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Playing Blackjack with Machine Learning
Published: Cash 3 results.
Monte Carlo Reinforcement Learning is a simple but effective machine learning technique, that can be used to determine the optimal strategy for episodic games (i.e. games which are guaranteed to terminate). The learning process involves starting with some non-optimal strategy, such as picking moves at random, and then incrementally improving that strategy by playing multiple games, and making small changes to the strategy at the end of each one.
In order to be able to define a strategy, we need to identify all the various game 'states' that can exist. A state is a description of the current situation in the game, which contains all the details that we need to consider when deciding what to do, and no irrelevant information. For example, when playing a game of blackjack the state will need to contain information about what cards we have, and what card the dealer is showing.
A strategy consists of a set of rules that the player can use to decide what to do in each state, we can think of it as a long series of instructions of the form:
- In State 1 do Action A
- In State 2 do Action B
- In State 3 do Action A
- In State 4 do Action C
- ..
In blackjack the player is initially dealt 2 cards from the pack, and the dealer has a single card. One way to represent the initial state of the game would be to simply indicate what these 3 cards are, for example: 'Player has A♠ and 3♦, Dealer has J♣'. When playing with a single deck of 52 cards, this gives 52 x 51 x 50 = 132,600 possible starting states.
Blackjack Machine
However we can reduce this number by discarding some irrelevant information. For example, the suit of the cards is ignored in blackjack, so we can remove this information from the state: 'Player has A and 3, Dealer has J'. The number of possible states is now much smaller: 13 * 13 * 13 = 2,197.
We can reduce the number of states in our example even further - in blackjack all face cards are treated as having a value of 10, and in general the individual card values do not matter, only the total value held by each player. The only exception to this rule is that Aces can have a value of either 1 or 11, so the state should indicate whether a player's hand contains an Ace or not.
In summary then:
- There are 10 possible Dealer states: 2,3,4,5,6,7,8,9,10,A
- There are 25 possible Player States:
- No Ace: 4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20
- With Ace: 13,14,15,16,17,18,19,20
- There are 10 x 25 = 250 total states
In order to develop a blackjack strategy using Monte Carlo Reinforcement Learning, we need to play many individual games. Each time we take an action we note which of our 250 states we were in, what action we took, and what the eventual outcome of the game was. A value called the 'return' can then be used to estimate how good/bad each action was. The return is calculated by deciding to what extent each of the individual actions that we took contributed to the eventual success or failure that occured at the end of the game. This calculation is performed using a discounting factor, which allocates more credit/blame to the later actions (which were closer to the point at which the result occurred) than to the earlier actions.
At first our actions are completely random, however because we are keeping a careful record of how much we won/lost by taking each action in each different state, as time goes on we can start to use this information to help pick the best action for the situation. One possible strategy would be to always select the action that has yielded the highest average return in the past, for example:
State: | Player total = 8 with No Ace, Dealer total: 10 |
Action = HIT | Action performed 4 times, total return = £20 |
Action = STICK | Action performed 2 times, total return = £4 |
So the mean return for the action HIT is 20 ÷ 4 = £5 and for the action STICK it is 4 ÷ 2 = £2, so it seems like the best action to take in this situation is to HIT.
The problem with always picking the action with the highest return however, is that as soon as one action has started to deliver some positive returns we will continue picking that action forever, and never try any of the others - one of which might actually be better than the one we first tried.
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A balance needs to be struck between exploration and exploitation. We want to try a variety of different actions, so that we have the opportunity to see which ones work and which ones do not, but we also want to exploit the profitable actions that we have already discovered. In order to achieve this balance we select the action with the highest mean return most of the time, but some proportion of the time we act randomly. This ensures that we will eventually explore all different actions, and be able to determine the best ones.
The frequency with which we should act randomly will vary according to the specifics of the game that we are playing, and experimentation is usually needed in order to determine the best value. As we continue to play the game, and our strategy becomes more reliable, we should gradually reduce the frequency with which random actions are taken, with this value approaching zero as we converge on the optimal strategy.
The graph below shows the results of applying this Monte Carlo strategy to the game of blackjack, played with a single deck of cards. The vertical axis indicates what proportion of the money that we wagered was lost. The horizontal axis shows how many games were played. Since the rules of blackjack always favour the dealer, it is not possible to actually make a profit in this game without counting cards, however a good strategy can reduce the dealer's edge to around 0.5%, which is roughly the level attained by our Reinforcement Learning agent in this experiment:
This video shows how the agent's strategy changed over the course of 5 million games. The coloured boxes indicate the action favoured by the agent in each state.
