# Surebet: a simple calculation formula

A surebet is a **bet** where you are **sure** to win regardless of the actual outcome.

This can be mathematically possible by placing bets on all the opposing outcomes of a contest (possibly with different bookmakers).

Of course the possibility of surebet is not systematic, and is even a rather rare opportunity.
You have to know how to detect it.

## Classic formula

The classically known calculation formula is as follows: in a win/loss bet the sum of the reciprocal of the odds must be less than 1. (on this page are the explanations and details of the mathematical calculations).__Win__with odds of*c*= 1.30_{v}__Defeat__with odds of*c*= 5.00_{d}

*c*+ 1

_{v}*c*= 11.30 + 15.00 ≃ 0.97 < 1

_{d}Although easy, these calculations are not done in your head, and therefore you always need to have a calculator in your pocket, or you use an online automatic calculator or 3-ways 1x2 type calculator.

## Simple formula

We prefer the much simpler form, using **net odds** or **net winning rates**

*t*> 1

_{v}t_{d}*t*= 0.30 et

_{v}*t*= 4 and then it is much simpler to calculate

_{v}*t*= 0.30×4 = 1.2 > 1

_{v}t_{d}Subsequently, below, we specify and prove this math formula.

## Math proof of the simplified formula

The simplified formula is not a completely "magic" formula. It is obtained mathematically, like the classic formula. This is how, for fans of algebraic mathematical calculation (or those who would like to delve into it).
The odds give the gross profit. What interests the bettor is rather the net profit: the gross profit from which we withdraw the stake which is ultimately not part of the profit.

Thus, if we bet 10 euros with odds of 1.30, the gross profit is 10×1.30=13 euros, while we have actually won "only" 3 = 13 - 10 euros.

__Victory__with odds of*c*= 1 +_{v}*t*_{v}__Defeat__with odds of*c*= 1+_{d}*t*_{d}

*c*= 1.30 = 1 + 0.30 and

_{v}**net odds of**

*t*= 0.30 = 30%.

_{v}Now, the previous formula is rewritten, writting the fractions on the same denominator Maintenant, la formule précédente se réécrit, en mettant sur le même dénominateur les factions

*c*+ 1

_{v}*c*<1 ⇔ 11 +

_{d}*t*+ 11 +

_{v}*t*<1 ⇔ 2 +

_{d}*t*+

_{d}*t*(1 +

_{v}*t*)(1 +

_{v}*t*) <1 ⇔ 2 +

_{d}*t*+

_{d}*t*< (1 +

_{v}*t*)(1 +

_{v}*t*)

_{d}*t*)(1 +

_{v}*t*) = 1 +

_{d}*t*+

_{v}*t*+

_{d}*t*

_{v}t_{d}*t*> 1

_{v}t_{d}Thanks to this formula, we can quickly detect, even approximately in a first step, a situation which could be a surebet, then only in a second step draw out our surebet automatic calculator to check and calculate the right stakes.

## Example

We consider the event:__Victory__with odds of*c*= 1.40 = 1 + 0.4_{v}__Defeat__with odds of*c*= 4.00 = 1+ 3_{d}

and with the formula, we calculate directly, in our heads, that

See also: