What is the Expected Value of Game 2 (blackjack) assuming you play all $100 on Game 2?

In Game 2 of blackjack, calculating the Expected Value (EV) requires understanding the probabilities of winning, losing, and the payoffs involved.

The formula for Expected Value is:

\[
EV = (P_{\text{win}} \times W) + (P_{\text{lose}} \times L) + (P_{\text{tie}} \times T)
\]

Where:
- $P_{\text{win}}$ is the probability of winning.
- $P_{\text{lose}}$ is the probability of losing.
- $P_{\text{tie}}$ is the probability of a tie.
- $W$ is the amount won (usually your bet doubled).
- $L$ is the amount lost (your bet).
- $T$ is the outcome in the case of a tie (usually $0$).

If you are playing with a $100 bet, and assuming standard blackjack rules where a win gives you a 1:1 payout, here’s what we need to consider:
- The **probability of winning** in blackjack depends on the house edge, which is around 42-49%, depending on the strategy.
- The **probability of losing** ranges from 49-56%.
- The **probability of a tie** (push) is about 8%.

The payoffs:
- A **win** means you'll gain $100 (bet amount) plus your bet back, so $200.
- A **loss** means you lose $100.
- A **tie** results in no change, so $0 net gain/loss.

Using a rough estimate for probabilities:
- $P_{\text{win}} = 0.45$
- $P_{\text{lose}} = 0.47$
- $P_{\text{tie}} = 0.08$

Now, calculating the EV:

\[
EV = (0.45 \times 100) + (0.47 \times -100) + (0.08 \times 0)
\]

Let’s calculate this.

Calculate the Expected Value of a $100 bet in blackjack using probability concepts. This solution covers the Expected Value formula and assumptions based on typical blackjack probabilities, providing insights into win, lose, and tie outcomes. Suitable for Grades 10-12.

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