Casino Gambling, Expected Value and Blackjack Strategy
January 30th, 2008 by Andrew Chen
I was kind of addicted to gamble before and I think the only way to treat it is to understand how casino make money on gamble.
I was addicted to gamble the first time when I experienced Las Vegas. That was the first year when I came over to the
I grew up in a very rigid education system in China so I was very much disciplined and I never gamble before. The first time when I put my 10 bucks on the gambling table my heart was almost popping out. That was exciting! I remember I bought 50 bucks with me and I won $50 bucks. That was my one and only free trip to Las Vegas.
I was caught by the idea of how easy money can be made in gamble. And there after I went to Las Vegas with friends once a short while. I lost money very time. Sometimes I won at the gambling table but I lost when I counted gas, room and board expenses in.
I didn’t have much money to lose as a student so my addiction to gamble was a small case in terms of financial. My addiction to gamble was remained in my mind and I was addicted in a way that I didn’t believe that I can not fine a way to beat the dealer. More or less I treated my trips to Las Vegas gambling experiments. My addiction was subsided or cued only after I read a book that was written by a professor, a Ph.D. in applied mathematics. I couldn’t find the book now and I didn’t remember the author’s name. He was banned from playing in major casinos because he won a lot of money before.
The book was mean to teach people how to win in Casino with the education of statistics and the training of card counting. With some statistical knowledge I acquired in college I was able to understand the book well. However at same time when I was convinced that I could beat the dealer I was also convinced that the “Expected Value” of a formal career was higher (if not a lot higher) than a professional gambler.
What is “Expected Values”? That is where the secret of gambling lies. The “Expected Value” of a game dictates whether you can win or lose money over the long term. It tells the average payout of a game. Usually all the games in casino are designed in a way that the average payout to player is negative. That is the “Expected Value” of a game to player is negative. Take the coin tossing game as an example the probabilities of hitting head or tail are both 50 percent. It doesn’t matter which side you bet on the chance you win is 50%. The chance you lose is also 50%. So the Expected Values is calculated as
Zero is the average payout of a coin tossing game. If you have money to keep betting on a coin tossing game, over the long term you will find you don’t lose or win much money. That is the reason why Casino doesn’t have coin tossing game because Casino can not make any money off the game over the long term.
Take roulette as an example, the wheel is equally divided into 38 pockets, 18 reds, 18 blacks and 2 greens. The probability that the ball drop on any of those pockets is
As you know it doesn’t matter whether you bet on red or black if the number comes out to be green you will lose. So dealer has 2 x 2.6315% = 5.2630% more chance to win. Your chance (or probability) of wining by betting on red or black is
Your chance of losing by betting on red or black is
The Expected Value of betting on red or black is
It is going to be a negative number, which means that you will lose money over the long term for sure. The more you play the more you lose.
How about we bet on a green then? The chance to hit a green is 2.6315% and the payout is 36 times the bet. But the chance you lose is (1-2.6315%) = 97.3685%. The Expected Value of betting on green (or any one number on the wheel) is
It is still going to be a negative number! In fact among all the Casino games slot machines have the highest negative Expected Value for player and they make the most money for the Casinos.
The only game that is possible to have a positive Expected Value for player is Blackjack. Blackjack is a more complicated game than roulette and any other games in that the probability of wining or losing is not static. It changes from hand to hand from card to card. It depends on what cards are remained in the deck. There are circumstances where the chance of wining is bigger than the chance of losing. If a player can identify those circumstance and increase bet accordingly the average payout (or Expected Value) can be positive. The player has to be very well trained in order to identifier those circumstances.
Let’s say a deck of cards can play 10 hands of blackjack. The chance you win in 8 hands of them is only 30% but the in the other two hands the chance you win is 55%. You can use the following strategy to achieve positive Expected Value. Bet 5 bucks on the 8 hands and bet 100 dollars on the two hands.
The expected value is calculated as the following
It is a positive number. But as I say the probability of wining and losing in Blackjack keeps changing during the game. The player has to be very well trained and use a systematic way to determine the time when the chance of winning is greater than 50% and increase bet accordingly.
I heard a while ago a team of Massachusetts students win millions from casino by playing Blackjack. In a team environment the upstream player can place small bet and its purpose of hitting or staying is only to increase the winning chance of the next player who places a lot larger bet. In that way the circumstance of having more than 50 percent wining chance is easier to be identified and it will be easier to achieve positive Expected Value during the game.
Well they can win millions only because they have millions to bet on. I ever did some calculation. For average people like me if the maximum bet I can place is $100 dollars and I can play 20 hands per hours then I can only make 8 dollars per hour. It is not going to pay my bills. So I finally have a clear mind.
But if someone offer me a million and told me to play with it I will certainly train myself very well on counting cards 
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