Blackjack trainer

EV (expected value) is the average result of a play, per unit bet, if you made it many times from exactly this spot. +0.20 means you win 20 cents per dollar on average; −0.50 means you lose 50 cents. Surrender is always −0.50 because you hand back half the bet.

Best play is the highest EV, even when every option is negative. Hard 15 against a ten is a losing hand whatever you do; hitting (about −0.50) and surrendering (−0.50) lose less than standing (about −0.54). You are not choosing how to win, you are choosing how to lose least.

The margin between the best and second-best play is what a mistake costs. 0.30 is expensive; 0.01 is a coin flip, and at a real table either choice is fine. Big margins are the ones to memorize.

Double and split are shown per unit of the original bet, but you put more money in, so their EV can go past ±1. Doubling at +0.58 versus hitting at +0.29 means the extra bet is worth making.

Dealer blackjack. When the dealer peeks, the values assume the dealer does not have blackjack, because if they do the hand ends before you decide anything.

Win / push / lose in the feedback are the chances of each result for the play you made and for the best play. Two plays can have similar EV with very different shapes: doubling wins less often than hitting but pays double when it does.

Bet sizing: unit and ramp. Two separate numbers. The unit comes from the bankroll: the Kelly anchor is bet fraction = edge \u00f7 variance, and blackjack's variance is about 1.3 per hand (swing \u00b11.14 per unit), so full Kelly is bankroll \u00d7 edge \u00f7 1.3. Full Kelly loses the whole bankroll about 13% of the time, so the practical rule is half Kelly or less: a unit of about bankroll \u00f7 1000 for a 1-to-12 spread (equivalently, a bankroll of 100\u00d7 your top bet); bankroll \u00f7 500 is aggressive, with a 10 to 15% risk of ruin. A 10,000 roll supports a 10 unit topping out near 120. The ramp comes from the count: off the top the house has about 0.5% (6 decks, S17, DAS, late surrender) and each true count point returns about 0.5%, so break-even is near +1: bet 1 unit at +1 or below, 2 at +2, 4 at +3, 6 at +4, 8 at +5, 10 to 12 from +6. That ladder is roughly half Kelly throughout (at +3 with a 10,000 roll: 0.01 \u00f7 1.3 \u00d7 10,000 = 77 full Kelly, 38 half, about 4 units of 10). What limits it: penetration (a 1-to-12 spread at 50% is worth far less than 1-to-8 at 80%; below about 65% it is close to break-even), the table minimum (if it is above bankroll \u00f7 1000 the ramp over-bets at the bottom), and attention (spreading 1-to-12 gets noticed; leaving at low counts or 1-to-6 across two hands draws less for similar value). A good spread with decent penetration is worth about 0.5 to 1% overall, and over 1,000 hands one standard deviation is about 36 units against an expected win of 6 to 10, so long losing stretches are normal.

What "the cards still unseen" means. The engine knows how many of each rank are left in the shoe (four aces, six sixes, and so on) and enumerates every way the hand can finish from exactly that mixture. It is not Hi-Lo or KO: those compress the same information into one number so a person can keep it in their head. The counting tools here are for practising that skill; the odds on the table are always the exact figures.

Chart versus this shoe. The chart is computed from a fresh shoe and is what basic strategy means. The box on the table uses only the cards not yet seen. They disagree only on close calls, and the difference is the card count doing its work.

Dealer strength. The dealer has no choices, so his upcard tells you most of what will happen. With a 2 to 6 he usually holds a stiff total and must draw, and a third of the deck busts it: a 5 or 6 busts about 42% of the time, a 4 39%, a 2 or 3 only 35 to 37% because it takes more cards to get stuck. That grading is why doubles and splits reach furthest against 5 and 6 and why 12 hits against a 2 or 3 but stands against 4 to 6. From 7 up he mostly makes upcard-plus-ten (7 makes 17, ten makes 20) and busts only about a quarter of the time, so your stiff hands must draw and your 17 to 19 are only as good as the total he is likely to make. The ace busts least (17%) but spreads its results from 17 to 20, which is why 11 still doubles and soft 18 hits against it. The table under the chart has the exact figures for your rules.

House edge. Playing the chart perfectly at these rules loses roughly half a cent per dollar over time; "Compute house edge" in Table rules gives the exact figure and what each rule change costs. Every mistake adds to that; "EV left on table" is the sum of those costs in dollars for this session.

Risk of ruin in the scoreboard is the chance of losing the whole bankroll within the chosen number of hands at a flat bet, from the edge and the hand-to-hand swing of about 1.15 bets. It is an approximation that ignores doubling and splitting, which make the real swing a little larger.

Swing. EV is the average; the swing (standard deviation, in bets) and the win and lose chances describe the shape around it. Turn on "Swing and win chance per action" in the menu to see them for every play. Two plays with the same EV can feel very different, and a play with more upside usually costs expectation: splitting tens against a 6 gives up about 0.14 bets of EV, roughly doubles the swing, and wins the round less often (45% against 80%), because half the time one of the two hands loses. Over many rounds only the EV survives; the swing is the price of excitement, and the app tells you what it costs.

Excitement plays. A deviation is an excitement play when its swing is at least twice the best play's (for example a double, swing about \u00b11.9, where the chart hits, swing about \u00b10.9) and it costs no more than 0.05 of a bet in expectation. The verdict names the swings and, when there is one, the shot at a result the best play cannot give. The feedback names the upside, the matching downside and the price, and Progress counts it as a "thrill": a variance preference with a known cost, not a knowledge gap. Above 0.05 the same deviation is a mistake and is reported as one, with the note that the upside does not pay for it. The calmer side of a close call is tagged a safe play.

Card counting. The full explanation (Hi-Lo and KO, with the true count and what the number is for) is in the Count panel under "How counting works"; turn the count on in the settings menu to see it. In short: Hi-Lo adds 1 for each 2 to 6 seen and subtracts 1 for each ten or ace, so a positive count means the cards still to come are richer in tens and aces than a fresh shoe. That helps you more than the dealer: naturals pay 3 to 2 while the dealer's pay even, doubles and stands on stiff hands do better when the next card is likely a ten, and the dealer busts more often. The true count (running count per deck still unseen) says how much: each point is worth about half a percent of edge, so a flat-betting basic strategy player is behind at +1 and ahead at +2, which is why counters raise their bets. The count does not change the cards; it changes your estimate of what is left. The engine already knows exactly what is left, so with the count on the hand box shows the fresh-shoe answer next to the live one; the difference is the count's effect on that hand. The Count panel lists the plays that switch with the count (the Illustrious 18 and the Fab 4 surrenders) and which are in force now.

Account. Optional. Anonymous play keeps everything in this browser. Signing in (nickname and password, nothing else) stores your stats, mistake list and accuracy map on the server, loads them on any device, and lets you post to the scoreboard. Visitor counts are kept anonymously per day by a first-party cookie; no addresses are stored.

Links. The page takes parameters: ?mode=play|drill|flash|test opens in that mode; for flash cards add &set=hard|soft|pair|swings|mistakes and &count=1; ?hand=88&up=6 makes that the first hand, at the table or as the first flash card. "Practice this" in a cell's bubble builds such a link.