What is the Expected Value of Game 1 (blackjack), assuming you play all $100 on Game 1? With a 49% winning chance 

The **Expected Value (EV)** of a game is a measure of the average outcome if you were to play the game multiple times. In this case, you are playing **Game 1 (blackjack)** with the following details:

- You bet **$100** on the game.
- The probability of winning is **49%** (or 0.49).
- The probability of losing is **51%** (or 0.51).
- For simplicity, let's assume the game has a **1:1 payout**, meaning if you win, you get your $100 back plus an additional $100 (total of $200), and if you lose, you lose the $100.

### Formula for Expected Value:
\[
\text{EV} = (\text{Win Probability}) \times (\text{Win Amount}) + (\text{Loss Probability}) \times (\text{Loss Amount})
\]

In this case:
- **Win Amount** = $100 (since you get $100 profit on winning),
- **Loss Amount** = -$100 (since you lose $100 if you lose).

Now plug in the values:
\[
\text{EV} = (0.49) \times (100) + (0.51) \times (-100)
\]

### Calculating EV:
\[
\text{EV} = 49 - 51 = -2
\]

### Interpretation:
The expected value of the game is **-2**, which means on average, you will lose **$2** for each $100 bet in this game if you play repeatedly.

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Would you like further details on how this works?

Here are 5 related questions to explore further:

1. How does the payout ratio affect the expected value in games of chance?
2. What is the variance in blackjack, and how does it impact long-term outcomes?
3. How does increasing the probability of winning change the expected value?
4. What is the difference between expected value and actual outcome in gambling?
5. Can strategies like card counting improve the expected value in blackjack?

**Tip**: In gambling, a negative expected value indicates that the house has an advantage, so long-term losses are more likely.

What is the Expected Value of Game 1 (blackjack), assuming you play all $100 on Game 1? With a 49% winning chance

Understand how to calculate the expected value of playing blackjack with a $100 bet and a 49% winning chance. This detailed guide covers the essential probability concepts and provides the formula for determining expected outcomes. Ideal for Grades 9-12 or anyone learning about gambling odds.

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