Advanced Maths and Simulation

Effects of Rules on House Edge: A Table of Changes

A table of approximate house edge changes for common blackjack rule differences, with the assumptions behind them and why the figures vary between sources.

On this page
  1. Reading the table with the right expectations
  2. Approximate effects of individual rules
  3. A calculation you can check: the 6 to 5 payout
  4. Why the sizes differ so much
  5. Interactions and caveats
  6. Putting the numbers in context

Reading the table with the right expectations

Blackjack rules differ from table to table, and each difference nudges the house edge up or down. The rule effect values below are rounded, approximate effects of the kind commonly produced by simulation and exact calculation, quoted for a typical multi-deck game played with perfect basic strategy. They are not the edge for any particular casino, and they are not exact: sources that use slightly different baselines or methods can disagree by a few hundredths of a percentage point.

The baseline matters. Each change below is measured against a reasonable standard game, and the sign tells you the direction: a positive number increases the house edge, a negative one reduces it.

Approximate effects of individual rules

Rule change Approximate effect on house edge Direction
Natural pays 6 to 5 instead of 3 to 2 about 1.4 percentage points worse for player
Dealer hits soft 17 instead of standing about 0.2 points worse for player
Doubling after splitting not allowed about 0.1 points worse for player
Late surrender offered roughly 0.05 to 0.1 points better for player
Doubling restricted to totals of 9 to 11 a few tenths of a point worse for player
Resplitting aces not allowed a few hundredths of a point worse for player
Dealer takes no hole card (loses extra bets to a dealer natural) about 0.1 points worse for player
One deck instead of eight roughly half a point better for player

Treat these as orders of magnitude. The detailed values depend on the number of decks and on which other rules are in force, because rules interact.

A calculation you can check: the 6 to 5 payout

The largest entry deserves a worked check. A natural occurs when the first two cards are an ace and a ten-value card. With a very large number of decks, the probability is 2 x (4/13) x (1/13) = 8/169, which is about 0.0473, or 4.7 percent of hands.

Per one-unit bet, a 3 to 2 payout pays 1.5 units and a 6 to 5 payout pays 1.2 units, a difference of 0.3 units on each natural. Multiply: 0.0473 x 0.3 is about 0.0142, or roughly 1.4 percent of the initial bet. That matches the table entry. It is a rough figure, since naturals that tie with a dealer natural pay nothing either way. This is why natural payouts are the first line to check on any table.

Why the sizes differ so much

Rules matter in proportion to how often they come up and how much money is at stake each time.

  • The natural payout applies to roughly one hand in twenty-one and changes the win by 0.3 units, so it adds up quickly.
  • The soft seventeen rule matters on only a fraction of hands, but when it applies it gives the dealer a small extra chance to improve.
  • Late surrender is a choice the player uses rarely, on a few bad hands, so its benefit is modest.
  • Doubling and splitting restrictions bite only when those options would have been used.

Interactions and caveats

Adding up table entries gives a rough guide only. Several caveats apply:

  • Effects are not strictly additive. A rule’s value depends on the other rules and on the number of decks.
  • The numbers assume the player uses the correct strategy for that rule set. A player using a chart built for different rules will do worse, which is why strategy adjustments matter.
  • A published figure for a rule is an average over a long run. It does not predict a short session, where statistical variance is much larger than any of these differences.
  • Online and live tables sometimes bundle rule changes together, so a favourable-looking rule may sit beside an unfavourable one.

Putting the numbers in context

Adding the small differences shows why two tables with the same name can have meaningfully different costs. At 0.5 percent, a player betting 10 units a hand for 100 hands expects to lose around 5 units on average (100 hands x 10 units = 1,000 units wagered; 1,000 x 0.005 = 5). Under a game with 6 to 5 naturals, an extra 1.4 percent would add about 14 units of expected cost over the same play (1,000 units wagered x 0.014 = 14). These are illustrations of average cost, not predictions: the actual result will usually be far from the average.

Blackjack has a house edge under standard rules, and no rule set removes it for a typical player. Choose your spending limit in advance, and if gambling is causing problems, contact a local support service.

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