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The math

Follow one ticket from price to payout. These worked examples separate what a ticket is expected to earn, what you put at risk, and what you actually get.

Start with the ticket cash flows

Expected value (EV) is what a ticket earns on average: each possible result weighted by its chance. For a standard house-side ticket, before fees:

Estimated EV = bettor’s stake − (estimated chance the parlay hits × payout)

The estimate is only as good as the probability behind it. Actual profit depends on the real result and costs. A market midpoint (halfway between the best buy and sell prices) is an estimate, not a known probability.

ONE EXAMPLE TICKET · BEFORE FEES
Estimated chance every leg wins20%
Bettor’s stake$10.50
Payout if the parlay hits$50.00
Expected payout · 20% × $50$10.00
Estimated EV · $10.50 − $10+$0.50
The real result is either +$10.50 or −$39.50, before fees. A ticket never settles at its EV.

Multiplying independent probabilities

If the legs (picks) are independent and their probabilities are accurate, the chance all of them win is their product. At 60% per leg:

EXAMPLE INDEPENDENT LEGS
One leg60%
Two legs · 0.60 × 0.6036%
Three legs21.6%
Four legs12.96%
Five legs7.776%
The independence assumption matters as much as the multiplication.

The engine skips related legs it detects, unless same-game pricing is on for that sport, and checks the order books behind each price. Correlations it misses and pricing errors can still throw off the estimate.

Margin is a markup

Your margin is a markup on the parlay’s fair value, the engine’s estimate of its true price. It is a percentage of that value, not of your amount at risk. Margins are shown in bps (basis points): 100 bps = 1%.

Quote price = fair value × (1 + margin)
A 5% MARKUP
Fair value20¢
Margin500 bps = 5%
Quote · 20¢ × 1.0521¢
Expected profit · 5 ÷ 1054.76% of stake
Expected profit as a share of stake = margin ÷ (1 + margin), if fair value is right and before fees.

A leg-count target is a margin on the whole parlay, not one added to every leg. Autopilot’s final margin can also reflect its cost floor and other adjustments.

The same EV, another way

Estimated EV = (quote price − fair value) × payout
CHECK THE UNITS
Quote price21¢ per $1 of payout
Fair value20¢ per $1
Difference1¢ per $1
Payout$50
EV · $0.01 × 50+$0.50
The same $0.50 as stake minus expected payout. Fees reduce it.

Sixty fills like this one add up to $30 of estimated EV before fees. Multiplying the 5% markup by the $39.50 at risk would give the wrong answer. EV adds up across tickets, but shared outcomes still widen the range of real results.

The same prices can produce different nights

Suppose 40 different tickets each match the example: $10.50 stake, $50 payout, and an estimated 20% chance to hit. The book takes in $420 and, under that model, expects eight payouts.

EXAMPLE NIGHTS · BEFORE FEES
Five tickets pay · $420 − 5 × $50+$170
Eight tickets pay · $420 − 8 × $50+$20
Eleven tickets pay · $420 − 11 × $50−$130
Scenarios, not the odds of each night.

One winning pick shared by several tickets can make them pay together. More fills do not always spread your risk, and trading more does not remove model error. Check the shared-outcome view alongside each ticket.

What the limits bound

Each limit caps something different. Per ticket and Total open cap how much is at risk. Fills per day caps a count. The daily and weekly loss limits are the ones that respond to losses. None of them promises a profit.

EXAMPLE SETTINGS · NOT A RECOMMENDATION
On hand$500
Per ticket$25
Total open$150
One team’s limit$60
The $150 limit covers what is at risk at the same time. Settled tickets free room for more fills.

Choose limits that match losses you can afford. Check settled profit and loss as the night goes on, and remember that separate tickets can share the same risk.

Shared outcomes change the book

Multiplying assumes independence. For related events, the real chance both happen can be higher or lower than the product, depending on how they are related.

EXAMPLE JOINT PROBABILITY
Outcome A55%
Outcome B50%
Product if independent27.5%
Suppose the real chance of both is35%
Product is too low by7.5 percentage points
35% is assumed for this example, not a measured sports probability.

By default, Pregame skips requests with duplicate legs, or legs from the same game, event, or team. If you turn on same-game pricing for a sport (Autopilot only), the engine can price some moneyline, spread, and total combinations with a measured correlation model, leaning toward a higher price. Across separate tickets, concentration still matters: one result can affect many tickets.

Small price errors can be large relative errors

A ONE-CENT ERROR
At a 60¢ fair value1.67% relative error
At a 2¢ fair value50% relative error
Relative error = price error ÷ fair value.

Neither error is automatically harmless; the ticket’s size sets the dollars. A $10 stake at a 2¢ quote buys a $500 payout and puts $490 of your money at risk before fees. Your parlay price range and dollar limits cap different parts of that risk.

Price and fill rate belong together

A wider margin can earn more per fill but win fewer auctions. Compare EV per fill times the chance of getting that fill, on similar requests and costs.

EXAMPLE AUCTION COMPARISON
Quote A · $0.20 EV/fill × 60% fill chance$0.12 per request
Quote B · $0.50 EV/fill × 35% fill chance$0.175 per request
Quote C · $0.90 EV/fill × 10% fill chance$0.09 per request
Assumed values and fill chances, before fees. Not a recommended live setting.

Autopilot learns from past auction results and aims for your target win rate, never below its cost floor. The pricing panel shows where its target came from and when it is using a fallback. Manual control uses the base margin you set instead.

One ticket, end to end

EXAMPLE TICKET · SAME NUMBERS THROUGHOUT
Fair value (chance to hit)20%
Quote with a 5% markup21¢
Shares, each paying $1 if the parlay hits50
Bettor’s stake · 50 × $0.21$10.50
Your amount at risk · 50 × $0.79$39.50
Estimated EV before fees+$0.50
Your result if the parlay loses+$10.50
Your result if every leg wins−$39.50
Real orders use whole micro-dollar amounts and explicit rounding. Fees are left out to isolate the economics.

On the Tickets page, the bettor’s stake and your amount at risk describe each ticket. Chance to pay is a live estimate; only a confirmed settlement records the result.

What to check at a glance

  • Engine state: has the desk confirmed it is quoting, or stopped?
  • Room left: how much is at risk, and how close is it to your limits?
  • Pricing source: is the target learned, a fallback, or your manual value?
  • Concentration: which shared outcomes affect the most tickets?
  • Data freshness: are prices and settlement checks current?
  • Settled results: how does settled profit compare with your estimates and costs?