50 and 1.33 money to stake on them is 5000 , how much should I stake on them to have a small loss

Business/Management

ScanSolve AI Answer

Step-by-step solution

4 steps

Let's figure out how to stake your money to minimize your loss by ensuring the same return regardless of which outcome wins.

  1. Define the variables.

    Let S₁ be the amount staked on the outcome with odds 3.50.
    Let S₂ be the amount staked on the outcome with odds 1.33.
    The total stake is 5000.
    So, S₁ + S₂ = 5000.

  2. Set up the condition for equal returns.

    To minimize loss, we want the payout to be the same no matter which outcome wins.
    Payout if outcome 1 wins = S₁ × 3.50
    Payout if outcome 2 wins = S₂ × 1.33
    We set these equal:
    S₁ × 3.50 = S₂ × 1.33

  3. Solve the system of equations.

    From S₁ + S₂ = 5000, we can express S₂ as S₂ = 5000 - S₁.
    Substitute this into the equal returns equation:
    S₁ × 3.50 = (5000 - S₁) × 1.33

    3.50 S₁ = 5000 × 1.33 - 1.33 S₁

    3.50 S₁ = 6650 - 1.33 S₁
    Add 1.33 S₁ to both sides:

    3.50 S₁ + 1.33 S₁ = 6650

    4.83 S₁ = 6650
    S₁ = 6650 / 4.83
    S₁ ≈ 1376.81

    Now find S₂:
    S₂ = 5000 - S₁
    S₂ = 5000 - 1376.81
    S₂ ≈ 3623.19

  4. Calculate the potential return and the loss.

    If outcome 1 wins: Return = 1376.81 × 3.50 = 4818.835
    If outcome 2 wins: Return = 3623.19 × 1.33 = 4818.8427
    The return is approximately 4818.84.

    The total money staked is 5000.
    The loss will be 5000 - 4818.84 = 181.16.

    To have the smallest loss, you should stake:
    S₁ = 1376.81 on the outcome with odds 3.50.
    S₂ = 3623.19 on the outcome with odds 1.33.
    This strategy results in a loss of approximately 181.16 regardless of which outcome wins.

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