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April 15, 2025

Hold, Vig, and Arbitrage: Understanding the Book's Edge

How sportsbooks make money through hold and vig, how to compare lines across books, and how to find guaranteed-profit arbitrage opportunities.

holdvigarbitrageline-shopping

What Is Hold?

Hold is the sportsbook's built-in margin — the percentage of total handle they expect to keep regardless of outcome. For a two-sided market, it is calculated from the implied probabilities:

Hold=pimplied,1+pimplied,2−1\text{Hold} = p_{\text{implied},1} + p_{\text{implied},2} - 1

A standard -110/-110 market has implied probabilities of 52.38% each, so the hold is 52.38+52.38−100=4.76%52.38 + 52.38 - 100 = 4.76\%. This means for every 100wageredacrossbothsides,thebookexpectstokeep100 wagered across both sides, the book expects to keep 4.76.

Why Hold Varies

Not all markets carry the same hold. Liquid, high-volume markets (NFL sides, major soccer matches) often have holds of 3-5%. Less liquid markets (props, lower leagues) can have holds of 8-15% or more. The hold tells you how much the book is charging for the privilege of betting.

Knowing the hold also lets you derive no-vig fair odds — what the line would be if the book charged zero margin. This is useful for finding true probabilities and comparing across books.

Comparing Vig Across Books

Different books price the same market differently. One book might offer -108/-112, another -110/-110, and a third -105/-115. They all have different hold percentages:

BookSide ASide BHold
Book 1-108-1124.3%
Book 2-110-1104.8%
Book 3-105-1154.4%

The lowest-vig book is not always the one with the best price for your side. You might find the best odds on Side A at Book 3 (-105) even though Book 1 has the lowest overall hold. This is why sharp bettors compare both total vig and individual line prices.

How Arbitrage Works

An arbitrage opportunity exists when the combined implied probabilities across different books sum to less than 100%:

1d1+1d2<1\frac{1}{d_1} + \frac{1}{d_2} < 1

where d1d_1 and d2d_2 are the best decimal odds for each side from any book. When this holds, you can bet both sides and guarantee a profit.

Optimal Stake Allocation

To guarantee equal profit regardless of outcome, allocate stakes inversely proportional to the odds:

si=Total Investmentdi⋅∑j1djs_i = \frac{\text{Total Investment}}{d_i \cdot \sum_j \frac{1}{d_j}}

Worked Example

Book A offers Team X at +130 (decimal 2.30). Book B offers Team Y at -120 (decimal 1.833).

12.30+11.833=0.435+0.546=0.981\frac{1}{2.30} + \frac{1}{1.833} = 0.435 + 0.546 = 0.981

Since 0.981<10.981 < 1, this is an arb with a guaranteed return of 1/0.981−1=1.94%1/0.981 - 1 = 1.94\%.

With a $1,000 total investment: bet $443 on Team X at Book A and $557 on Team Y at Book B. If Team X wins, you collect 443 \times 2.30 = \1019.IfTeamYwins,youcollect. If Team Y wins, you collect 557 \times 1.833 = $1021. Either way, you profit roughly \19-21.

Practical Limits of Arb Betting

Arbitrage sounds like free money, and mathematically it is. But in practice:

  • Books limit arb bettors — accounts that consistently bet both sides get restricted quickly
  • Line movement — by the time you place the second leg, the odds may have moved
  • Capital requirements — a 2% arb on 1,000yields1,000 yields 20. You need significant capital for meaningful returns
  • Timing — opportunities are fleeting, often lasting minutes

Arb betting is best used as an occasional supplement, not a primary strategy. The real value of understanding arbitrage is that it sharpens your sense of fair value.

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