Read the mathematical discrepancy detector

Three signals are observable: the no-vig fair gap, calibration drift, and arbitrage. All three can be computed from prices, or from prices plus outcomes after the fact, which means an analogue of them exists in a real market.

Two are look-ahead: model vs market, and positive EV. Both use the simulation's hidden true probability. They are enormously useful for understanding a mechanism and completely unavailable outside the lab.

Stripping the margin out of a price gives you the implied probability the price would carry if nobody were taking a cut. The gap between the fair and the priced implied probability is the vig you are paying, made explicit.

Read it as a cost rather than a signal. Every strategy has to clear this before it clears anything else, and a great deal of apparent edge is simply an unpaid accounting for it.

Calibration drift compares the observed win rate against the implied probability. It is observable, but only retrospectively — you need outcomes, which means it tells you whether prices were well calibrated, not whether the next one will be.

It is the most useful of the three for research. Systematic drift in a price band is a real finding about the pricing process; noise in a small sample is not, which is why it belongs next to the Wilson intervals on the Statistics pages.

Arbitrage is observable from prices alone and is the one signal that requires no view about probability at all — if the implied probabilities across a market sum to less than one, the structure itself is inconsistent.

In a synthetic setting it mostly serves as a sanity check on your configuration. If arbitrage is appearing routinely, your overround setting is probably doing something you did not intend.

Model vs market and positive EV are the two that make the lab pedagogically valuable. They show you exactly where the pricing was wrong relative to a truth you configured, which is a clarity no real market offers.

Use them to understand mechanism — how much mispricing is needed before a rule works, how variance obscures a real edge, how quickly margin eats a small advantage. Do not use them as evidence that anything is exploitable, because their entire input is a number the market does not have.

Alongside the detector, the Mathematical Advantages panel reports average edge, expected ROI per unit stake, break-even and average implied probability, the average simulated true probability, the vig setting, a CLV proxy comparing fair against priced implied probabilities, and a fractional Kelly stake hint.

The CLV proxy is worth singling out. Closing-line value is one of the few genuinely observable quality measures in real betting, and having a proxy for it here is a useful bridge between what the simulation can show and what a real market would let you check.