How the game of blackjack derives a house percentage and what factors affect it
This was a post on another message board. I figured it may be informative to people here so here it is.......
In a card counting class I attended that was presented by Howard Grossman, he posed this question to the class; "If a player decided to play by the same rules as the dealer, namely hit sixteen or less and stand on seventeen and higher, why would the house have an advantage over this player?" Having read the answer in a book by John Scarne, I replied; "Because when the player busts, the dealer doesn’t go ahead and hit his hand to see if he will bust." This is called the "favorable bust percentage" and will occur approximately 8% of all hands. In other words, in 8% of all hands, the player busts and loses immediately, despite the fact that the dealer also busts or would bust, if he had completed the hand.
But the player that makes playing decisions identical to the dealer doesn’t suffer an 8% house percentage (HP). The reason being is that when the dealer gets blackjack, he only wins even-money but when the player gets blackjack, he wins 3 to 2. The 3 to 2 payoff for blackjack reduces the HP against the player by 2.5 % for a total of 5.5%. Some of the other game rules that affect HP are:
Dealer hits soft 17 + .2%
Re-split aces - .04%
Double down after split - .14%
Another factor that affects HP is the number of decks used:
Two decks + .32%
Four decks + .48%
Six decks + .54%
Eight decks + .58%
The last factor that affects HP is the playing decisions a player makes:
Proper standing on a stiff hand vs. a dealer upcard of 2-6 - 3.2%
Double down properly - 1.6%
Hitting soft hands properly - .3%
Proper splitting - .4%
This last factor is commonly referred to as "basic strategy" and quite simply is the mathematically proven correct way to decide hitting, double down and splitting decisions. If you add the total of all four of those percentages, you will discover that they total – 5.5%. So, in single deck game, correct basic strategy overcomes the house’s 5.5% HP and reduces it to zero and this is without the player even counting cards!
Of course, for many years, very few players played correct basic strategy and this is why single deck games continued to make money for the casinos. But with more and more educated players hitting the games, casinos decided they needed to make a rule change that would guarantee them a HP. This is why you now see casinos only paying 6 to 5 for a player’s blackjack. This rule change added 1.20% to the casino’s HP and is generally considered sufficient not only to overcome a player playing perfect basic strategy but also a card counter as well.
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