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The math

Follow one ticket from price to payout. These worked examples separate estimated value, committed capital, and the result you actually receive.

Start with the ticket cash flows

Expected value is a probability-weighted estimate. For a standard house-side ticket, before fees:

Estimated EV = premium − (estimated hit probability × payout)

The estimate is useful only to the extent that the probability is useful. Actual profit depends on the resolved result and costs. A market midpoint is not a known true probability.

ONE ILLUSTRATIVE TICKET · BEFORE FEES
Estimated chance every leg wins20%
Bettor’s premium$10.50
Possible total payout$50.00
Expected payout · 20% × $50$10.00
Estimated EV · $10.50 − $10+$0.50
The actual ticket net is either +$10.50 or −$39.50, before fees. It does not settle at its EV.

Multiplying independent probabilities

If selected outcomes are independent and their probabilities are accurate, the probability of all of them winning is their product. Using 60% for each leg gives:

ILLUSTRATIVE 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 rejects detected related legs and checks the books behind its marks. Remaining correlations and pricing errors can still affect the estimate.

Margin is a markup

Pregame applies a margin to the estimated parlay fair value. It is a percentage of that value, not a percentage of the collateral at risk.

Quote price = estimated fair value × (1 + margin)
A 5% MARKUP
Estimated fair value20¢
Margin500 bps = 5%
Quote · 20¢ × 1.0521¢
Gross expected hold · 5 ÷ 1054.76% of premium
Gross expected hold is margin ÷ (1 + margin), assuming the fair estimate is correct and excluding fees.

A leg-count target is a margin for the whole parlay. It is not an instruction to add that same margin to every leg. Autopilot’s final margin can also reflect its cost floor and applicable adjustments.

The same EV, another way

Estimated EV = (quote probability − estimated fair probability) × payout
CHECK THE UNITS
Quote price21¢ per $1 of payout
Estimated fair value20¢ per $1
Difference1¢ per $1
Payout size$50
EV · $0.01 × 50+$0.50
This is the same $0.50 as premium minus expected payout. Fees reduce net EV.

For 60 fills with these same economics, total estimated EV is $30 before fees. Multiplying a 5% markup by $39.50 of capital at risk would give the wrong answer. Expected values add across tickets; shared outcomes still affect the range of actual results.

The same prices can produce different nights

Suppose 40 different tickets each have the example economics: $10.50 premium, $50 payout, and an estimated 20% hit probability. The book collects $420, with eight payouts expected under that model.

ILLUSTRATIVE OUTCOMES · BEFORE FEES
Five tickets pay · $420 − 5 × $50+$170
Eight tickets pay · $420 − 8 × $50+$20
Eleven tickets pay · $420 − 11 × $50−$130
These are scenarios, not probabilities assigned to those nights.

A shared winning pick can cause several tickets to pay together. More fills do not necessarily diversify the book, and repeated trading does not remove model error. Read the shared-outcome view alongside the individual tickets.

What the limits bound

Limits should be understood in dollars and in time. Per-ticket and total open risk describe committed capital. Daily fills describes a count. None of those fields is a promise about daily profit or maximum daily loss.

ILLUSTRATIVE SETTINGS · NOT A RECOMMENDATION
Wallet balance$500
Per-ticket capital cap$25
Total open-risk cap$150
A team exposure cap$60
The $150 cap applies to simultaneous open exposure. Settlement can release room for more fills.

Choose limits that reflect losses you can bear. Check confirmed settled net as the session progresses, and remember that separate tickets can share the same underlying risk.

Shared outcomes change the book

Multiplication assumes independence. For related events, the joint probability can be higher or lower than the simple product. The direction and size depend on the relationship.

ILLUSTRATIVE JOINT PROBABILITY
Outcome A55%
Outcome B50%
Product under independence27.5%
Suppose the joint probability is actually35%
Understatement7.5 percentage points
35% is an assumption for this example, not a measured sports probability.

Pregame rejects detected duplicate, same-game, same-event, and shared-team legs within a request. 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 estimate1.67% relative error
At a 2¢ fair estimate50% relative error
Relative error = price error ÷ estimated fair value.

Neither error is automatically harmless. The trade’s size determines the dollars involved. A $10 premium at a 2¢ quote buys $500 of possible payout and requires $490 of house capital before fees. The fair-price band and capital limits constrain different parts of that exposure.

Price and fill rate belong together

A wider margin can produce more estimated value per accepted trade and fewer accepted trades. The useful comparison is expected net value per fill multiplied by the likelihood of getting that fill, using comparable requests and costs.

ILLUSTRATIVE 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 probabilities, before fees. This does not identify a profitable live setting.

Autopilot learns from resolved auctions and uses your target win rate subject to its economic floor. The pricing panel labels its source and fallback state. Manual control uses your authored base margin instead.

One ticket, end to end

ILLUSTRATIVE TICKET · SAME NUMBERS THROUGHOUT
Estimated fair probability20%
Quote with a 5% markup21¢
Shares at $1 potential payout each50
Premium · 50 × $0.21$10.50
Capital at risk · 50 × $0.79$39.50
Estimated EV before fees+$0.50
Net if the parlay loses+$10.50
Net if every leg wins−$39.50
Actual orders use integer amounts and explicit rounding. The example leaves out fees to isolate the economics.

On the Sweat room, capital at risk and premium describe the position. Live chance to pay is an estimate. Confirmed settlement determines the recorded result.

What to check at a glance

  • Engine state: has the desk confirmed it is quoting or stopped?
  • Available capacity: how much capital is committed, and how close is it to your limits?
  • Pricing source: is the displayed target learned, a fallback, or your manual value?
  • Concentration: which shared outcomes affect the most tickets?
  • Data freshness: are prices and settlement checks current?
  • Confirmed results: how does settled net compare with your estimates and costs?