Blackjack

How it works

You start with a $100 bankroll and bet $5, $10, $20, or $50 per hand from a real 4-deck shoe (208 cards) that depletes across hands, only reshuffling when it runs low. Rules as implemented: dealer stands on all 17s (S17), blackjack pays 3:2, you can Hit, Stand, or Double Down (first decision only, doubling your wager for exactly one more card). There is no split and no surrender - strategy that relies on either does not apply here.

During your turn the game shows two exact numbers computed from the actual remaining shoe: the probability your next card busts you (it enumerates every card left and checks the resulting hand, so soft hands correctly read 0%) and the probability the dealer eventually busts given the visible upcard, computed by recursion over the S17 drawing rule without replacement.

On each fresh two-card hand you must answer a Hi-Lo counting check (2-6 count +1, 7-9 count 0, 10/J/Q/K/A count -1) before a pit-boss timer runs out. The timer starts at 70 seconds and tightens by 5 seconds per correct answer down to a 15-second floor. Time out or miss the count and you draw a warning - three warnings and the house bars you, ending the run.

How scoring works

Payouts are total money returned, per the code: a natural blackjack returns 2.5x your wager (a $10 bet returns $25, profit $15). A regular win or a dealer bust returns 2x ($10 returns $20). A push returns exactly your wager. A bust or dealer win returns $0. Doubling down doubles the wager at stake before settlement.

Your counting performance moves an explicit, deliberately exaggerated edge: it opens at -2% (the house's advantage over a non-counter) and shifts by exactly +2% or -2% per correct or wrong answer. The implied win chance on the next hand is 50 plus the edge, clamped between 15% and 85%, and the shoe is probabilistically reordered in whoever's favor holds the edge. Real Hi-Lo is worth about 1% - the game inflates it so you can feel it inside one session.

Use the exact bust number, not a rule of thumb

For a hard 16, every card from 6 through king busts you - 8 of the 13 ranks. In an untouched 4-deck shoe that is 128 of 208 cards, about 61.5%, and the in-game readout adjusts that exactly for every card already dealt. For a hard 12 only the four 10-value ranks (10/J/Q/K) bust you - 64 of 208, about 30.8% - since an ace simply counts as 1. Soft hands read exactly 0%: the ace demotes from 11 to 1 and absorbs any card.

Compare that number to the dealer-bust readout. Standing wins only if the dealer busts, so standing on a stiff hand (12-16) is a bet that the dealer-bust probability beats your alternatives. Against a 4, 5, or 6 upcard the S17 recursion produces its highest bust numbers - that is the shoe-exact version of 'stand against a bust card'. Against a 9, 10, or ace it produces its lowest, and taking a roughly 60% bust risk on 16 can still beat standing into a hand that rarely busts.

Double down only when one card is enough

Doubling deals exactly one card and then forces the dealer's turn - you give up the right to hit again in exchange for doubling the stake. That trade is only good when a one-card hand is strong: totals of 10 or 11, where no card can bust you (bust readout 0%) and any 10-value card makes 20 or 21. Doubling a stiff total doubles your money behind a hand that busts most of the time.

The payoff math: a $10 double that wins returns $40 on $20 staked. Since a win pays 1:1, doubling raises EV exactly when your win probability on the one-card line exceeds what the flexible hit/stand line achieves - which is why it is reserved for the totals above.

Protect the count - it is worth 2% a question

Each counting answer moves your edge by exactly 2 percentage points, symmetric in both directions, starting from -2%. Two correct answers put you at +2%; two misses put you at -6%. The Hi-Lo tally is trivial per card (2-6 are +1, 7-9 are 0, tens and aces are -1) - the difficulty is purely the tightening clock, which drops from 70 seconds toward the 15-second floor precisely because you keep being right.

Warnings are tracked separately from the edge, and three of them end the run no matter how large your bankroll is. When the timer is nearly out, submitting a fast honest attempt beats letting it expire - both a miss and a timeout cost a warning, but only an unanswered check forfeits the chance at the +2%.

A worked example

You bet $10. You are dealt 10-6 (hard 16); the dealer shows a 9.

Bust check: the ranks that bust 16 are 6, 7, 8, 9, 10, J, Q, K. Fresh 4-deck shoe: 8 ranks x 16 copies = 128 of 208 cards, roughly 61.5% before removing the dealt cards; the HUD shows the exact fraction for the live shoe.

Dealer-bust check: a 9 upcard reaches 17+ without busting most of the time under S17, so the recursion reports one of its lowest bust numbers. Standing means you win only in that minority of dealer busts.

You hit and draw a 4 - hard 20. Now only an ace busts you. You stand; the dealer flips 9-7 for 16, must hit under S17, and draws a 10 for 26 - dealer bust. Payout: 2 x $10 = $20 returned, +$10 profit.

Counting side: your visible cards were 10 (-1), 6 (+1), dealer 9 (0), your 4 (+1), then the revealed 7 (0) and 10 (-1). Running count 0. Answering the check correctly moved your edge from -2% to 0% for the next deal.

Common mistakes

• Treating a soft total like a hard one. A,6 can never bust on one card - the game literally displays 0% - so standing on soft 17 surrenders free improvement.

• Doubling on stiff totals. Doubling 12-16 doubles the stake behind a hand that busts the majority of the time; the play exists for 10 and 11.

• Standing on 16 against a 9, 10, or ace because 61% bust risk feels scary. Compare it to the dealer-bust readout - standing into a strong upcard loses more often than the hit does.

• Letting the heat timer expire instead of answering. A timeout costs a warning AND forfeits the possible +2% edge; a fast attempt risks only the same warning.

• Playing basic-strategy lines that do not exist here. There is no split and no surrender in this implementation - pairs are just their hard total.

Why interviews test this

Blackjack is the canonical conditional-probability-without-replacement setting, which is exactly why it shows up in quant interviews: every card seen changes the distribution of every card to come. The bust readout here is the honest version of the interview question 'what is the probability the next card busts you, given what you have seen?' - an enumeration over a finite depleting population, not an independent draw.

Card counting is also the cleanest toy model of edge detection: a tiny persistent statistical edge (about 1% in real Hi-Lo), harvested by bet timing under constraints. Interviewers use it to test whether a candidate separates the size of an edge from the variance around it - and whether they notice that most hands, like most trades, are close to fair either way.