Key takeaways

• Each leg's stake is the total stake times that outcome's implied probability, divided by the sum of all the implied probabilities.

• On $1,000 at +105 and +102, the exact split is $496.31 and $503.69 for a $17.44 profit. Rounding to whole dollars costs 64 cents. Rounding to $10 costs $7.44.

• When a sportsbook caps one leg, the capped stake sets the size of every other leg.

• On a thin arb, the fee on a prediction-market leg can decide whether there's a profit at all. At Kalshi's or Polymarket US's taker rate, a $16.80 arb turns into a small loss. On a Novig pre-game straight it stays $16.80.

How arbitrage stake sizing works

An arb exists when the best prices on every outcome of an event add up to less than 100% implied probability. Once you've found one, the money has to be split so every outcome pays back the same amount, because a lopsided split turns a sure profit into a bet on one side.

The split comes straight from the prices. Every leg gets a share of the total stake equal to its implied probability's share of the combined total. Get that right, then decide how much precision the books will let you keep. The arbitrage calculator does the arithmetic, and the rest of this guide covers why its numbers look the way they do.

The formula for a two-way arb

Convert each price to implied probability first. For positive American odds, it's 100 divided by (odds plus 100). For negative odds, it's the odds' absolute value divided by (that value plus 100).

Take a game where one book has Side A at +105 and another has Side B at +102:

• Side A at +105: 100 / 205 = 48.78%

• Side B at +102: 100 / 202 = 49.50%

• Combined: 98.29%, which leaves a 1.71% margin

Each stake is the total times that side's share of the 98.29%. On $1,000:

• Side A: $1,000 × 48.78 / 98.29 = $496.31, returning $1,017.44 if it wins

• Side B: $1,000 × 49.50 / 98.29 = $503.69, returning $1,017.44 if it wins

Both outcomes pay $1,017.44 against $1,000 staked, so the locked profit is $17.44.

What rounding costs you

Nobody bets $496.31. A stake with cents in it looks unusual on a sportsbook's risk screen, and arbing guides from tool vendors recommend rounding for that reason. Every rounding step gives back a little of the edge.

Here's the same $1,000 arb rounded to different increments:

Whole dollars cost 64 cents here. Rounding to $10 gives up 43% of the edge, because $500 and $500 no longer match the prices. The thinner the margin, the faster coarse rounding eats it, and on a sub-1% arb a $10 increment can push the worst case below zero.

Two habits keep the cost down. Round the leg at the book you're most worried about and let the other leg absorb the difference. Then rerun the numbers on the rounded stakes before placing anything, since the calculator shows the worst-case profit after rounding, not before.

Three-way markets with a draw

Soccer moneylines have three outcomes: home, draw and away. The math is the same with one more term in the sum.

Say the best prices across books are home +140, draw +245 and away +270. Those are illustrative numbers, the kind that turn up when FanDuel, DraftKings and a prediction market such as Novig each price one outcome slightly differently.

• Home at +140: 41.67%

• Draw at +245: 28.99%

• Away at +270: 27.03%

• Combined: 97.68%, a 2.32% margin

On $1,000, the exact stakes are $426.57, $296.74 and $276.69, and every outcome returns $1,023.76 for a $23.76 profit. Rounded to $5, the stakes are $425, $295 and $275 ($995 in total), and the worst case drops to $22.50.

Three legs means three prices that can move before you finish, so three-way arbs carry more execution risk than two-way ones. Place the leg most likely to move first.

When a book caps one leg

Stake limits change the order of operations. If a sportsbook will only take $200 on Side A at +105, the bankroll stops being the starting point and the capped leg takes over.

Size the other leg so its payout matches the capped leg's payout:

• Side A: $200 at +105 returns $410

• Side B: $410 / 2.02 (the decimal price of +102) = $202.97

That's $402.97 staked for $7.03 in profit. The capped leg sets the size of the whole arb, however much bankroll you have. The account limits guide covers how those caps get set at FanDuel, DraftKings, BetMGM and Caesars.

How fees change the split

Sportsbooks build their margin into the price, so a sportsbook leg carries no separate fee. Prediction markets usually charge one, and on a thin arb that fee decides whether there's a profit.

Take the $1,000 arb above and put Side B on a prediction market at 49.5¢, the equivalent of +102. The $504 stake buys 1,018 contracts. The taker fee on those contracts depends on where you trade:

Kalshi's taker fee is 0.07 × contracts × price × (1 − price), rounded up to the next cent, which comes to $1.75 per 100 contracts at 50¢. Polymarket US uses the same formula with a 0.0695 coefficient on sports. Novig charges nothing on pre-game straight trades, and its live straights use 0.03 on most sports and 0.06 on college football, hockey and baseball. Maker orders, which rest on the book instead of taking a price, cost $0 on Novig and earn a small rebate on Polymarket US, so posting an order is one way to cut the fee if the arb holds long enough to fill.

Count the fee as part of the stake before deciding a market is an arb. A 1.7% margin doesn't survive a fee worth 1.8% of the total stake.

Common stake-sizing questions

Should both stakes always be equal?

Only when both prices are the same. Equal stakes on unequal prices leave one outcome paying more than the other, and the worst case is the one that counts.

Is it better to round up or down?

Round so the total stays at or under your bankroll, and recheck the worst case. On the $1,000 example, rounding Side A up to $500 and Side B down to $500 produces the $10 result in the table.

Can I size by profit instead of by total stake?

Yes. Pick the payout you want, divide it by each leg's decimal price, and the stakes fall out. A $1,000 payout at +105 and +102 needs $487.80 and $495.05.

Does stake size affect whether an account gets limited?

Arbing guides list stake patterns among the signals sportsbooks watch, along with bet timing and which prices an account takes. Odd amounts and large stakes on off-market prices are the patterns they warn about.

Run your own numbers

Enter your prices and total stake in the arbitrage calculator. It shows the exact split, lets you round to whole dollars, and reports the worst-case profit after rounding.