Expected value and Kelly sizing for Yes/No shares
Expected value tells you whether a bet is worth taking at a price, if your own probability estimate is right. For a Yes share at price p with your probability q, the expected profit per $1 staked is q / p − 1, before fees.
Kelly sizing
The Kelly criterion gives the bankroll fraction that maximises long-run growth: f = (q − p) / (1 − p) for a binary share. Full Kelly is very aggressive and assumes your estimate is exact. Most people use a quarter or a half of it.
The catch
Your edge is only as good as your probability. If you cannot explain why the market is wrong, assume it is not. The EV calculator shows the result across a range of your own estimates so you can see how fragile an edge is.