Blackjack Hit Or Stay Calculator

Blackjack Decision Formula:

\[ EV_{hit} = \sum (prob_{outcome} \times value_{hit}) \] \[ EV_{stay} = \sum (prob_{outcome} \times value_{stay}) \] \[ \text{Decision} = \max(EV_{hit}, EV_{stay}) \]

Expected Value Hit (EV_hit):

Expected Value Stay (EV_stay):

Optimal Decision:

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1. What is the Blackjack Hit or Stay Calculator?

The Blackjack Hit or Stay Calculator helps determine the mathematically optimal decision in blackjack by comparing the expected values of hitting versus staying based on probability and potential outcomes.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ EV_{hit} = \sum (prob_{outcome} \times value_{hit}) \] \[ EV_{stay} = \sum (prob_{outcome} \times value_{stay}) \] \[ \text{Decision} = \max(EV_{hit}, EV_{stay}) \]

Where:

\( EV_{hit} \) — Expected value of hitting
\( EV_{stay} \) — Expected value of staying
\( prob_{outcome} \) — Probability of a specific outcome (0 to 1)
\( value_{hit} \) — Value or payoff if you choose to hit
\( value_{stay} \) — Value or payoff if you choose to stay

Explanation: The calculator compares which action (hit or stay) has the higher expected value based on the probabilities and potential outcomes you provide.

3. Importance of Expected Value in Blackjack

Details: Understanding expected value helps players make mathematically optimal decisions that maximize long-term gains and minimize losses in blackjack.

4. Using the Calculator

Tips: Enter the probability of the outcome (between 0 and 1), the value if you hit, and the value if you stay. The calculator will determine which decision has the higher expected value.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this calculator?
A: The calculator provides mathematically precise results based on the inputs you provide. Accuracy depends on how well you estimate the probabilities and values.

Q2: Should I always follow the calculator's recommendation?
A: The calculator shows the mathematically optimal decision. In practice, you might consider other factors like the count of remaining cards or your risk tolerance.

Q3: What's a typical probability range in blackjack?
A: Probabilities vary based on the specific situation but generally range from 0.1 to 0.9 for most common scenarios.

Q4: How do I determine the values for hit/stay?
A: Values can represent potential winnings, the probability of winning the hand, or other metrics depending on your analysis.

Q5: Can this be used for other gambling decisions?
A: Yes, the expected value concept applies to many gambling scenarios, though the specific inputs would differ.