Alpha

Also known as: α, alpha frequency, bluff success threshold

The fold frequency a bluff needs to break even, equal to bet divided by (pot plus bet); the complement of MDF.

Alpha (\(\alpha\)) is the fold frequency a pure bluff requires to break even. With bet \(b\) into pot \(p\): \[\alpha = \dfrac{b}{p+b}.\] If the opponent folds more than \(\alpha\), a bet of any two cards profits; if they fold less, the bluff loses chips on its own. Alpha is the bettor's-eye view; MDF is the caller's-eye view, and they are exact complements: \(\alpha + \text{MDF} = 1\).

Alpha drives the bluff-to-value ratio at equilibrium. A bigger bet has a higher \(\alpha\) (needs folds more often) and therefore supports more bluffs relative to value — that's why overbets carry the most bluffs and small bets the fewest. It also explains why bigger sizings are scarier: they demand the caller defend a smaller fraction of range (lower MDF), so more of their range gets folded out.

Don't confuse alpha with the equity your bluff needs at showdown — alpha is purely the fold-or-not break-even, assuming the bluff has no equity when called. When your bluff has backdoor or draw equity, the real bar is lower.