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% Document Info
\author{BetBetter}
\pdfinfo{
  /Title (betting-odds-and-implied-probability.pdf)
  /Creator (Cheatography)
  /Author (BetBetter)
  /Subject (Betting Odds and Implied Probability Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Betting Odds and Implied Probability Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{BetBetter} via \textcolor{DarkBackground}{\uline{cheatography.com/219378/cs/48582/}}}
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\noindent
\begin{multicols}{3}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}BetBetter \\
  \uline{cheatography.com/betbetter} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 8th November, 2026.\\
   Updated 8th November, 2026.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\end{multicols}}




\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{One price, three formats}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Decimal 2.50}} = stake back x 2.50 (a \$10 bet returns \$25, profit \$15) \newline % Row Count 2 (+ 2)
{\bf{Fractional 3/2}} = profit 3 for every 2 staked (same as 2.50) \newline % Row Count 4 (+ 2)
{\bf{American +150}} = profit \$150 on a \$100 bet (same as 2.50) \newline % Row Count 6 (+ 2)
{\bf{American -200}} = stake \$200 to win \$100 (decimal 1.50) \newline % Row Count 8 (+ 2)
Convert: \newline % Row Count 9 (+ 1)
Decimal = 1 + fraction (3/2 -\textgreater{} 2.50) \newline % Row Count 10 (+ 1)
Decimal from +A = 1 + A/100 \newline % Row Count 11 (+ 1)
Decimal from -A = 1 + 100/A \newline % Row Count 12 (+ 1)
+A from decimal d \textgreater{}= 2: (d - 1) x 100 \newline % Row Count 13 (+ 1)
-A from decimal d \textless{} 2: 100 / (d - 1) \newline % Row Count 14 (+ 1)
Free converter: \{\{link="https://betbetter.world/tools/odds-converter"\}\}betbetter.world/tools/odds-converter\{\{/link\}\}% Row Count 17 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{All three formats describe the same bet; only the way of writing it changes.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Are the odds right? Checking calibration}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Calibration}} = do events priced at X\% happen about X\% of the time? \newline % Row Count 2 (+ 2)
1. Remove the margin from each closing price \newline % Row Count 3 (+ 1)
2. Group outcomes into bands (50-60\%, 60-70\% ...) \newline % Row Count 4 (+ 1)
3. Compare the average priced chance with the share that won \newline % Row Count 6 (+ 2)
4. Judge gaps against the standard error: sqrt(p x (1-p) / n) \newline % Row Count 8 (+ 2)
{\bf{What open data shows:}} across 18,238 settled two-outcome markets (Nov 2024 - Jul 2026, five sports), outcomes landed within about 2 points of the margin-free price in every band. Small gaps like that are often inside sampling error. \newline % Row Count 13 (+ 5)
Full dataset (36,476 rows, CC BY 4.0): DOI 10.5281/zenodo.21764674 \newline % Row Count 15 (+ 2)
Study: \{\{link="https://betbetter.world/studies/market-calibration"\}\}Do betting odds tell the truth?\{\{/link\}\}% Row Count 18 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Example: p = 0.8, n = 2,000 gives a standard error of about 0.9 points, so a 1.5-point gap is not significant.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Price to chance (implied probability)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Decimal d:}} chance = 1 / d \newline % Row Count 1 (+ 1)
2.50 -\textgreater{} 1 / 2.50 = 40\% \newline % Row Count 2 (+ 1)
1.50 -\textgreater{} 66.7\% \newline % Row Count 3 (+ 1)
{\bf{Fractional a/b:}} chance = b / (a + b) \newline % Row Count 4 (+ 1)
3/2 -\textgreater{} 2 / 5 = 40\% \newline % Row Count 5 (+ 1)
{\bf{American +A:}} chance = 100 / (A + 100) \newline % Row Count 6 (+ 1)
+150 -\textgreater{} 100 / 250 = 40\% \newline % Row Count 7 (+ 1)
{\bf{American -A:}} chance = A / (A + 100) \newline % Row Count 8 (+ 1)
-200 -\textgreater{} 200 / 300 = 66.7\% \newline % Row Count 9 (+ 1)
Short-cut: an even-money price (2.00, 1/1, +100) means 50\%.% Row Count 11 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{This is the chance the price implies before the bookmaker margin is removed.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Key terms}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Implied probability}}: the chance a price suggests (1 / decimal odds) \newline % Row Count 2 (+ 2)
{\bf{Margin / vig / overround}}: how far the implied chances add up above 100\% \newline % Row Count 4 (+ 2)
{\bf{Fair (no-vig) odds}}: odds after the margin is removed \newline % Row Count 6 (+ 2)
{\bf{Closing price}}: the last price before the event starts \newline % Row Count 8 (+ 2)
{\bf{Favourite-longshot bias}}: favourites and longshots being priced too short or too long on average \newline % Row Count 10 (+ 2)
{\bf{Brier score}}: average squared error of a forecast chance (a coin flip scores 0.25) \newline % Row Count 12 (+ 2)
{\bf{Calibration}}: priced chances match how often things happen% Row Count 14 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Odds are forecasts. Knowing how to read them is a statistics skill, not a betting tip.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Removing the margin (the vig)}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Both sides of a two-way market add up to more than 100\%. The extra is the bookmaker's margin. \newline % Row Count 2 (+ 2)
{\bf{Example:}} Team A 1.80, Team B 2.10 \newline % Row Count 3 (+ 1)
Implied: 1/1.80 = 55.6\%, 1/2.10 = 47.6\% \newline % Row Count 4 (+ 1)
Total = 103.2\% -\textgreater{} margin about 3.2\% \newline % Row Count 5 (+ 1)
{\bf{Fair chance (simple method):}} divide each by the total \newline % Row Count 7 (+ 2)
A = 55.6 / 103.2 = 53.9\% \newline % Row Count 8 (+ 1)
B = 47.6 / 103.2 = 46.1\% \newline % Row Count 9 (+ 1)
{\bf{Fair odds}} = 1 / fair chance \newline % Row Count 10 (+ 1)
A = 1.86, B = 2.17 \newline % Row Count 11 (+ 1)
Other methods (Shin, power, odds ratio) spread the margin differently between favourite and longshot.% Row Count 14 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Typical margins, Jul-Sep 2026, 69.6M markets: about 4.8\% on who-wins bets and 7.6\% on player props.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

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