ArbCity FAQ

Each price is turned into the chance it implies. If the two chances add up to less than 100%, the books disagree enough that betting both sides pays off whoever wins. Type the odds for both sides and your stake on one side. The other stake is set so both outcomes pay back the same amount.

Stake B = Stake A × decimal odds A ÷ decimal odds B
Profit = smaller payout − (Stake A + Stake B)

One book has +110 and another has −105 on the other side. You want $1,000 in total.

What is an arbitrage bet? You bet both sides of the same game at two different sportsbooks. When the books disagree enough on the price, the two bets together pay more than you put in, whoever wins.

Why round Stake B to the dollar? Odd amounts like $103.64 can get an account flagged. Rounding to the dollar costs a few cents, and the number shown already includes that.

What can go wrong? The odds can move before you place the second bet, a book can void a bet or limit your account, and two books can settle the same market differently. The profit only holds if both bets stand. Place the side most likely to move first.

A bonus bet pays its profit but not its stake. You hedge just enough on the other side, with real money at another book, so both outcomes leave you the same cash.

Hedge = bonus × (bonus decimal odds − 1) ÷ hedge decimal odds
You keep = bonus × (bonus decimal odds − 1) − hedge

A $100 bonus bet at +400, hedged at −450 on the other side.

Find −400 on the hedge instead and you keep $80.00, a 80.0% conversion.

What odds should I use a bonus bet on? Longer odds usually convert better, because the stake you never get back matters less on a big price. Around +300 to +500 is common.

What is a good conversion? Turning 70% or more of a bonus bet into cash is solid. Above 75% is very good.

Each leg is turned into decimal odds and the legs are multiplied together. Every leg has to win for the parlay to pay.

Parlay odds = decimal 1 × decimal 2 × …
Payout = stake × parlay odds

Three legs at −110 each, $100 on the parlay.

What happens if a leg pushes? Most books drop that leg and pay the rest as a smaller parlay. Remove the leg to see the new payout.

Why does my book pay less? Some books shade parlay prices, especially for legs in the same game. The calculator multiplies the prices as listed, which is how standard parlays from different games pay.

What does EV mean? Expected value: what the parlay is worth on average if you know the fair price of each leg. It assumes the legs have nothing to do with each other.

A profit boost multiplies what a winning bet pays in profit. Add hedge odds and the calculator sizes a bet on the other side so you make the same either way.

Boosted decimal = 1 + (decimal − 1) × (1 + boost)
Hedge = stake × boosted decimal ÷ hedge decimal

A 50% boost on +200, $100 stake, hedged at −250.

Is a boost worth taking without a hedge? Usually yes, if the boost is big enough to beat the vig. Enter the fair odds to see the EV of the boosted bet.

Why is my max stake lower than I want? Most boosts cap the wager. Enter the capped amount as your stake.

You already placed a bet. The hedge is a bet on the other side. Equal profit sizes it so you make the same whichever side wins. Break-even only covers your stake if your bet loses, and keeps more upside if it wins.

Equal profit: hedge = stake × your decimal ÷ hedge decimal
Break-even: hedge = stake ÷ (hedge decimal − 1)

$100 on +300, hedged at −200.

When should I hedge? When you would rather lock in a result than ride the bet, often on the last leg of a parlay or a future. Hedging gives up some of the upside for certainty.

Can I type my own hedge amount? Yes. Type it in the Hedge stake box and the calculator shows both outcomes. Clear the box to go back to the suggested amount.

All four boxes are the same price written four ways. Type in any one and the other three update.

Decimal = 1 + American ÷ 100 (plus odds)
Decimal = 1 + 100 ÷ |American| (minus odds)
Implied % = 100 ÷ decimal

−110 in each format.

Why do both sides add up to more than 100%? That extra is the book’s cut, the vig. Two sides at −110 each imply 52.38%, which adds up to 104.76%.

The payout is your stake times the decimal odds. It includes your stake back. The profit is the payout minus the stake.

Payout = stake × decimal odds
Profit = payout − stake

$50 at +240.

Does this work for a bonus bet? A bonus bet pays only the profit, not the stake. Use the profit line, or the Bonus Bet calculator to hedge it.

If a no-sweat bet loses, the book refunds the stake as a bonus bet. That refund is worth less than cash, so you set how much of it you usually turn into cash (70% is typical). The hedge is sized so you end up the same either way.

Hedge = stake × (decimal odds − refund %) ÷ hedge decimal
Result = stake × (decimal odds − 1) − hedge

$100 no-sweat bet at +200, hedged at −200, refund worth 70%.

What refund value should I use? What you usually keep when you convert a bonus bet. If you get about $70 cash from a $100 bonus bet, use 70%.

A book’s prices on both sides add up to more than 100%. The extra is the vig, the book’s cut. Taking it out leaves each side’s fair chance and fair price. Multiplicative is the standard way. Additive and Power shade longshots differently.

Implied % = 1 ÷ decimal odds, for each side
Fair % = implied % ÷ (sum of implied %)
Hold = 1 − 1 ÷ (sum of implied %)

A market at −150 and +130.

Which method should I use? Multiplicative works for most markets. Power gives longshots a little less of the vig and favorites a little more, which tends to match how books price lopsided games.

Expected value is what a bet is worth on average if you know its true chance of winning. Enter the true odds or a win %, or both sides of a sharp market and the vig is taken out for you.

EV % = win chance × decimal odds − 1
EV $ = stake × EV %

$100 at +120 on a true coin flip (50%).

Where do true odds come from? Most bettors use a sharp book’s prices with the vig removed. Enter both sides of that market and the calculator does it for you.

The Kelly criterion sizes a bet from your edge and the odds so your bankroll grows fastest over time. Most bettors use half or a quarter of it, because the win chance is an estimate.

b = decimal odds − 1
Full Kelly = (b × win chance − (1 − win chance)) ÷ b
Bet = bankroll × Kelly × size

$1,000 bankroll, +120, 50% win chance.

Why does it say no bet? At that price and win chance the bet loses money on average, so Kelly says to stake nothing.

Can I type a prediction market price? Yes. Type 63 or 63% and it turns into American odds (−170) when you leave the box. Decimal odds like 2.5 and fractions like 5/2 work too.

Where are my saved calculations kept? On your phone or computer only. Nothing is sent anywhere, and there are no accounts.

Does it work without a connection? Yes. After your first visit the calculators open offline. Add ArbCity to your home screen and it opens like an app.