Odds & maths

A great deal. In a six-deck game with the dealer standing on soft 17, double after split allowed and 3:2 naturals, perfect basic strategy leaves a house edge of roughly 0.4 to 0.5% of the initial bet, so a player betting £10 a hand expects to lose about 5p per hand on average. Casual players who mimic the dealer or play by feel typically give up several times that amount; published estimates put the untrained edge at around 2% or more. The difference is entirely in the decisions, not the bets. Read more →

Ordinary basic strategy is total-dependent: it looks only at your total and the dealer's upcard. Composition-dependent strategy also considers which cards make up the total. The classic example is hard 16 against a 10: with ten–six you hit, but with three or more cards (say 4–5–7) you stand, because the small cards you hold are the ones you would want to draw. These exceptions are worth only a few hundredths of a per cent in a six-deck game, so learn the basic chart first; this site's trainer teaches the total-dependent version. Read more →

It depends entirely on the rules and on how well you play. In a six-deck game where the dealer stands on soft 17, doubling after splits is allowed, there is no surrender and naturals pay 3:2, perfect basic strategy leaves an edge of roughly 0.4 to 0.5% of the initial bet. A 6:5 payout adds about 1.4 points, hitting soft 17 adds about 0.2, and sloppy play adds more still. The edge is expressed per initial bet, so doubles and splits are not counted in the denominator. Read more →

Counting the thirteen ranks as equally likely: hard 12 busts on 4 of 13 draws (31%), 13 on 5 (38%), 14 on 6 (46%), 15 on 7 (54%) and 16 on 8 (62%). Hard 11 or less cannot bust on one card. These are the figures for a full-composition shoe; the cards already on the table shift them slightly. Soft hands cannot bust on a single draw at all, because the ace reverts to counting one. Read more →

About 28% of all hands overall, but it varies sharply with the upcard. Published figures for a dealer standing on soft 17 are roughly 35% from a 2, 37% from a 3, 40% from a 4, 42% from a 5 and 6, then 26% from a 7, 24% from an 8, 23% from a 9, 23% from a 10 and 17% from an ace once a natural has been ruled out. That cliff between 6 and 7 is why basic strategy stands on stiff hands against 2 to 6 and hits them against 7 and up. Read more →

In a six-deck shoe there are 24 aces and 96 ten-value cards among 312 cards. The number of two-card combinations is 312 × 311 ÷ 2 = 48,516, of which 24 × 96 = 2,304 are naturals, so the probability is 2,304 ÷ 48,516 = 4.75%, about one hand in 21. For a single deck it is 4 × 16 ÷ 1,326 = 4.83%. The dealer has the same chance, which is why two naturals push roughly once in every 440 hands. Read more →

Among the common table games, yes, provided you play basic strategy at a 3:2 table: a house edge of around half a per cent is lower than baccarat's banker bet (about 1.06%), the craps pass line (about 1.41%) and far lower than most slot machines. The qualification matters. A 6:5 blackjack table played by feel can have an edge of 3% or more, worse than several alternatives. The odds are good only because of the decisions you make, which is unusual among casino games. Read more →

Expected value (EV) is the average result of a decision if it were repeated an enormous number of times, expressed as a fraction of the bet. Hard 16 against a 10 has an EV of about −0.54 if you stand and about −0.54 if you hit under six-deck S17 rules, with hitting a hair better; both lose, but basic strategy picks the one that loses least. EV says nothing about the next hand, only about the long-run average, and a winning outcome never proves a decision was correct. Read more →