's Jack, standing is optimal. Hitting risks busting or reaching 17-18 which are weak against a 10-value card, while the soft hand's flexibility is best preserved by not drawing.

With a soft 19 (Ace-8), I have a strong hand that beats the dealer's 10-value upcard in most scenarios. Standing is optimal because hitting risks busting or only marginally improving, while doubling down is unnecessary given the hand's strength.

With 12 against dealer's 10-value Jack, hitting is standard basic strategy. Busting risk is acceptable (4 cards improve the hand) compared to standing on a weak total against a strong dealer upcard.

With a hard 14 against dealer's Jack (10-value), hitting is the correct basic strategy play. Standing on 14 loses to most dealer outcomes, while hitting gives a chance to improve to 17+ or bust less frequently than the dealer will.

With a hard 19 against dealer's 10-value Jack, standing is the correct play. The dealer's upcard is strong but my 19 is likely to win or tie, and hitting risks busting or receiving a card that improves my hand only marginally (only an Ace helps).

With a soft 16 (Ace-5) against dealer's Queen upcard, standing is optimal. The dealer likely has 10 or blackjack, and hitting risks busting while doubling exposes additional chips with unfavorable odds.

With a hard 17 against dealer's 7, standing is the optimal play. Dealer's 7 is a moderate threat but hitting risks busting (any card 5 or higher) while 17 is likely to win or push.

With a hard 12 against dealer's 4 (a bust card), standing is optimal. The dealer busts roughly 42% of the time from a 4 upcard, while hitting risks busting my hand immediately with a high probability.