Blackjack Insights
Despite the vast amount of information on the Internet regarding Blackjack strategies and card-counting methods as depicted in the movie "21", I soon discovered some truths and realities. Here are my findings on Blackjack.
The dealer has overwhelming advantage over the player due to two main rules:
- A tie goes to the dealer as a win.
- A player's hand going bust (over 21) means the dealer wins even if the dealer's hand is bust.
In most casinos, a tie is a "push" which means the player does not lose the bet for the hand. Do avoid casinos and games where a tie goes to the dealer as a win.
If you search the Internet on the topic "Blackjack", you will find ample information on strategies and card-counting methods coupled with a healthy (or not) dose of theory, odds and probabilities. Most of the information I encountered did not answer a simple question in my mind. What is the winning percentage for dealer versus player?
Not being able to find sufficiently satisfactory information to answer my question, I wrote a relatively simple simulator to play Blackjack hands between a dealer and a player. The dealer strategy is very straight-forward - hit (take another card) if the total of the cards is below 17, otherwise stand.
In my simulator, I implemented two player strategies:
- A trivial strategy that mimics the dealer method of hit below 17, otherwise stand.
- A basic strategy as explained in this Wiki page.
I ran the simulator on over 1 billion hands to ensure randomness and statistical stability were given full accord. Here are the results.
Trivial Strategy
1,234,567,890 hands with 8 decks and 416 cards (trivial)
730,971,695 dealer wins (59.2087%)
503,596,195 player wins (40.7913%)
129,431,284 ties without which dealer wins 48.7248%
97,982,045 both bust without which dealer wins 51.2722%
eliminating ties and both bust, dealer wins 40.7882%
-40229431 net win/loss for bet > 1.0
player earnings -3.52445e+008 (net player wins -227375500)
execution time 860.591sec
Basic Strategy
1,234,567,890 hands with 8 decks and 416 cards (basic)
709,389,490 dealer wins (57.4605%)
525,178,400 player wins (42.5395%)
113,877,920 ties without which dealer wins 48.2364%
52,709,725 both bust without which dealer wins 53.1911%
eliminating ties and both bust, dealer wins 43.9669%
-31165527 net win/loss for bet > 1.0
player earnings -2.80829e+008 (net player wins -184211090)
execution time 870.465sec
As can be observed, the "overwhelming advantage" in numerical terms is ~60% dealer winning percentage versus ~40% player winning percentage. The basic strategy improves the player winning success but only by less than two percentage points.
The last couple of lines in the results for' win/loss and player earnings' reveal very important findings on card counting and applying it to advantage betting. Here is a reference page on "How to bet based on the True Count using the Hi-Lo system".
In my simulator, I implemented an advantage betting method based on the hi/lo card counting method. My aggressive betting system computes a fractional true-count from the integral running-count. If there is an advantage indicated by true-count >= 2.0, then I bet the true-count value. Otherwise my bet is 1.0 to represent the minimum bet.
In 'player earnings -2.80829e+008 (net player wins -184211090)', "net player wins" is from the constant bet of 1.0 on every hand while the "player earnings" is from my aggressive betting method described above. See sample-log which shows the win/loss for aggressive betting where I lose more than I win.
