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.