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Advanced Arbitrage Betting Strategy For 3 Outcomes with Examples Arbitrage betting formulas

Advanced arbitrage betting finder

The most successful sports bettors are the ones who take the risk out of betting. To do this, you must master the art of arbitrage betting. Arbitrage betting takes the chance out of betting, and can guarantee results. This article is written for those who have a solid understanding of what arbitrage betting is, as this content will go to the next level of “arbing”. In this article, you will find valuable formulas that will open up a world of guaranteed bets that cannot lose money if you are able to arbitrage bet correctly.

Before jumping into these formulas, it should be noted they can be slightly intimidating at first. Don’t be thrown off by this, as it is as simple as plugging in numbers and doing basic math to find the info you are looking for. These formulas will tell bettors if an arb is possible, how much to wager to guarantee profit, and how much profit is to be made from a certain opportunity.

With proper understanding and execution of these formulas, bettors will have access to thousands of risk-free betting opportunities that can’t be seen by those who do not use these formulas. These formulas take the chance out of betting. If the numbers make sense in the formula, then there is an arbitrage betting opportunity that is guaranteed to either make money, or at least break even.

With this preface out of the way, let's get into the key you will be referring to for these arbitrage betting formulas.

Arbitrage betting formulas 

1-X-2 - Team 1 / Draw / Team 2 (Type of Arbitrage Bet)
V - Total money wagered
V1 - Money wagered on Bet 1
V2 - Money wagered on Bet 2
V3 - Money wagered on Bet 3
K1 - Odds of Bet 1
K2 - Odds of Bet 2
K3 - Odds of Bet 3
L - Unique variable that will have different value depending on certain outcomes

The first arbitrage betting formula we’re breaking down is the 1-X-2 arbitrage bet. Referring to our key, we know that this is a type of arbitrage bet that relies on three different possible outcomes, Team 1 winning, a draw, or Team 2 winning. Football is the most popular sport to use this formula with for obvious reasons.

The 1-X-2 type arb bet has the following arbitrage conditions:
L = 1/K1+1/K2+1/K3<1

This condition is the first step of arbing, which is finding a combination of betting odds on the same event that will allow for an arbitrage situation. The K variables in this formula represent the odds that you must find from different sportsbooks in order to find an arbitrage opportunity on a certain betting event. These K variables are placeholders for the betting odds of the three possible outcomes.

Oddsmagnet.com is the ideal website to use when searching for these odds, as they do all the work for you by comparing dozens of different bookmakers’ odds. Once you have found odds that will create an arb opportunity, it will be time to see how much money you must place on each outcome in order to guarantee a profit. Remember the number that is the outcome of this formula, as it will be the number used as your (L) variable in the following steps.

The following is the next step in the 1-X-2 formula:
V1 = V/(LxK1)
V2 = V/(LxK2)
V3 + V/(LxK3)

The outcomes of these formulas will be the amount of money you would wager on each result if you are looking for an unbiased outcome. The next step in the process is to plug in these wager sizes to estimate what your payouts will be on each result happening. This is what the formula for this step looks like:


After this step, you have all the data you need to place your guaranteed winning bet. Lets plug some example numbers in to show just how simple these formulas are to execute. For our example, let’s assume that you have £1000 and have found your arbitrage betting opportunity on a football match between Arsenal and Chelsea. You are looking to find out how much you must bet on each outcome to ensure that you make a profit. In this example, an Arsenal win pays out at 2.50 odds, a draw at 3.10 odds, and a Chelsea win at 4.10 odds.

With this data, we plug the odds into our first formula of L=1/K1+1/K2+1/K3<1

L=1/2.50+1/3.10+1/4.10 <1

After calculating , we know that L = .9664 or 96.64%

With this example, the number 96.64% comes in under 100%, indicating the arbitrage opportunity. This number represents the profit margin that your odds are creating for yourself. Subtract 100% by 96.64% and you will get 3.36% profit to be made on your investment, regardless of result. This percentage will be used as a decimal in the formula of your next steps, so make sure to have that number accessible. In this case, L = .9664.

After finding the L variable, the next step will be to calculate how much to bet on each outcome. It is no good to have an arbitrage opportunity if you don’t know how much to bet on each possible outcome, as there would be no way to guarantee a profit. Plugging in the numbers that we now know into the formula below will tell us exactly how much money to put on each possible outcome in order to guarantee a profit.

V1 = V/(LxK1) (Arsenal Win)
V1 = £1,000/(.9664x2.50)
V1 = £413.90
V2 = V/(LxK2) (Draw)
V2 = £1,000/(.9664x3.10)
V2 = £333.79
V3 = V/(LxK3) (Chelsea Win)
V3 = £1,000/(.9664x4.10)
V3 = £252.38

After plugging our data into the formula, we have a clear indication as to how much money should be placed on each result in order to guarantee that a profit is made. From these calculations, £413.90 should be placed on an Arsenal win, £333.79 should be placed on a draw, and £252.38 should be placed on a Chelsea win.

The last step in this formula is to input this new data in order to see the payouts of each possible bet outcome.
K1xV1>V (Arsenal Win)
K2xV2>V (Draw)
K3xV3>V (Chelsea Win)


After the final calculations, our formulas have indicated that this is a legit arbitrage betting opportunity. In addition, it has also calculated how much to bet on each possible outcome, as well as how much each payout will be. When each outcome will yield the same amount of profit, the trade is called an unbiased stake. It is clear that each outcome will yield a winning amount that is more than the £1,000 that has been wagered on this event. This is confirmation that we have both the right odds and the right bet size to properly execute a successful arb.

The most important aspect of arbitrage betting is making sure that you have all possible outcomes of an event covered. That way, you can guarantee that the bets you are making are risk free. This formula gives bettors a tool to use against the bookies when there are three possible outcomes to an event. All you have to do is find the best possible odds on all three outcomes from different bookmakers, and plug the data into the given formula. While there is not always going to be an arbitrage opportunity, it is worth it to search. Each time you do find one, you are guaranteed to win as much money as you can dig up with the betting odds you are able to find.

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