For those interested in the math behind a 2 game parlay here it is. If you just want to know the odds go to the end:
To determine the breakeven win percentage needed to make the
parlay bet more profitable than
betting each game separately, let's break it down step by step.
Step 1: Expected Profit from Straight Bets
Each individual bet is at
-110 odds, meaning you risk
$110 to win $100 (or
$1110 to win $1000 in your scenario).
- Win probability needed to break even on a single bet:
110(110+100)=110210≈52.38%\frac{110}{(110+100)} = \frac{110}{210} \approx 52.38\%(110+100)110=210110≈52.38%
- Let P be the probability of a single bet winning.
- Expected return for betting each game separately:
EVstraight=2P−1EV_{\text{straight}} = 2P - 1EVstraight=2P−1
Since you place two separate bets, the expected return per dollar is:
EVtotal straight=2(2P−1)EV_{\text{total straight}} = 2(2P - 1)EVtotal straight=2(2P−1)
Step 2: Expected Profit from the Parlay Bet
A
parlay bet pays
2.6:1, meaning if you risk
$1110, you win
$2886 if both bets hit.
- The probability of both games winning is P2P^2P2.
- Expected return per dollar for the parlay:
EVparlay=3.6P2−1EV_{\text{parlay}} = 3.6P^2 - 1EVparlay=3.6P2−1
Step 3: Find the Breakeven Probability
To find when the
parlay is more profitable than betting separately, we set:
EVparlay≥EVtotal straightEV_{\text{parlay}} \geq EV_{\text{total straight}}EVparlay≥EVtotal straight3.6P2−1≥2(2P−1)3.6P^2 - 1 \geq 2(2P - 1)3.6P2−1≥2(2P−1)3.6P2−1≥4P−23.6P^2 - 1 \geq 4P - 23.6P2−1≥4P−23.6P2−4P+1≥03.6P^2 - 4P + 1 \geq 03.6P2−4P+1≥0
Step 4: Solve the Quadratic Equation
3.6P2−4P+1=03.6P^2 - 4P + 1 = 03.6P2−4P+1=0
Using the quadratic formula:
P=−(−4)±(−4)2−4(3.6)(1)2(3.6)P = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(3.6)(1)}}{2(3.6)}P=2(3.6)−(−4)±(−4)2−4(3.6)(1)P=4±16−14.47.2P = \frac{4 \pm \sqrt{16 - 14.4}}{7.2}P=7.24±16−14.4P=4±1.67.2P = \frac{4 \pm \sqrt{1.6}}{7.2}P=7.24±1.6
Approximating:
P=4±1.267.2P = \frac{4 \pm 1.26}{7.2}P=7.24±1.26P=5.267.2≈0.73orP=2.747.2≈0.38P = \frac{5.26}{7.2} \approx 0.73 \quad \text{or} \quad P = \frac{2.74}{7.2} \approx 0.38P=7.25.26≈0.73orP=7.22.74≈0.38
Since we are looking for a
profitable strategy, we take the
higher value:
P≈73%P \approx 73\%P≈73%
Final Answer
To make the
parlay a better bet than
betting each game separately, you need to be
correct at least 73% of the time on your individual picks.
Credit: ChatGPT
