House Edge in Blackjack

The following table shows some calculations concerning the house edge when basic strategy is used. They describe the best possible situation for the player when basic strategy is applied perfectly. These calculations were extracted from computer simulations of millions of hands. The starting point is the zero edge game, which is one deck, dealer stands on soft 17, no double downs on splits, no re-splits of aces and no surrender.

Certain rule variations cost a bit of margin, while others increase it. A six-deck game with surrender and doubles after splits (as considered in the basic strategy table in the previous chapter) is approximately 0.2% in favor of the player when the player makes no mistakes. This means that the expectation of play, at 100 hands per hour with a uniform $10 bet would be about two dollars. (Of course, the standard error of that expectation is quite high, so that random variation from the expectation could run into many hundreds of dollars, both positive and negative!). This expectation, by the way, takes into account the productivity of double downs and splitting, even though they are additional bets, and it assumes no side bets, like insurance.

A casino will favor any rule that increases its edge, but sometimes it will be pushed by the competition for customers to adopt rules more popular with the players. The average blackjack player so mishandles even basic strategy that the house makes a ton of money even if the theoretical edge slightly favors the player.

Compare these margin calculations with HiLo, the most prevalent counting technique. Using the edge for the four to six deck game from the table above, basic strategy with uniform $10 bets would lose at the rate of $5 per 100 hand (an hour, more or less). Using HiLo with bet variation and strategy variation, the outcome would be about plus $5.35 per hour, a swing of over $10. Of the $10.35 “won” by counting in this manner, approximately $9 comes from knowing how to vary the bets in accordance with the count. The remaining $1.35 comes from strategy modifications. Of these, the main contributor is selectivity in buying insurance against a dealer natural ($0.65), and selectively standing on hard 15 or 16 against a 10 (in lieu of a hit). The remaining strategy modifications cumulatively add very little to the plus column.

Because surrender adds so much to the player’s edge, it can also be relied upon to increase winnings when applied to card counting. As an approximation, surrender should add an additional 65% to the benefit of card counting. Thus, in the example, using card counting when surrender is offered would boost the difference over basic strategy from $10.35 to a little over $17!

Recall that not all of this money is “net.” It is not in comparison to zero, but in comparison with the outcome of basic strategy, which, in this example started out with a negative expectation in the -0.5% neighborhood. Card counting will not make a player rich very quickly with $10 average bets, but at least it will keep the money flowing in the right direction.