Expected Loss Across Mixed Wagers

Expected loss across mixed wagers

Expected loss across mixed wagers is the sum of the expected losses of each wager type in a session. Expected values add even when outcomes are correlated, which is what makes it possible to price a main bet and its optional side bets as independent line items.


Say a session puts $400 on a wager with a 1% edge and $100 on one with an 8% edge. Expected losses: $4 and $8. Combined, $12 on $500 of turnover, a turnover-weighted edge of 2.4%.


The weighting matters. Averaging 1% and 8% arithmetically gives 4.5%, nearly double the true figure, because it ignores that four fifths of the money went to the cheaper bet. Every calculation of expected loss in casino games multiplies each percentage by the amount actually staked on it, and the same applies when stakes change from one round to the next.


What the $12 does not describe is risk. Correlated bets and rare large payouts can stretch the distribution of outcomes enormously while the expected losses still add neatly. Reading a session's risk takes more than one weighted percentage.