Blackjack

Overview

Blackjack is the only major casino game where skill demonstrably changes the math. A player using basic strategy against typical Strip rules (dealer hits soft 17, double after split allowed, blackjack pays 3:2) faces a house edge of roughly 0.5%. Deviate from basic strategy and that number climbs fast — by 2-3% if you play "by feel," and as high as 4-5% if you take insurance, never double, and stand on 16 against a dealer 10. Our table here uses 1 deck with dealer hits soft 17, blackjack pays 3:2, and no insurance offered. We removed insurance because it's a sucker bet — the math is below.

How to play

Each hand starts with two cards to you and two to the dealer (one face down). Face cards count as 10, aces count as 1 or 11 — whichever helps you. A "natural" or "blackjack" is an Ace plus any 10-value card on the first two cards, and pays 3:2 (a $10 bet wins $15). You then choose to hit (take another card), stand (keep your total), double down (double your bet, take exactly one card, then auto-stand), or split (only if your two cards match — turns one hand into two with a matching second bet). Bust at 22+ and you lose immediately, regardless of what the dealer ends up with. The dealer reveals their hole card and hits until reaching 17 or higher. On a soft 17 (Ace + 6), our dealer hits — this is the worse rule for the player and adds about 0.22% to the house edge versus standing on all 17s.

Optimal strategy

Basic strategy is a fixed decision matrix derived from probability — it tells you the mathematically optimal play for every possible (your hand, dealer up-card) combination. The headline rules: always split aces and 8s; never split 5s or 10s; double 11 against any dealer card 2-10; double 10 against dealer 2-9; double 9 against dealer 3-6; stand on hard 17+; hit hard 8 or less; stand on soft 19+; hit soft 17 or less. The hard-15-against-10 spot is the worst place to be — you'll lose more than half these hands no matter what, but hitting loses slightly less than standing. Never take insurance — it's a side bet on whether the dealer has blackjack, which is really a bet that the next card is a 10. There are 16 ten-value cards out of 52, so the true probability is 16/49 ≈ 32.6%, but insurance pays 2:1 (implying the casino thinks the chance is 33.3%). The expected loss on insurance is about 5.9% of the side bet — among the worst on the table.

The math behind the house edge

The house edge of 0.5% means that over a long sample, a player betting $100 per hand using perfect basic strategy will lose, on average, $0.50 per hand. The standard deviation per hand is roughly $115, which is why short sessions can swing wildly in either direction even at perfect play. Card counters can move the edge in the player's favor (around +1% with a competent Hi-Lo count and proper bet ramp), which is why casinos shuffle aggressively, use multiple decks, and back-off counters. On our single-deck table, the theoretical edge against basic strategy is closer to 0.17%, but we shuffle every hand, eliminating any counting value. Bet sizing matters: at perfect strategy, the Kelly-criterion optimal bet is essentially zero (since edge is barely positive even for counters). For entertainment play, flat-bet 1% of your roll per hand to maximize session length.

Origin & history

Blackjack descends from the French game "Vingt-et-Un" (Twenty-One), popularized in the 18th century. The name "blackjack" comes from a U.S. promotional bonus offered around 1900 — 10:1 payout if the player got an Ace of Spades plus a black Jack (Jack of Clubs or Spades). The bonus is long gone but the name stuck. Edward Thorp's 1962 book "Beat the Dealer" launched card counting into the public consciousness — casinos responded by adding decks, cutting off the last quarter of the shoe, and inventing continuous shufflers. Today, single-deck blackjack with 3:2 payouts is rare; most casinos use 6 or 8 decks and many short-deal "blackjack" tables pay 6:5, which silently jacks the house edge from 0.5% to about 1.9%.

Payout table