- HIT - request another card from the dealer
- STK - do not request any more cards from the dealer
- DBL - double the current bet and draw one further card
- SUR - surrender, losing half the current bet and ending the game
We can see that the agent quickly learns to HIT when it has a low value hand, and to STICK when its hand is high. Its strategy becomes fairly stable after about 500,000 games, however small adjustments continue to be made to a few of thestates right up until the end of the training period.
Blackjack is one of the most popular casino games of all times. The game is a classic at land-based casinos and has become a clear favorite at online casinos as well.
There are many ways to play a traditional game of blackjack at casino sites. One can play at a live blackjack table, where a real dealer doles out the cards to all players at the table in real-time, or one can play blackjack online, against a machine, where each game is engineered by computerized results.
Each carries advantages and disadvantages, based on the likes and dislikes of the player partaking in the game. On this page, we'll look into some of the differences between the two.
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Online Blackjack Or Live Dealer Blackjack: Which One Is Best?
If you are wondering if you should go with online blackjack or live dealer blackjack, the truth is there is no single answer to the question. The answer will mostly depend on the type of experiences you enjoy the most.
Are you more of a social person or would you rather have a more private experience? Do you like to dictate the pace of the game or would you rather let the dealer handle it? How much do you value privacy?
In the table below, we explore some of the key differences between the two types of play:
Playing Live Dealer Blackjack | Playing Online Blackjack |
---|---|
More of a social experience. You can talk to the dealer or other players using the chat. | You play by yourself against a computer. |
Live dealers can make mistakes and some players find they may be easier to beat than a computer. | Playing against a computer keeps the odds and the RTP regular. |
Limited selection of Blackjack games to play. | Broader range of game options. Top online casinos offer 10-20 different blakcjack variations. |
The dealer dictates the pace of the game, making the experience more similar to that of a land-based casino. | You may find the pace dictated by the dealer to be fast or too slow and may prefer to set the pace yourself. |
#1 – RNG Ensures Fairness
The most obvious difference between playing blackjack against a machine and live table games is the use of a computerized Random Number Generator, otherwise known as the RNG.
In online blackjack, the RNG provides entirely randomized shuffling of the virtual deck, or decks, of cards in use.
Electronic Blackjack
Legitimate casinos have their RNGs tested regularly by third party audit companies to ensure fairness and transparency.
Unlike a human dealer, the RNG has can't be affected to favor certain players and doesn't have any knowledge of how the previous gaming session played out.
#2 – House Edge Is Lower In Online Blackjack
You should note, however, that in both types of game, the house edge is determined by the particular rules and payouts of the game being played, as well as the knowledgeable decision-making of the player.
Online blackjack tends to have a lower house edge and the fact that there are more game variants available allows the player to pick and choose and go with the blackjack variant with the highest RTP.
Blackjack Machine With Hi-lo Option
In general, online casinos offer between one and three variations of live dealer blackjack, which gives you more limited options when it comes to picking the game with the lowest house edge.
How To Win Blackjack Machine
#3 – A Private Vs. A More Social Experience
In online blackjack, the player gets to set the pace of the game – which tends to make it quicker to play as you won't have to wait for the dealer or another player to make a move. The game is also 100% private (you are playing alone against a computer) and you get to choose your bets, which is a pro for many players
Another feature some players enjoy is that online blackjack often allows much lower stakes ranges than live tables – as cheap as $1 per play. Live dealer blackjack bets, on the other hand, generally start at a minimum of $5.
Players who feel intimidated by the live scene may also prefer the online video version of the game. Rather than having more experienced players on each side of them, some players prefer the singularity and leisurely nature of online blackjack.
Players can take as long as they like to make decisions, which affords them a greater opportunity to practice basic strategy.
#4 – Many Players Value The Human Factor In Live Blackjack
Although online blackjack has many advantages, many players don't like RNG blackjack because it lacks the human factor. They feel that playing against a machine makes the experience rather cold.
The live dealer blackjack experience, on the other hand, is much more lively and authentic and resembles more closely that of playing at a land-based casino.
Live blackjack is run in real-time by human dealers from a physical studio or land-based casino. You get to chat with both the dealer and other players on the table via the live chat feature.
Picked A Favorite Yet? Start Playing Online Or Live Blackjack Today!
As you've seen, there is not a clear cut answer when it comes to picking a favorite between online and live blackjack. While some people may find the live blackjack experience more fun and exciting, others may prefer to set their own pace when playing and may value the privacy of playing alone against a computer.
The good news is all of our top-recommended online casinos offer both types of play. Choose one of the legitimate casinos we recommend and open an account today. You can try your hand at both online and live blackjack and pick your favorite option.