50 and 1.33 money to stake on them is 5000 , how much should I stake on them to have a small loss
ScanSolve AI Answer
Step-by-step solution
4 stepsLet's figure out how to stake your money to minimize your loss by ensuring the same return regardless of which outcome wins.
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.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 × 1.33Solve 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) × 1.333.50 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 ≈ 1376.81Now find S₂:
S₂ = 5000 - S₁
S₂ = 5000 - 1376.81
S₂ ≈ 3623.19Calculate 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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