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About

In the world of probability and statistics, 'Value' exists when the probability of an outcome is higher than the probability implied by the odds offered. Professional risk managers and bettors do not rely on hunches; they rely on Positive Expected Value (+EV).

This tool performs two critical functions: First, it compares the Bookmaker's Odds against your Assumed True Probability to determine if a value edge exists. Second, if an edge is found, it uses the Kelly Criterion—a formula used by financial investors to maximize logarithmic wealth—to suggest exactly how much of your bankroll should be risked on that specific event to balance growth and safety.

betting math expected value kelly criterion probability calculator

Formulas

1. Value Calculation:

Value % = (Probability × Odds) 1

2. Kelly Criterion (Optimal Stake):

f* = (b × p) qb

Where b is (Odds - 1), p is probability of winning, and q is probability of losing (1-p).

Reference Data

Decimal OddsImplied ProbabilityBreakeven %
1.1090.9%Requires >91% win rate
1.5066.7%Requires >67% win rate
2.0050.0%Requires >50% win rate (Coin Flip)
2.5040.0%Requires >40% win rate
3.0033.3%Requires >33.3% win rate
5.0020.0%Requires >20% win rate
10.0010.0%Requires >10% win rate
100.001.0%Long shot

Frequently Asked Questions

+EV means that if you placed the same bet an infinite number of times, you would make a profit. For example, if you get odds of 2.0 (50%) on a coin toss, but the coin is weighted to land heads 60% of the time, that is a +EV bet.
If the Kelly Criterion suggests 0%, it means the bet has Negative Expected Value. Mathematically, you should not bet anything because the odds offered are worse than the true probability of winning.
Full Kelly can be volatile (suggesting large stakes). Many users prefer 'Half Kelly' or 'Quarter Kelly' (multiplying the result by 0.5 or 0.25) to reduce variance and protect their bankroll from bad streaks.
Absolutely not. This tool calculates probability advantages. Even a 90% probability event will lose 10% of the time. This is a tool for long-term strategy, not short-term prediction.