Probability To Odds Conversion Calculator – Convert Probability to Odds

This probability to odds calculator helps convert the likelihood of success given specific odds ratios using PWin = A / (A + B), PLose = B / (A + B) formula.

The Probability of Winning Formula using odds notation A:B is a fundamental concept in probability theory and statistics.

Probability To Odds Calculator

Odds (A:B)	PWin Calculation	PWin	PLose Calculation	PLose
1:1	1/(1+1)	0.500	1/(1+1)	0.500
2:1	2/(2+1)	0.667	1/(2+1)	0.333
3:1	3/(3+1)	0.750	1/(3+1)	0.250
4:1	4/(4+1)	0.800	1/(4+1)	0.200
1:2	1/(1+2)	0.333	2/(1+2)	0.667

Probability To Odds Conversion Formula

PWin = A / (A + B)

Where:

• A represents favorable outcomes
• B represents unfavorable outcomes
• A:B represents the odds ratio for winning

Let’s say you have odds of 3:2 for winning a game:

• A = 3 (favorable outcomes)
• B = 2 (unfavorable outcomes): PWin = 3 / (3 + 2) PWin = 3/5 PWin = 0.60 or 60%

This means there's a 60% probability of winning with 3:2 odds.

Probability of Losing Formula (A:B)

The Probability of Losing Formula complements the winning probability and uses the same odds notation:

PLose = B / (A + B)

Where:

• A remains the favorable outcomes
• B remains the unfavorable outcomes
• A:B still represents the odds ratio for winning

With 3:2 odds:

PLose = 2 / (3 + 2)
PLose = 2/5
PLose = 0.40 or 40%

Verification of Formulas

Check is that PWin + PLose should always equal 1 (or 100%):

PWin + PLose = [A/(A+B)] + [B/(A+B)] = (A+B)/(A+B) = 1

Let’s explore various odds scenarios using both formulas:

• Even Odds (1:1)
  • PWin = 1/(1+1) = 0.50 (50%)
  • PLose = 1/(1+1) = 0.50 (50%)
• Favorable Odds (4:1)
  • PWin = 4/(4+1) = 0.80 (80%)
  • PLose = 1/(4+1) = 0.20 (20%)
• Unfavorable Odds (1:3)
  • PWin = 1/(1+3) = 0.25 (25%)
  • PLose = 3/(1+3) = 0.75 (75%)

How to Convert Probability To Odds

Step-by-Step Conversion Process

• Start with the probability (P)
• Calculate A:B ratio using:
  • If P is probability of winning:P = A/(A+B)
  • Solve for A:B ratio

Let’s convert a 75% (0.75) probability to odds:

• Given:
  • P = 0.75
  • Using PWin = A/(A+B)
• Solve for ratio: 0.75 = A/(A+B) 0.75(A+B) = A 0.75A + 0.75B = A 0.75B = 0.25A B = (0.25A)/0.75 B = A/3
• Therefore: A:B = 3:1, this means 3 favorable outcomes for every 1 unfavorable outcome

Converting 0.40 Probability to Odds

• Given:
  • P = 0.40
  • Using PWin = A/(A+B)
• Solve for ratio: 0.40 = A/(A+B) 0.40(A+B) = A 0.40A + 0.40B = A 0.40B = 0.60A B = (0.60A)/0.40 B = 1.5A
• Therefore: A:B = 2:3, this means 2 favorable outcomes for every 3 unfavorable outcomes

Verification Table

Initial Probability	Calculation Steps	Resulting Odds	Verification
0.75	0.75 = A/(A+B)	3:1	3/(3+1) = 0.75
0.40	0.40 = A/(A+B)	2:3	2/(2+3) = 0.40
0.60	0.60 = A/(A+B)	3:2	3/(3+2) = 0.60
0.25	0.25 = A/(A+B)	1:3	1/(1+3) = 0.25

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