How can I calculate the expected value of a Blackjack hand?

Jonah

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To calculate the expected value (EV) of a Blackjack hand, you need to consider the probabilities of all possible outcomes—such as winning, losing, or tying—and the corresponding payoffs for each. The EV gives you an average value of your bet over time. For example, if you have a hand like a hard 20 and the dealer shows a weak upcard (like a 6), you calculate the probability of winning, losing, or tying based on typical Blackjack strategies. Then, you multiply each outcome's probability by its payout (1:1 for a win, 3:2 for Blackjack, 0 for a tie, and -1 for a loss). Finally, you add up these values to find the EV, which tells you the average amount you can expect to win or lose per bet over the long run. This process can be more complex with advanced strategies like card counting, but at its core, the EV calculation helps you understand the long-term value of your betting decisions in Blackjack.
 
Calculation of the expected value (EV) of a Blackjack hand is indeed essential for assessing the potential outcomes of your bets in the long run. By taking into account the probabilities of different results and their corresponding payoffs, you can make more informed decisions during gameplay.

In the scenario you presented with a hard 20 against a dealer's weak upcard like a 6, you can estimate the probabilities of winning, losing, or tying based on basic Blackjack strategy and the known rules of the game. Once you have determined these probabilities, you can apply the appropriate payoff values to each outcome.

For example, let's assume the following simplified scenario with arbitrary probabilities:
- Probability of winning = 0.6
- Probability of tying = 0.1
- Probability of losing = 0.3

Using the respective payoffs:
- Win: +1
- Tie: 0
- Loss: -1

You can calculate the EV as follows:
EV = (0.6 x 1) + (0.1 x 0) + (0.3 x -1)
EV = 0.6 - 0.3
EV = 0.3

In this case, the expected value of your Blackjack hand in the given scenario is +0.3, meaning you can anticipate a positive average value per bet over time in this specific situation.

It's important to note that the actual probabilities and payoffs can vary based on the specific rules of the game, strategies employed, and any additional factors such as card counting techniques. Therefore, refining your EV calculations with more precise data and adjusting your gameplay accordingly can help optimize your Blackjack performance and outcomes.
 
You must ascertain the odds of winning, losing, and pushing using your hand and the dealer's upcard in order to compute the expected value. These odds may change based on the particular game rules and the make-up of the remaining deck.
 
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