BlackJack’s Data In a Nutshell and Counting Strategy
Have you ever wanted to fly to Vegas and spend time having excitement with nightlife and casinos, pumping some endorphins and dopamine into your brain? Me too! But as you arrived in Vegas or any other casinos aroundthe world. One question that might come through your mind if you are not a professional gambler is that “What game should I play?”
According to the article of 888 casinos, Blackjack has the lowest house’s edges of all the games. It means that you have more probability to win against the houses in Blackjack than other kinds of games.
(Read more:https://www.888casino.com/blog/expected-value)
Rule of the game:
The goal of this game is very simple, to make your hands value as closest to 21s but not to over it. Otherwise, you will automatically lose. Each player will receive 2 cards, face-up, while the dealers will deal one face-up and one face-down for themselves. The game starts with the players' turns first. Now for the third card, you have many options whether to stand, draw, double-down, etc. For simplicity, we will cut all advanced options out and simplify to only stand or draw games. To stand means that you are satisfied with your hand and do not want to draw more. To draw means your hand is bad and therefore needs 3rd, 4th, or 5th cards to increase your hand value. Usually, the blackjack or hand that contains the value of 21s will receive a 3:2 payoff compared to the betting size, and the dealers will stand at 17s or higher.
“It’s not about the cards you’re dealt, but how you play the hand.”
-Randy Paush
The comparative statistics in the long run:
There is plenty of Blackjack data available online. You can simulate one too by using plenty of public codes. For example, the code by Macro Santos.
https://github.com/marcosan93/Blackjack-Card-Counter-Simulator/blob/master/blackjack.py
Here, the dataset used in this article is from Kaggle. It consisted of 900,000 hands history played at the single deck, a simplified version of the game with 6 players.
900,000 Hands of Blackjack Result | Kaggle
First, let’s explore some correlation among the variables given in the dataset.
As can be seen here, the first and second cards are highly correlated with the probability to win for the players. The dealers will lower their probability to win if they draw the third and subsequent cards, while the fourth card will give the same effect for the players.
Next, check whether the game was played in fair condition or not. I construct the density chart for the first, second, and third cards as follows.
The density plot showed a highly chance to be a fair game since we cannot notice any non-normal distribution for each player. The chance of each card seems to be equal. The reasons for 10s to be denser than any others because every single face card is counted as 10 (i.e. K, Q, J, T). While A can be either 1 or 11, depends on the criteria of 21s.
On the dealer side, the line graph above showed the same thing from the players' perspective. In another word, no suspicious patterns are detected and this game should be played as ‘Fair game’ ,with the distribution being equally distributed in the long term. This implies that the game is ‘True Random’.
Best Non-System Strategy in BlackJack
There are many ways that you can play the game, including using luck, supernature power, or statistically calculated methods. Before we can decide on any strategies we wish to use, let’s see some results in the big picture first.
The graph above showed the probability percentage of each hand value in all situations. By no doubt, the winning hands are started from 18s since the dealers will stand at least for 17s. The probability to lose in any situation will be less than half for 18s onward. Meaning that at least you should draw up to 18s. But is this really true?
There are some hands that are called ‘Indecisive hands’. The hand value between 12s to 17s is very hard to decide. Since the statistic showed us that getting more points will reduce our chance to lose, yet those hands also very like to bust (more than 21s) if we draw another card. Then what should we do?
The above charts presenting the count of winning and losing in case of drawing 3rd cards for those indecisive hands. The number of times that players win is slightly better when they draw the 3rd card. This implied for any indecisive hands, you would better draw more.
Expected Payoff:
After we know all the simple tricks and stats, now let’s see whether the players can actually beat the house in the simulation!
The chart presents the expected payoff. In this case, we assume the flat betting size of $10. That means if we hit the blackjack, the house will have to pay $15. After a little calculation, I get that the expected payoff of this simulation is -0.277. The number is slightly different from the expected advantages calculated by 888casinos as discussed in the first part. However, it still favors the house.
Let’s see about players’ hands, Shall we?
The heatmap shows the average payoff matrix between the sum of players' 2 first cards and the face-up card of the dealer. The result told us that the expected payoff for face-up dealer's hands is not different, except for an ‘A’ due to the fact that there is a high chance of dealers will get a Blackjack and the ideal hands are 10s and 21s for low sum values as well as high sum values respectively.
The counting card strategy
Have you ever watched Hangover or 21? Do you remember the counting card scene? Have you ever wondered what are they doing and how? Well, those actors were just counting the cards! But how did it work?
There is no clear evidence about who invented the counting card strategy. It is the system that assigned the value corresponding to each card and popular among the blackjack players. The system has many kinds of sub-types but the main principle for every type are the same. By giving the positive to the low cards and negative to the high cards, then true count or running count it. If the total count is very positive means that most of the low cards are out. If you force to draw the 3rd cards, it will heavily increase the chance of bust and favor the house. Contradictory applied to the negative one. There are plenty more details at a higher level of card count wait for you to explore!
Unfortunately, same as us. Many casinos nowadays know this secret. Therefore they banned whoever does it straightforwardly and increased the number of decks to make it harder for the system to beat the house. However, with the help of 1andDone’s code, I have simulated two popular counting methods with the backtest for you: the zen count and the Hi-lo count. With his code, you can freely adjust all the rules and the strategies to test. Big thanks to him.
For the code, please visit; https://github.com/1andDone/blackjack
Hi-lo
Here is the comparison between the normal strategy where players just play as normal, Hi-lo count, and the Back count which the player just counts and waits for the significant signal over 10000 runs.
The result showed a huge difference between the normal players and the Hi-lo counting. we notice that the system takes some time before it actually works. That’s why, in this case, the backtest gets the most profit in the table.
Zen Count
For the zen count, it seems like this system does not work well as shown from the graph. Actually, the result comparing with the non-strategy is almost identical. However, the backtest guy still got the job done as he is the one player that could make a profit from the table. The special function of this system is the bet spread. The amount of bet size in each round is not always flat. Instead, it depends on the true count value of the card.
For more information about betting strategy: See ‘Card counting system’
Conclusion:
Blackjack is an easy-to-learn and fun-to-play game. That eventually came with the strategies more than just draw or stand. To play this game, luck is just a part of it. As the stats provide you the highest chance to win as discussed.
The counting system might actually not work all the time. Some of it takes time. If you wish to use it, you will not only need to have a good remembering skill but also enough initial money to pay for the house in the beginning stage. However, keep in mind that no matter how good counting card skill are, the expected payoff of this game is still negative. Furthermore, the house can re-shuffle the decks at any time! In that case, you would have to start over again. So, my suggestion is you just play for fun and bet at your own risk. Because if there was a way to beat the casinos, we would not have had such a huge profit report from them as we see today.