Let’s say that I made a bet for three matches with two outcomes each. Odd is 1.8 on each match, same for winning and losing. Now, if I win the first match, can you calculate how much should I bet against myself to win the profit. My total possible winnings on main ticket are 1.8 * 1.8 * 1.8 * stake

To calculate how much you should bet against yourself after winning the first match in a series of three, let's break down the situation.

### Step 1: Total possible winnings on the main bet (all three matches won)
The formula for the total possible winnings if you win all three matches is:

\[
\text{Total possible winnings} = 1.8 \times 1.8 \times 1.8 \times \text{stake}
\]

This simplifies to:

\[
\text{Total possible winnings} = 1.8^3 \times \text{stake} = 5.832 \times \text{stake}
\]

### Step 2: Scenario after winning the first match
After winning the first match, the odds for the remaining two matches are:

\[
1.8 \times 1.8 = 3.24
\]

At this point, if you continue betting with your original stake, your possible winnings from the remaining two matches are:

\[
3.24 \times \text{stake}
\]

### Step 3: Calculating the hedge (betting against yourself)
Now, to hedge against losing the main bet, you'd place a bet on the opposite outcome of the remaining two matches. To ensure you guarantee profit, you want the hedge bet to cover your stake while still securing some profit.

#### Hedge Calculation:
Let:
- \( x \) be the amount to bet against yourself on the opposite outcome of the remaining two matches.
- If the opposite outcome happens (you lose either of the remaining matches), you win this bet at odds of \( 3.24 \).

The equation to ensure a guaranteed return (break-even or profit) should balance the winnings from both outcomes.

1. **If you win all matches** (no hedge needed), you win:

\[
5.832 \times \text{stake}
\]

2. **If you lose either of the remaining two matches**, your hedge bet \( x \) will win, and the payout from the hedge bet will be:

\[
3.24 \times x
\]

To guarantee profit, you want to cover your initial stake and still win some money. A good starting point is to ensure that:

\[
3.24 \times x = \text{stake} + \text{profit}
\]

Let’s say you want a guaranteed minimum profit. For instance, if you just want to recover your stake, set the profit to zero. In that case:

\[
3.24 \times x = \text{stake}
\]

Thus:

\[
x = \frac{\text{stake}}{3.24}
\]

This is the amount you should bet against yourself to guarantee a break-even outcome.

### Conclusion:
If you want to guarantee a break-even outcome after winning the first match, you should bet:

\[
x = \frac{\text{stake}}{3.24}
\]

against yourself on the next two matches.

Would you like a more detailed explanation or calculations based on a specific stake?

---

### 5 Relative Questions:
1. What would happen to your total winnings if you increased the stake after the first match?
2. How would the hedging amount change if the odds for the remaining two matches were different?
3. Can you calculate the expected value of betting without hedging?
4. What happens if you lose the first match—how does this affect your overall strategy?
5. What other betting strategies could you use to minimize your risk?

### Tip:
When hedging, it's important to balance the risk and reward—small hedge bets can reduce risk while still keeping a potential upside on the original wager.

Let’s say that I made a bet for three matches with two outcomes each. Odd is 1.8 on each match, same for winning and losing. Now, if I win the first match, can you calculate how much should I bet against myself to win the profit? My total possible winnings on main ticket are 1.8 * 1.8 * 1.8 * stake.

Discover how to hedge your bets after winning the first match in a series of three with odds of 1.8 for each match. Learn the key formulas and concepts behind calculating the optimal bet size to guarantee a profit. This problem covers hedging strategies and probability calculations, suitable for advanced high school to early college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation