Blackjack advantage trainer — basic strategy, the Hi-Lo count, and the bankroll math behind winning.
Find your hand down the left edge, the dealer's upcard across the top. The cell where they meet is the mathematically correct play.
Example — "hard 13 vs dealer 7": your cards total 13 with no usable ace, and the dealer's face-up card is a 7. Read down to 13, across to 7 → the cell says Hit.
Hard hand — no ace, or an ace forced to count as 1. 10 + 3 = hard 13.
Soft hand — has an ace still worth 11, so the next card can't bust you. A + 4 = soft 15.
Pair — two cards of the same rank (8 + 8); you may split them into two hands.
Dealer upcard — the one card the dealer shows face-up; every decision is made against it.
Hit = take a card · Stand = take none · Double = double the bet + exactly one card · Split = break a pair into two hands.
Chart assumes 4+ decks, dealer stands on soft 17, double-after-split allowed — the standard shoe game.
Dealer 2–6 are weak ("bust cards"); 7 through A are strong. That one split explains most of the chart:
• Stiff hands (hard 12–16): stand against 2–6 and let the dealer bust; hit against 7–A, because standing on 15 vs a 10 just loses.
• Hard 17+ always stand · hard 8 or less always hit — you can't bust.
• Double 9, 10, 11 against weak dealer cards — press your edge when the dealer's in trouble.
• Always split A-A and 8-8. Never split 10-10 (that's a 20) or 5-5 (double it as a 10).
Edge for a sharp Hi-Lo counter is ~0.5–1.5%. Per-hand SD is ~1.15 flat, but a real betting spread pushes it to ~2–3 units. Defaults model a modest $5k roll spreading 1–12.
N₀ is the hands you must play before expected win equals one standard deviation — below it, variance dominates and results say nothing about skill.
Every card gets one value. Add it as the card hits the table — you never track suits or ranks, only the running total.
A shoe rich in tens and aces favors you — more blackjacks (paid 3:2), more dealer busts, more winning doubles. A high positive count means the deck is loaded in your favor. That, and only that, is your green light to bet big.
The running count alone is misleading. +6 with one deck left is a monster edge; +6 across six decks is nothing. Normalize it.
Estimate decks remaining by eyeballing the discard tray. True count is the real edge signal — every +1 of true count is worth roughly +0.5% to you. You cross into a player advantage around true +1.
This is where 100% of the money is made — spreading your bet with the true count. Play decisions barely move the needle; the bet ramp is the engine. Example 1-to-12 spread:
At or below the pivot you bet the table minimum (or leave). You only have real money out when the deck owes you. A "unit" should be ~1% of your bankroll or less — the ramp is illustrative, not gospel.
Perfect basic strategy is the prerequisite — counting only adds ~0.5–1.5% on top of it. These index plays capture most of the counting edge on decisions. Learn insurance and 16-v-10 first; they're worth the most.
| Hand | Dealer | Deviation | When |
|---|---|---|---|
| Insurance | A | Take it | TC ≥ +3 |
| 16 | 10 | Stand (else hit) | TC ≥ 0 |
| 15 | 10 | Stand (else hit) | TC ≥ +4 |
| 10,10 | 5 | Split (else stand) | TC ≥ +5 |
| 10,10 | 6 | Split (else stand) | TC ≥ +4 |
| 10 | 10 | Double (else hit) | TC ≥ +4 |
| 12 | 3 | Stand (else hit) | TC ≥ +2 |
| 12 | 2 | Stand (else hit) | TC ≥ +3 |
| 11 | A | Double (else hit) | TC ≥ +1 |
| 9 | 2 | Double (else hit) | TC ≥ +1 |
| 10 | A | Double (else hit) | TC ≥ +4 |
| 9 | 7 | Double (else hit) | TC ≥ +3 |
| 16 | 9 | Stand (else hit) | TC ≥ +5 |
| 13 | 2 | Stand (hit below) | TC ≥ −1 |
| 12 | 4 | Stand (hit below) | TC ≥ 0 |
| 12 | 5 | Stand (hit below) | TC ≥ −2 |
| 12 | 6 | Stand (hit below) | TC ≥ −1 |
| 13 | 3 | Stand (hit below) | TC ≥ −2 |
The full Illustrious 18 (Schlesinger), 6-deck S17. Read every row the same way: take the listed action when the true count is at or above the index, otherwise the fallback. The bottom five are "stands you abandon into hits" once the deck turns cold. The trainer grades these live in Play a Shoe, and the drill below quizzes them.
And the Fab 4 — the count-based surrenders (when late surrender is on):
| Hand | Dealer | Deviation | When |
|---|---|---|---|
| 15 | 10 | Surrender | TC ≥ 0 |
| 15 | A | Surrender | TC ≥ +1 |
| 15 | 9 | Surrender | TC ≥ +2 |
| 14 | 10 | Surrender | TC ≥ +3 |
The honest edge. A sharp counter runs a ~0.5–1.5% advantage — real, but thin, with brutal variance. You can be perfect for 40 hours and still be down. It takes tens of thousands of hands for skill to outrun the swings, so bankroll and bet-sizing (risk of ruin) matter more than any single decision. Counting is legal — it's just memory and mental math — but casinos can and will bar you: watch for shallow deck penetration, continuous shuffle machines (uncountable), and a pit boss "backing you off." Practice the arithmetic here until it's automatic; that's the part you actually control.