Blackjack Win Percentage
Card Counting for the Casino Executive by Bill Zender
Let's suggest, that in our attempt to determine some H/A value for Twenty-one, we start with the understanding that one hand will be dealt from a freshly shuffled deck (single) and that the player will use the exact same strategy that the house uses. In this case, the player will "mimic" the house, hitting all 16s and standing on all 17s, unable to split or double down.
What if the Player "mimics" the dealer?
* The Dealer will bust 28% of the time.
Mathematically, it can be determined that the dealer will bust out approximately 28% of the time. Of course, if the player "mimics" the dealer he will also bust out 28% of the time. But the most important fact regarding why the game of Twenty-one wins for the house is:
* The Player will bust before the dealer 28% of 28% or about 8% of the time.
This is the reason why the casino has an edge over the player because if the players bust out first, the dealer's hand does not have any effect on the final outcome. Does this mean that the house has an 8% H/A over the "mimic" player? We have to add one more ingredient:
* The player gets a bonus for Blackjacks.
The Blackjack bonus, which occurs approximately once every 21 hands, pays three units for every two units wagered, altering the H/A by about 2.5%. This leads us to our final result of 5.5%.
* A "mimic" player's house advantage is 5.5%.
But how many of you have seen someone who actually mimics the dealer? Not very many. So, this leaves room for speculation that a "truer" house advantage in Twentyone could be more or less than our calculations.
The next question we must ask is: "Can a player improve the "mimic" strategy and lessen the house advantage?" Let's examine four different changes the player can make and note the gains made over the "mimic" player.
What effect will the player have by changing his strategy?
Proper standing with a stiff vs stiff
(Player holding a total of 12-16 vs the upcard of 2-6) 3.2% gain
Double Down properly 1.6% gain
Hitting soft hands properly .3% gain
Splitting proper combinations .4% gain
5.5% gain overall
By using a proper or BASIC STRATEGY, the player can gain 5.5% over the "mimic" strategy and actually reduce the houses advantage to nothing. How can this be? These calculations indicate that the correct house advantage in Twenty-one is zero. If this is true, how have the casinos been making money on Twenty-one all this time? First, not many players know the correct strategies for playing Twenty-one. Below is a list of approximate house advantages for the different styles of players:
Blackjack players' parameters - The worst and the best
Worst 15% H/A
Mimic 5.5% H/A
Average 1.4% H/A
Basic strategy Even (0% H/A)
The "worst" player is arrived at by Peter Griffin in his book, The Theory of Blackjack. Griffin states that the "world's worst player..." by violating a list of rules including always insuring, standing on all stiffs against the dealer showing a high card, hitting on all stiffs against the dealer showing a small card, never doubling down, splitting incorrectly and failing to hit any soft hand, "...seems unlikely that any but the deliberately destructive could give the house more than a 15% edge."
The "average" player has been determined by Griffin in his presentation at the 7th Gambling Conference held in Reno, Nevada, August 1987. His paper, Mathematical Expectation for the Public's Play in Casino Blackjack concluded that the average player's H/A is 1.41%.
Griffin actually concluded the average player's disadvantage as being 1.41% greater than the basic strategy edge.
