Tools
Working betting math
Eight calculators that do the arithmetic correctly, validate what you type, and explain what the answer means. They run entirely in your browser, nothing is sent anywhere, and they are free.
Before you use these
A calculator cannot check your assumption
Educational use only
Every one of these tools takes your estimate of a probability and does exact arithmetic on it. If the estimate is wrong, the output is confidently wrong, and the staking tools will tell you to bet into a losing proposition without hesitating. The math is the easy part; the estimate is the whole problem.
Nothing here is betting advice or a recommendation to stake anything. If gambling is causing you harm, the responsible gambling page lists help resources.
Fundamentals
Prices and margin
Odds converter
American to decimal and back, with the implied probability that price carries before the book margin is removed.
e.g. -110 or +150. Cannot fall between -100 and +100.
e.g. 1.9091 or 2.50. Must be greater than 1.
- Implied probability
- 52.38%
- American
- -110
- Decimal
- 1.9091
- Profit per unit
- 0.9091
Implied probability 52.38%.
Implied probability here still includes the book margin. Use the no-vig calculator to strip it out before comparing against your own estimate.
No-vig fair price
Removes the book margin by proportional normalisation, so the outcomes sum to exactly 100 percent. Works for two-way and three-way markets.
American odds
American odds
Leave blank for a two-way market
- Outcome 1 fair
- 50.00% · +100
- Outcome 2 fair
- 50.00% · +100
- Sum of raw implied
- 104.76%
- Book hold
- 4.55%
Fair probabilities 50.00%, 50.00%. Book hold 4.55%.
Proportional de-vigging assumes the margin is spread evenly across outcomes. On heavy favourites and big longshots real books load more margin onto the longshot, so treat the output on lopsided markets as an approximation.
Book hold
How much of every unit wagered the book keeps at these two prices, assuming balanced action. This is the cost you pay before any opinion is involved.
American odds
American odds
- Book hold
- 4.55%
- Overround
- 104.76%
- Break-even win rate
- 52.27%
Book hold 4.55%.
A standard -110 / -110 market holds about 4.55 percent. Hold is what the book expects to keep with money split evenly, not its actual realised margin.
Value
Edge and staking
Expected value
What one unit staked at this price is worth on average, given your own estimate of the true probability. Everything depends on that estimate being right.
Your estimate, not the price. Between 0 and 100.
American odds
Used only to scale the result
- EV per unit
- +5.00%
- EV on 1 unit
- +0.0500u
- Break-even probability
- 52.38%
- Your edge
- +2.62 pts
Expected value +5.00% per unit.
The break-even probability is what the price alone requires. Your edge is the gap between your estimate and that number — and it has to be larger than your own error bars to mean anything.
Kelly stake
The stake that maximises long-run growth if your probability estimate is exactly right. It never is, which is why this defaults to quarter Kelly.
Your estimate. Between 0 and 100.
American odds
Any currency; the output uses the same units
Fractional Kelly gives up a little theoretical growth for a large reduction in variance and a margin of safety against your own estimation error.
- Recommended stake
- 1.38% · 13.75
- Full Kelly
- 5.50%
- EV per unit
- +5.00%
Recommended stake 1.38% of bankroll.
Kelly assumes a known edge and an independent bet. If your probability estimate is wrong, staking math cannot rescue it — it only changes how fast a wrong estimate drains a bankroll. Educational use only; this is not a recommendation to stake anything.
Measurement
Grading and managing a position
Closing line value
Did the price you took beat the price the market closed at? Both sides are de-vigged first, because comparing raw prices measures the book margin as much as the market read.
American odds on your side
Needed to remove the margin
American odds
American odds
- CLV
- +4.03 pts
- Fair probability at entry
- 43.80%
- Fair probability at close
- 47.83%
- Beat the close
- Yes
Closing line value +4.03 percentage points.
Positive CLV means you bought the side cheaper than the market's final answer. It does not predict your result on this bet, and it is meaningless once the event has started.
Hedge
The stake on the other side that returns the same amount whichever way the event lands. With real prices on both sides that equalised amount is usually a small loss.
Units or currency
American odds you took
American odds on the other side now
- Hedge stake
- 180.00
- Total outlay
- 280.00
- Return either way
- 300.00
- Locked result
- +20.00
Hedge stake 180.00, locked result +20.00.
Hedging converts an uncertain position into a certain one. If the locked result is negative, that is the vig on both sides being paid — the calculation is telling you the truth, not failing.
Promo expected value
What a profit boost actually adds, at the cap the promotion allows. A headline percentage on a small cap is worth less than a modest one on a large cap.
Your estimate for the underlying market
American odds before the boost
e.g. 50 for a 50% profit boost
The cap the promotion allows
- Incremental EV at cap
- +6.75
- Boosted price
- +180
- EV without boost
- -1.00%
- EV with boost
- +26.00%
Incremental expected value +6.75 at the cap.
A profit boost multiplies the profit, never the returned stake: +100 with a 50 percent boost pays +150, not +200. A boost can add value to a bet that is still negative expectation overall.
Verification
These are tested, not just written
Reference cases covered
- +200 converts to decimal 3.00; -110 converts to 1.9091 and back.
- -110 on both sides de-vigs to exactly 50/50 and holds 4.55%.
- A three-way market normalises to exactly 100%.
- 55% at -110 is exactly +5.00% EV and exactly 5.5% full Kelly.
- Zero or negative edge clamps the Kelly stake to zero.
- Kelly never returns more than the whole bankroll.
- An unchanged market produces exactly zero CLV.
- Hedging both sides at -110 locks in a loss.
- A 50% profit boost on +100 pays +150, not +200.
- Odds of 0, 50, and -99 are rejected; blank input is rejected.
Why it is built this way
The formulas sit in a single module with no React and no DOM, so they can be tested directly rather than through the interface. Thirty test cases cover the reference values, the domain boundaries, and the edge cases that quietly produce nonsense — negative edges, prices that cannot exist, and blank fields read as zero.
The same functions produce the numbers shown on the Pulse and Opportunities demos. The prices there are invented; the arithmetic on top of them is the same arithmetic you get here.