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Blackjack: basic strategy and the house edge

Played with the strategy below, blackjack paying 3 to 2 with a dealer who stands on soft 17 leaves the casino 0.57% of each stake. The same player who simply stops at 17 and never doubles or splits gives it 5.67%. The chart is computed by our program from the rules, not copied.

Basic strategy chart

Rules: the dealer stands on soft 17 and peeks for blackjack, you may double on any two cards and after a split, split once, and split aces take one card each. Find your hand on the left and the dealer's up-card at the top.

S Stand · H Hit · D Double · P Split · Columns: the dealer’s up-card

Hard totals
Your hand2345678910A
5HHHHHHHHHH
6HHHHHHHHHH
7HHHHHHHHHH
8HHHHHHHHHH
9HDDDDHHHHH
10DDDDDDDDHH
11DDDDDDDDDH
12HHSSSHHHHH
13SSSSSHHHHH
14SSSSSHHHHH
15SSSSSHHHHH
16SSSSSHHHHH
17SSSSSSSSSS
18SSSSSSSSSS
19SSSSSSSSSS
Soft totals (with an ace counted as 11)
Your hand2345678910A
A,2HHHHDHHHHH
A,3HHHDDHHHHH
A,4HHHDDHHHHH
A,5HHDDDHHHHH
A,6HDDDDHHHHH
A,7SDDDDSSHHH
A,8SSSSSSSSSS
A,9SSSSSSSSSS
Pairs
Your hand2345678910A
A,APPPPPPPPPP
10,10SSSSSSSSSS
9,9PPPPPSPPSS
8,8PPPPPPPPPP
7,7PPPPPPHHHH
6,6PPPPPHHHHH
5,5DDDDDDDDHH
4,4HHHPPHHHHH
3,3PPPPPPHHHH
2,2PPPPPPHHHH

What the rules cost

Infinite-deck model (the standard approximation): dealer peeks for blackjack, double on any two cards, one split, split aces take one card each, no surrender.
Rules, with basic strategyHouse edgeChange against the first line
Blackjack pays 3 to 2, dealer stands on soft 17, double after split allowed0.57%—
Dealer hits soft 170.79%+0.22%
No double after a split0.69%+0.12%
Blackjack pays 6 to 51.92%+1.35%

A blackjack paying 6 to 5 instead of 3 to 2 is the most expensive rule on the list: it adds 1.35% to the house edge. A dealer who hits soft 17 adds 0.22%.

How often the dealer busts

Chance the dealer finishes over 21 when standing on all 17s, before any peek for blackjack.
Dealer's up-cardDealer busts
235.4%
337.4%
439.4%
541.6%
642.3%
726.2%
824.5%
922.8%
1021.2%
A11.5%

The dealer busts most often with a 5 or 6 showing and least often with an ace, which is why the chart stands on hard 13 to 16 against a 2 to 6, and on 12 against a 4 to 6, and keeps drawing against high cards.

Questions

Does basic strategy beat blackjack?

No. It is the way of playing that loses the least; the casino keeps its edge of 0.57% under these rules. Card counting can change the odds but is outside the scope of this site, and casinos may refuse such players.

How often am I dealt a blackjack?

About 4.73% of hands, roughly once every twenty-one hands. That is why the payout for a blackjack matters so much.

Why is the model an infinite deck?

With an infinite deck every card has the same chance on every draw, which makes the calculation exact and the chart valid for games with many decks. Games with one or two decks differ slightly.

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