Betting Math and Probability Facts

Betting is about odds, risk price and discipline. The coefficient is not a "forecast from the bookmaker," but the price of probability with a margin premium. If you learn to translate coefficients into probability, understand variance and manage a bank, rates cease to be intuition and turn into controlled entertainment with understandable risk boundaries (and not an "income strategy").

💡 Law and Responsibility: Check for legality and age restrictions in your jurisdiction. Play only with the money you are willing to lose.

1) Coefficients ↔ probability: basic formulas

Decimal Factors (Euro Format)

Implide probability (excluding margin):

[
p_{\text{implied}} = \frac{1}{\text{Odds}}
]

Example: 2. 50 → (p = 1/2. 50 = 0. 40) (40%).

Fractional (UK): a/b → decimal = (1 + a/b).

American (US):

Plus (+ 150): (\text {decimal} = 1 + 150/100 = 2. 50)
Minus (− 200): (\text {decimal} = 1 + 100/200 = 1. 50)

💡 On a line with two or more outcomes, the sum of the odds over 100% is the margin (around).

2) Bookmaker margin (vig, around) and "fair" -coef

For two equally likely outcomes, you see, for example, 1. 91 / 1. 91.

Impression: (1/1. 91 ≈ 52. 36%) each → sum ≈ 104. 7%.

Margin ≈ 4. 7%.

To estimate the "fair" probability, ration:

[
p_{\text{fair},i} = \frac{p_{\text{implied},i}}{\sum p_{\text{implied}}}
]

And "fair" coefficient (= 1/p_{\text{fair}}).

3) What is "valuy" (value) and where it happens

Definition: the rate is currency if your probability estimate (p _) is higher than the "fair" probability implied by the market after margin deduction.

Criteria in decimal format:

[
\ text {EV} = p _\cdot (\text {Odds} -1) - (1-p_ )\quad\Rightarrow\quad\text {value if }\text {EV}> 0
]

Example: koef 2. 50 (fair without margin ≈ 2. 63), your score (p _ = 42%).

EV (= 0. 42 \cdot 1. 5 - 0. 58 = 0. 63 - 0. 58 = +0. 05) per betting unit (formally a plus), but the short-course result will be noisy.

4) Variance and distance: why EV plus can lose for months

The result is a random variable with high variance.

The long distance smooths out noise but requires a large number of independent bets.

Express trains (multi-bets) multiply the variance: EV can only be higher with independent and felted legs, but volatility increases sharply.

5) Bankroll management: stake share and stop rules

Flat rate: constant amount/share of the bank (conservatively: 0. 5-2% on the rate).

Kelly (calli share) - theoretically optimal with known (p _) and Odds:

[
f = \frac{p_(\text{Odds}-1) - (1-p_)}{\text{Odds}-1}
]

In practice, the estimates (p _) are inaccurate → use half/quarter Kelly or a simple flat.

Stop rules: limit of loss/day/number of bets; tilt pause.

Dogon/martingale ban: Progressions don't change EVs, but they blow up the risk of ruin.

6) Dependence of outcomes, "correlation" and traps

Bets within a single event are often correlated (totals and wins, "goal + win"). You cannot add probabilities linearly.

Express trains from dependent events overestimate the chance of success by eye.

Consider the closing line (CLV): if your bets systematically "outplay" the closing line (take a better number than the final market), this is an indirect sign of a long-term edge.

7) Simple models for odds estimates (with caveats)

Binomial/Bernoulli: for yes/no events (goal/no in the interval, keeping serve in tennis, etc.).

Poisson (football): assessment of the distribution of goals based on the average λ of the teams and corrections for strength/home field.

Logit/ello/ratings: for doubles (win/draw/loss).

💡 Any model requires verification and updating: injuries, compositions, motivation, calendar density, etc. quickly become obsolete.

8) Parlay/Express vs Ordinary

Ordinal = lower variance, understandable EV accounting.

Express = visually "tasty payout," but the risk soars; the slightest underestimation of one leg kills the bottom line.

Make express trains consciously (and only with the independence and bulk of each leg), or use the ordinal as a base.

9) Typical cognitive errors in betting

Gambler's fallacy: "I haven't been in for a long time - I have to" - no.

Hot hand fallacy: "the team has a series of victories - it is "hot"" - trends are often overestimated by the market.

Fitting into the past (overfitting): the model "knows" yesterday, but breaks tomorrow.

Selective confirmation: we notice successful bets, ignore unsuccessful ones. The cure is a rigorous journal.

10) Accounting and control: the magazine is your best friend

Keep a table: date, sport/league, market, coefficient, your score (p_), amount, result, CLV (your score vs closing), notes.

Once a month see: ROI, standard deviation, share of "broken lines," discipline by limits. It cools emotions and helps you see reality.

11) Arbitration and forks: caveats

Theoretically, arbitration (line discrepancies) gives a risk-free EV +, practically: limits, delays, identification, rate rollbacks, change in coefficients. Without strict processes and speed - high operational and counterparty risk.

12) Mini formulas and cheat sheet

Implide probability: (p = 1/\text {Odds})

EV (decimal format): (EV = p _ (\text {Odds} -1) - (1-p_))

Around (two-way market): (O =\sum 1/\text {Odds} _ i) → margin ≈ (O-1)

Normalization of "fair" probabilities: (p_{\text{fair},i} = (1/\text {Odds} _ i )/\sum (1/\text {Odds}))

13) Conscious Player Checklist

I translate the coefficients into probability and see the margin.

I put a small share of the bank, without dogons.

I do not collect dependent express trains "for beauty."

I keep a journal and compare my copy with the closing line.

My probability estimates rely on data/model rather than "feeling."

I remember: bets are entertainment, not a source of guaranteed income.

Mini-FAQ

Do the coefficients "suggest" a real probability?

They reflect market valuation + margin. This is the starting point, not the truth.

Should you use Kelly?

Only as a landmark and with a decrease (½ or ¼ Kelly). With inaccurate (p _), full Kelly is too aggressive.

Why is my ROI "galloping"?

Variance. You need a long distance and discipline. Express trains and low limits increase the volatility of the results.

Better one "confident" express or three ordinars?

More often - three ordinars: less variance, easier to control EV and bank.

The math of betting is three whales: probability, pricing (ratio + margin) and risk management. Translate odds into odds, look for valuy only where there is a reasonable probability estimate, keep the rate of a small share of the bank and keep records. Then the bets cease to be chaos and clickbait, but become a transparent (and still risky) game with rules that you understand.