Interactive blackjack strategy and bust probability chart
Tap a card to choose your hand and the dealer’s upcard, or randomize a new combination. Compare standing, hitting, doubling, splitting and hitting until any total from 12 through 21. Each result separates player wins, dealer wins, pushes and player busts. Tap a percentage to inspect its explanation.
Why does a dealer six bust so often?
A dealer must draw until at least 17. A six therefore often requires several cards, creating many paths past 21. The probability changes with soft-17 rules. Open the dealer explanation and follow every next-card branch to see how made hands and busts add up.
Which rules change the advice?
Soft 17, surrender, blackjack payouts and split permissions change the modeled expected return. Free Bet includes free doubles and splits, while dealer 22 pushes. Double Down Madness begins with one player card and permits repeat doubling. Casino paytables vary; match the actual table’s settings. No claim is made that a preset reproduces every El Cortez table.
Transparent mathematical assumptions
Blackjack uses recursive enumeration with independent infinite-deck card probabilities, not finite-shoe removal. The dealer has checked and does not have blackjack. Recommendations maximize net expected return among modeled actions, not the chance of a win. Split hands use at most one resplit per initial branch (four hands total), and displayed split outcome percentages describe the first resulting hand. The model excludes insurance, side bets, table limits and card counting. Madness assumes the displayed hand has a one-unit current wager; multiply returns by your current stake. Percentages are rounded.
Rules references: Nevada Double Down Madness rules, Massachusetts Free Bet Blackjack rules. This is an educational probability model; no strategy guarantees a win.